Using the deterministic approach model for project portfolio selection problem (PPSP) solutions

AO Mogbojuri; OA Olanrewaju

doi:10.1016/j.heliyon.2023.e19129

. 2023 Aug 19;9(9):e19129. doi: 10.1016/j.heliyon.2023.e19129

Using the deterministic approach model for project portfolio selection problem (PPSP) solutions

AO Mogbojuri ^1,^∗, OA Olanrewaju ¹

PMCID: PMC10474411 PMID: 37662808

Abstract

Selection of projects using a robust technique is rare as most of the techniques are not considered useful due to the limitation on the number of projects that can be selected as well as cost saving projects not being selected. This study investigated the validity of a hybrid model − integrated analytical hierarchy process-goal programming (AHP-GP) − to avoid project portfolio selection problems delaying community development.

The proposed model includes two steps: AHP to determine the project criteria, the relative importance of weights, and priority preferences, while the GP model was formulated to select the optimal projects. An empirical study on government agencies was carried out to validate the proposed model, and the results compared against GP as a standalone to solve the same problem. The results proved that the hybrid model (AHP-GP) was better than the GP model. AHP-GP has proved to be a robust mechanism most suitable for managerial use due to its ability to handle multi-criteria decision-making (MCDM) situations. This study showed that the hybrid model can select more projects and will create more jobs in the communities concerned compared to the single model (GP). The novelty of this study is the introduction of an integrated model formed from two distinct models as a deterministic approach to solving project portfolio selection problems.

Keywords: Analytic hierarchy process, Community benefits, Goal programming, Multi-criteria decision making, Project portfolio selection problem

1. Introduction

According to Ref. [1], choosing either the right or the wrong set of projects can mean the difference between success and failure for firms. The procedure for choosing projects and overseeing project portfolio selection can help companies gain a better understanding of their projects, as well as the risks and benefits associated with them. Project portfolio selection is a critical function in organizations that significantly impacts benefits. As a result, one of the main analyses is the selection of the best set of projects, as a set of suitable ventures to improve community growth [2]. Reference [3] defines a project as a one-of-a-kind endeavour constrained by completion time, budget and resources. It states that the project's main goal is to finish on schedule while staying within budget and [human] resource limits [3]. According to the Project Management Institute (PMI), a portfolio is a collection of projects, programs, subsidiary portfolios, and operations aimed at achieving strategic goals [4]. A project portfolio refers to an organization's group of projects and their relationships undertaken within a specified time [5]. Project selection is the process of thoroughly evaluating individual projects or groups of projects and then selecting a set of them to implement in order to meet the parent organization's objectives [6]. Project portfolio selection is the process of selecting a suitable set of projects to which limited resources such as facilities, people, duration, and cost can be allocated. It refers to the process of assessing an individual project or multiple projects to determine which ones to implement to help the organization achieve its goals [7]. There are several objectives to consider when selecting a project. These include selecting projects providing the greatest benefit, choosing projects that take the least time or require the smallest budget, and so on [8]. Usually, the goal of project portfolio selection is to select the best group of projects to meet the given objectives while complying with the necessary constraints (e.g., resources, time, risk) [9]. This is a significant point, especially for project-oriented firms, as inferior project selection might threaten further projects. However, it is ambitious to expect a policy maker to be able to select projects without experiencing considerable concern when the process is complicated by almost overwhelming data, competing criteria, and even ambiguity during the decision-making process [9]. Project selection is an analytical decision particularly in project-related firms. It is continually faced with cases presenting various criteria which must be evaluated when selecting suitable projects. Managers and decision-makers must make a selection from the most appealing and profitable projects by weighing up several factors indicative of the project's viability [10]. Meanwhile, the project selection process assigns limited resources to a group of projects based on the organization's objectives. It is a challenging and complex decision-making process since project selection is often characterized by many conflicting, and inequitable criteria [10]. Project selection is an elaborate decision-making process determined by a diversity of aims, some of which may be disputed. The enormous number of projects from which a subset (portfolio) must be selected illustrates the complexity of the project selection problem [11]. The selection of a project portfolio has become a significant aspect of most organizations' project management activities [1]. Firms can acquire information about all the projects, prioritize specific rojects, and oversee the selected projects for the whole of the project lifecycle by properly managing their project portfolio [1]. Project selection processes are necessary because they assist organizations in selecting the most appropriate projects in order to be successful and efficient in their resource allocation [12]. They also present the organization with a list of prioritized projects, which increases the likelihood of success because such projects reflect the company's strategic goals as well as the interests of stakeholders [12]. However, the basic aim of the project selection process is to find a portfolio of projects that will achieve the firm's given goals while remaining within the constraints of available funds and the decision maker's requirements [13]. Multiple, contradictory objectives, some of which may be qualitative, the risks and uncertainties associated with the projects to be evaluated, and the relationships that may exist between the projects all contribute to the complexity of project portfolio selection [13]. Many firms allocate significant resources to the analysis of a large number of project proposals in order to select project portfolios that maximize performance, comply with resource limits, and reduce risk [14]. Most project-based organizations have a long list of proposed projects contending for a limited set of resources such as capital, workforce, and facilities [15]. To explain project selection problems, several mathematical programming approaches have been established. Multi-criteria decision making (MCDM) is one of these approaches and procedural methods for handling elaborate engineering problems [16]. MCDM methodologies have gained considerable attention because of their ability to evaluate different proposals [16]. According to Ref. [17], project selection frequently involves multiple criteria and it is critical to apply MCDM to arrive at a suitable assessment. The multi-criteria decision-making (MCDM) support methods enable the aggregation and computation of multiple criteria, whether conflicting or not, to select, classify, rank, or order a collection of choices for a specific issue [18].

In an extensive review by Ref. [19], the authors stated that the practice of including multi-criteria decision analysis (MCDA) approaches in tackling the selection of project portfolio problem has gained support in the present day as several scholars and experts have demonstrated the suitability of MCDA approaches in relation to multiple, conflicting and disproportionate criteria. A number of scholars focused on applying MCDA approaches integrated with optimization approaches to address resource and other restrictions in two different ways according to their review which spanned the years 2001 to 2020 [19]. They came to the conclusion that MCDA approaches are deployed as a support mechanism for optimization approaches, and that there are a variety of feasible MCDA approaches that can be applied in the selection of portfolios, but there is no agreement on which methods are the most productive and each firm tends to select one or more methods that are appropriate to their company's objectives and project criteria or attributes [19]. Thus, this study aims to develop an analytical hierarchy process-goal programming (AHP-GP) model to solve project portfolio selection problems (PPSP) for community development and benefits in line with the allocation of funds. This study is organized as follows: the second section outlines the multi-criteria decision making (MCDM) tools in project portfolio selection problems (PPSP), and section three contains the methodology and case study. Section four focuses on the results of the study, with section five presenting the discussion. The last section presents the conclusion.

2. Previous studies

Many scholars have researched or studied multi-criteria decision making (MCDM) tools in PPSP. Reference [20] proposed a model to handle projects for the Aircraft Controls Group, which could also be useful to other firms that have to manage several projects with limited resources. A goal programming (GP) model was developed in this study to identify which initiatives to undertake in order to maximize benefits over a four-year term, as well as determine machine procurement schemes and anticipated manpower needs. The model reflected the scenario in the short term with a limited number of programs, but it also revealed considerable potential for growth to cope with 12–15 programs over a longer period of time [20]. According to Ref. [21] the administration of healthcare firms is regularly confronted with the problem of allocating capital between possible projects. A goal programming model which provides an integrated framework for selecting a set of projects aligned with the organization's objectives was formulated to overcome this problem [21]. The issue of choosing a viable geographic information system (GIS) software lot for a specific GIS project is a MCDM problem. An AHP model was formulated by Ref. [22] to solve the GIS software selection problem. Because of its effectiveness in handling qualitative and quantitative criteria employed in the selection of software issues, AHP proved to be a coherent MCDM technique for selection of GIS software [22]. It also reduces the amount of time and effort required to make decisions. In the study of [12] on information technology (IT) Project Portfolio Selection using AHP was based on a framework that considered stakeholder points of view to cover all possible environments. The framework provided a decision support system (DSS) that was versatile, extendable, and interactive for selecting IT projects for portfolio management [12]. A zero-one goal programming (ZOGP) solution was developed by Ref. [23] to coordinate projects in marketing compatible with the aims of the organization. In the study, the approach led to a deeper understanding of the essence of transaction between the numerous elements that influence the decision makers' (DMs) project selection [23]. Reference [24] developed a dual fuzzy goal programming (FGP) approach to assess the project management (PM) resolution with several objectives in unknown environments. The findings provided a methodical decision-making framework that allows the policy maker to interactively modify the set of parameters until the preferred efficient solution is found [24]. Reference [25] identified the criteria for project selection (PS) that adequately combined the prerequisites of a variety of organizations (Private College Perspective) using the AHP technique to aid the PS within an ample criteria. In the study, the AHP method easily assisted the group of administrators to recognize suitable projects that most matched the company's functional demands and prioritize these projects accordingly [25]. Reference [26] reviewed the aspects of selection of contractors using AHP as a potential decision-making method for project management. Prequalification criteria were prioritized using AHP, and a descending order list of contractors was created to choose the best contractor to take on the project [26]. Reference [27] developed the Fuzzy Analytic Hierarchy Process (FAHP) to assess the priority order of the PS issues, decide on the criteria weights, and achieve the project predisposition scaling in the management of the portfolio. Reference [2] presented a two-stage hybrid mathematical programming model by integrating the Fuzzy Analytic Hierarchy Process (FAHP) with the Fuzzy Inference System (FIS) to select an optimal project portfolio to maximize project benefits and minimize project risks. Their hybrid methods considered both the quantitative and qualitative criteria in the cybersecurity industry that demonstrated the model's efficacy. Reference [28] evaluated the criteria for ministry collateral project selection in Build-Operate-Transfer (BOT) or Public Private Partnership (PPP) project finance. The study demonstrated that developing an alternative to government's infrastructure collateral project is a multi-faceted decision-making problem and a goal programming model was developed to enable the ministry to make a decision on the selection of a collateral project [28]. The dominant criteria [to be] applied by customers in the choice of contractors to pinpoint the weighted criteria by adopting the AHP approach from modern practice in Malaysia was developed by Ref. [29]. The AHP approach as a decision support technique is needed to remove the risks of project non-performance anticipated as a result of a contractor's poor performance. Reference [30] developed the MCDM method as a viable PS aid using FAHP that assessed and prioritized five important viable project criteria. According to their study, the approach showed the importance of criteria to be considered in viable PS in the sequence order of project cost, newness, variability, competence and knowledge, and computer intelligence respectively [30]. In the study of [31], they proposed an (AHP) and Weighted Additive Fuzzy Goal Programming (WAFGP) method for the selection of information system (IS) projects in all types of linear membership functions. According to their study, an integrated AHP-WAFGP approach provided better support for information system (IS) project selection decisions by selecting projects that better satisfy the various decision goals and utilize the available resources [31]. In another study [32], they proposed a formation approach that integrated a modified Delphi approach, an AHP and GP to devise a suitable collection of smart city projects. According to their study, the hybrid method provided a formation method to aid administrators at the public agency to appraise the smart city projects, as well as offering perceptions into the decision process for choosing a realistic portfolio of projects within the municipal administration [32]. Their analysis also stated that the completion of a smart city project depended on public participation and the municipality's size. Reference [33] developed a GP model to describe the lack of precision and variability correlated with the objectives and measures of the model for marine renewable energy projects selection in a strategic decision making process. Many studies from the above reviews revealed that AHP and GP methods were applied separately in PPSP with insufficient literature on integration of the methods. Therefore, the study will focus on integration of AHP and GP in PPSP for community development and benefits. The AHP will determine both the relative importance of weights and priority preferences, not by using expert's opinions or literature, but through decision makers using the AHP questionnaire. The GP will select the best projects for multi-objectives in a medium scale real-life situation.

3. Methodology

In this study, the proposed model of project selection will integrate two MCDM methods called AHP and GP. According to Ref. [8] MCDM methods are approaches that help to determine the best appropriate option among the alternatives in accordance with the predetermined criteria and goals.

Meanwhile, the MCDM method's purpose is to arrive at consensus-based value judgements using group decision-making principles. The lack of clarity among experts frequently leads to decision-making bias. AHP and GP are two different powerful decision-making tools because they can handle multi-criteria decision making (MCDM), but goal programming (GP) can provide the best solution based on organizational goals and limitations for multiple objectives optimization [32]. This study focuses on a government agency whose mandate was to develop a community by selecting and executing projects for School, Housing and Jetty including walkways to improve the lives of citizens and provide a better quality of life within the state/province.

3.1. Analytic hierarchy process (AHP)

AHP is a decision-making process for converting unstructured situations into a hierarchical structure. AHP is a technique for assessing, prioritizing, ranking, and evaluating decision-making options and various other elements in an ordered situation. AHP is also a technique for organizing and analyzing complicated decisions that combines mathematical and psychological techniques [34]. It is a reliable multi-criteria decision-making method that has been used to solve complicated and unstructured problems in a wide range of decision-making scenarios, such as but not limited to defence, health, education, agriculture, and forest management [35]. By providing a structured approach to calibrate quantitative scales for measuring qualitative performances, the AHP model utilizes hierarchical structures to demonstrate a problem and evaluate e alternatives for users. The AHP model is adaptable, allowing stakeholders in the development to assign a priority (comparative weight) to each factor via pairwise comparison [35]. AHP has been used to assist in the problem-solving process in a variety of areas, including project selection, location selection, resource allocation, risk management, technology selection, conflict resolution, project evaluation, and benchmarking [36]. In AHP models, criteria and alternatives are organized into ordered structures in at least three levels, in order to prioritize the criteria within each level [37]. The AHP basic steps include the following:

Step 1

Determination of the problem. The main action in applying AHP is to determine the problem and purpose.

Step 2

Structuring the problem according to different levels constituting goal/s, criteria, sub-criteria and alternatives.

Step 3

Indicate a pairwise comparison matrix (n x n) by comparing each element in the corresponding level and calibrating them on the 1–9 Saaty scale.

Step 4

Determine the significance of the pairwise comparison by establishing a matrix of the relative rankings for each level of sub-criteria weights.

Step 5

Establishment of a global priority ranking to ascertain the best possible course of action

Step 6

Decide on the best option according to the outcome of the global priority ranking [8,32,38,39]. [35,36].

3.2. Goal programming model

Goal programming (GP) is one of the techniques that has been created to cope with decision-making on problems with several objectives. This model enables many objectives to be considered at the same time, with decision-making focused on finding the optimal solution from a range of viable alternatives. The object of goal programming is to keep deviations from the established targets to a minimum. This is in contrast to linear and mixed-integer linear programming models, where the objective is to minimize or maximize the parameter. When all the constraints are difficult to comply with, goal programming is extremely useful. GP is a useful approach for solving decision-making issues in which the goal is to minimize the deviation between goal achievement and aspiration levels. Because of its intrinsic flexibility in managing decision-making problems with several conflicting objectives and inadequate or imprecise information, it is the most extensively applied multi-objective technique in management science. It is the attainment function that determines the degree to which the unwanted deviational variables of the model's goals are minimized [40].

Goal programming is a type of mathematical programming model that presents a way of solving a multi-goal optimization issue. The decision maker must use the goal programming model in order to affirm an absolute priority order among the goals and provide a target value for each of the goals [41].

Thus, a proposed pre-emptive and weighted goal programming model is formulated as follows:

Equation 1.

(1)

Subject to

Equation 2.

(2)

Equation 3.

(3)

b_{i} = 0 o r 1

The objective function is the aggregate of all the deviational variables in Equation (1). Equation (2) is the goal constraint function, and Equation (3) is the selection with binary variable and deviational variables which are equal to or exceed zero. The last constraint means the project is selected or not. $b_{i}$ = 1, means project i is selected, while $b_{i}$ = 0 means project i is not selected.

$P_{i}$ = Priority
$W_{i}$ = Weight
$m$ = the number of goals
$n$ = numeral of decision variables
$z$ = the objective function denoted as the aggregate of totally deviational variables
$b_{j}$ = the decision variables of jth
$a_{i, j}$ = the coordinated of the jth decision variables
$d_{i}^{+}, d_{i}^{-}$ = positive and negative deviations i.e., overachievement and underachievement variables
$G_{i}$ is the aspiration level or goal associated to the objective i. [8,32,42].

3.3. Case study

For the application and merits of the proposed model for project portfolio selection, a government agency whose mandate was to develop a community by selecting and executing projects like School, Housing and Jetty including walkways to improve the lives of citizens and provide a better quality of life within the state/province was used as a case study. The challenges of the agency were basically budget constraints, or limited funds, to execute projects, and also to select appropriate projects without bias and sentiment. Therefore, an integrated MCDM tool was proposed to overcome the stated challenges. The proposed projects’ details are shown in appendix A.

4. Results

4.1. The AHP model steps are implemented as described in section 3.1

1.
Develop the matrix criteria.

Matrix criteria are indicated in Table 1 to develop important weights and priorities of decision preference from the scores.

2.
Establish a pairwise comparison matrix of each sub-criteria and determine relative priorities.
3.
Computation of relative important weights, priorities and consistency ratio.

Table 1.

Project selection criteria.

Click one number per row below using the following scale		1: Necessary	2: Absolutely Necessary	3: Very Necessary	4: Important	5: Absolutely Important	6: Very Important	7: Absolutely Important	8: Extremely Important	9: Extremely Very Important. SCORES
Criteria	Sub Criteria	1	2	3	4	5	6	7	8	9
Social Effect [11]	Job creation [43]
	Social amenities [38]
	Quality of life/Benefits for human life [32,44]
	Economic developments to communities [45,46]
Social Integration [Authors]	Eliminate unrest in the areas [Authors]
	Political impact/alignment/context [27]
	Political risk that depends on the policy [43]
	Community acceptance [47]
Operating Factor [Authors]	Location of project [Authors]
	Abandonment of project [Authors]
	Completion time [48]
	Project risk [44]
Regulatory Agency [27]	Technical Support of Project Department [Authors]
	Local contractor's competency
	Quality of job [Authors]
	Work experience of PM [27]
	Facilities of local contractor [Authors]
Project Alternatives	School
	Housing
	Water Jetty and Walkways

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Sources: [11,27,32,38,[43], [44], [45], [46], [47], [48]]; Authors.

Spice Logic software was used to compute each criterion [to a] pairwise comparison and the priority of each sub-criteria including the consistency ratio (CR) in Table 2, Table 3, Table 4, Table 5. The accepted consistency ratio is CR $<$ 0.1. The final, or global weight and priority rankings are shown in Table 6.

Table 2.

Pairwise comparison of social development.

Social Development	Job Creation	Social Amenities	Quality of Life	Economic developments to communities	Priorities
Job Creation	1	2	0,5	0,333	0,165
Social Amenities	0,5	1	0,333	0,333	0,107
Quality of Life	2	3	1	0,5	0,283
Economic developments to communities	3	3	2	1	0,445

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CR = 0,026.

Table 3.

Pairwise comparison of social integration.

Social Integration	Eliminate unrest in the areas	Political impact/alignment	Political risk that depends on the policy	Community Acceptance	Priorities
Eliminate unrest in the areas	1	0,167	1	0,143	0,066
Political impact/alignment	6	1	6	0,5	0,345
Political risk that depends on the policy	1	0,167	1	0,143	0,066
Community Acceptance	7	2	1	1	0,532

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CR = 0,014.

Table 4.

Pairwise comparison of operational factors.

Operational Factor	Location of Project	Completion Time	Project Risk	Facilities of Local Contractor	Priorities
Location of Project	1	1	1	9	0,321
Completion Time	1	1	1	9	0,321
Project Risk	1	1	1	9	0,321
Facilities of Local Contractor	0,111	0,111	0,111	1	0,036

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CR = 0.

Table 5.

Pairwise comparison of developmental decision strategy.

Developmental Decision Strategy	Technical Support of Project Department	Local Contractors Competency	Alignment with organization mission/objectives	Work experience of PM	Priorities
Technical Support of Project Department	1	1	0,111	0,111	0,05
Local Contractors Competency	1	1	0,111	0,111	0,05
Alignment with organization mission/objectives	9	9	1	1	0,45
Work experience of PM	9	9	1	1	0,45

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CR = 0.

Table 6.

Final, or global weight and priority ranking.

Project	Final Weight and Priority Ranking
School	0,593 (1)
Housing	0,332 (2)
Wooden Jetty	0,075 (3)

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4.2. Goal programming model formulation from the final or global weight obtained from AHP

The model was formulated using the final or global weight obtained from AHP method in table 6.

$\begin{array}{c} M i n i m i z e Z = \\ P_{1} (0.593 d_{1}^{-} + 0.332 d_{2}^{-} + 0.075 d_{3}^{-}) S e l e c t P r o j e c t s f o r S o c i a l B e n e f i t s \\ \begin{array}{c} P_{2} (d_{4}^{+} + d_{5}^{+} + d_{6}^{+}) M i n i m i z e C o s t f o r P r o j e c t s (S c h o o l, W a t e r J e t t y a n d H o u s i n g) \\ P_{3} (d_{7}^{-} + d_{8}^{-} + d_{9}^{-}) M a x i m i z e n u m b e r o f j o b s c r e a t e d \end{array} \end{array}$

This is the integration of AHP-GP model below:

Equation 4.

(4)

Subject to:

Priority 1

Select projects (School, Water Jetty and Housing) for community satisfaction. [Maximize $(d_{1}^{-} + d_{2}^{-} + d_{3}^{-})$ ]

School Projects from Table A.1 in Appendix A.

\begin{array}{c} 6 b_{1} + 6 b_{2} + 6 b_{3} + 6 b_{4} + 6 b_{5} + 6 b_{6} + 6 b_{7} + 6 b_{8} + 6 b_{9} + 6 b_{10} + 6 b_{11} + 6 b_{12} + 3 b_{13} \\ + 6 b_{14} + 6 b_{15} + 6 b_{16} + 6 b_{17} + 6 b_{18} + 6 b_{19} + 6 b_{20} + 6 b_{21} + 6 b_{22} + 6 b_{23} + 6 b_{24} + 6 b_{25} \\ + 6 b_{26} + 6 b_{27} + 6 b_{28} + 6 b_{29} + 6 b_{30} + 6 b_{31} + 6 b_{32} + 6 b_{33} + 6 b_{34} + 6 b_{35} + 6 b_{36} + 6 b_{37} \\ + 6 b_{38} + 6 b_{39} + 6 b_{40} + 6 b_{41} + 6 b_{42} + 6 b_{43} + 6 b_{44} + 6 b_{45} + 6 b_{46} + 6 b_{47} + 6 b_{48} + 6 b_{49} \\ + 6 b_{50} + 3 b_{51} + 6 b_{52} + 6 b_{53} + 6 b_{54} + 6 b_{55} + 6 b_{56} + 6 b_{57} + 6 b_{58} + 3 b_{59} + b_{60} + 6 b_{61} \\ + 6 b_{62} + 6 b_{63} + 6 b_{64} + 6 b_{65} + 12 b_{66} + 12 b_{67} + 6 b_{68} + 6 b_{69} + 6 b_{70} + 6 b_{71} + 6 b_{72} \\ + 6 b_{73} + 3 b_{74} + 6 b_{75} + 3 b_{76} + 6 b_{77} + d_{1}^{-} - d_{1}^{+} = 454 \end{array}

Water Jetty projects from Table A.2 in Appendix A.

\begin{array}{c} b_{1} + b_{2} + b_{3} + b_{4} + b_{5} + b_{6} + b_{7} + b_{8} + b_{9} + b_{10} + b_{11} + b_{12} + b_{13} + b_{14} + b_{15} + b_{16} \\ + b_{17} + b_{18} + b_{19} + b_{20} + b_{21} + b_{22} + b_{23} + b_{24} + b_{25} + b_{26} + b_{27} + b_{28} + b_{29} + b_{30} \\ + b_{31} + b_{32} + b_{33} + b_{34} + b_{35} + b_{36} + b_{37} + b_{38} + b_{39} + b_{40} + b_{41} + b_{42} + b_{43} + b_{44} \\ + b_{45} + b_{46} + b_{47} + b_{48} + b_{49} + b_{50} + b_{51} + b_{52} + b_{53} + b_{54} + b_{55} + b_{56} + b_{57} + b_{58} \\ + b_{59} + b_{60} + b_{61} + b_{62} + b_{63} + b_{64} + b_{65} + b_{66} + b_{67} + b_{68} + b_{68} + b_{70} + b_{71} + b_{72} \\ + b_{73} + b_{74} + b_{75} + b_{76} + b_{77} + b_{78} + b_{79} + b_{80} + b_{81} + b_{82} + b_{83} + b_{84} + b_{85} + b_{86} \\ + b_{87} + d_{2}^{-} - d_{2}^{+} = 87 \end{array}

Housing projects from Table A.2 in Appendix A.

\begin{array}{c} 3 b_{1} + 3 b_{2} + 3 b_{3} + 3 b_{4} + 3 b_{5} + 3 b_{6} + 3 b_{7} + 3 b_{8} + 3 b_{9} + 3 b_{10} + 3 b_{11} + 3 b_{12} + 3 b_{13} \\ + 3 b_{14} + 3 b_{15} + 3 b_{16} + 3 b_{17} + 3 b_{18} + 3 b_{19} + 3 b_{20} + 3 b_{21} + 3 b_{22} + 3 b_{23} + 3 b_{24} + 3 b_{25} \\ + 3 b_{26} + 3 b_{27} + 3 b_{28} + 3 b_{29} + 3 b_{30} + 3 b_{31} + 3 b_{32} + 3 b_{33} + 3 b_{34} + 3 b_{35} + 3 b_{36} + 3 b_{37} \\ + 3 b_{38} + 3 b_{39} + 3 b_{40} + 3 b_{41} + 3 b_{42} + 3 b_{43} + 3 b_{44} + 3 b_{45} + 3 b_{46} + 3 b_{47} + 3 b_{48} + 3 b_{49} \\ + 3 b_{50} + 3 b_{51} + 3 b_{52} + 3 b_{53} + 3 b_{54} + 3 b_{55} + 3 b_{56} + 3 b_{57} + 3 b_{58} + 3 b_{59} + 3 b_{60} + 3 b_{61} \\ + 3 b_{62} + 3 b_{63} + 3 b_{64} + 3 b_{65} + 3 b_{66} + 3 b_{67} + 3 b_{68} + 3 b_{68} + 3 b_{70} + 3 b_{71} + 3 b_{72} + 3 b_{73} \\ + 3 b_{74} + 3 b_{75} + 3 b_{76} + 3 b_{77} + 3 b_{78} + 3 b_{79} + 3 b_{80} + 3 b_{81} + 3 b_{82} + 3 b_{83} + 3 b_{84} + 3 b_{85} \\ + 3 b_{86} + 3 b_{87} + 3 b_{88} + 3 b_{89} + 3 b_{90} + 3 b_{91} + 3 b_{92} + 3 b_{93} + 3 b_{94} + 3 b_{95} + 3 b_{96} + 3 b_{97} + 3 b_{98} + 3 b_{99} + 3 b_{100} + d_{3}^{-} - d_{3}^{+} = 300 \end{array}

Priority 2

Minimize cost of projects for School, Water Jetty and Housing from Tables A.1, A.2 and A.3 in Appendix A

$[M i n i m i z e (d_{4}^{+} + d_{5}^{+} + d_{6}^{+})]$

Cost of School Projects

\begin{array}{c} 17 b_{1} + 17 b_{2} + 17 b_{3} + 17 b_{4} + 17 b_{5} + 17 b_{6} + 17 b_{7} + 17 b_{8} + 3 b_{9} + 3 b_{10} + 3 b_{11} \\ + 17 b_{12} + 17 b_{13} + 17 b_{14} + 13 b_{15} + 13 b_{16} + 13 b_{17} + 17 b_{18} + 17 b_{19} + 3 b_{20} + 13 b_{21} \\ + 13 x_{22} + 13 x_{23} + 13 x_{24} + 13 x_{25} + 13 x_{26} + 13 b_{27} + 13 b_{28} + 13 b_{29} + 13 b_{30} + 13 b_{31} \\ + 13 b_{32} + 13 b_{33} + 13 b_{34} + 13 b_{35} + 13 b_{36} + 13 b_{37} + 13 b_{38} + 13 b_{39} + 13 b_{40} + 13 b_{41} \\ + 13 b_{42} + 13 b_{43} + 13 b_{44} + 17 b_{45} + 17 b_{46} + 13 b_{47} + 13 b_{48} + 13 b_{49} + 13 b_{50} + 7 b_{51} \\ + 17 b_{52} + 13 b_{53} + 13 b_{54} + 13 b_{55} + 13 b_{56} + 13 b_{57} + 13 b_{58} + 13 b_{59} + 7 b_{60} + 13 b_{61} \\ + 13 b_{62} + 13 b_{63} + 13 b_{64} + 13 b_{65} + 34 b_{66} + 26 b_{67} + 13 b_{68} + 13 b_{69} + 7 b_{70} + 13 b_{71} \\ + 13 b_{72} + 13 b_{73} + 7 b_{74} + 13 b_{75} + 7 b_{76} + 13 b_{77} + d_{4}^{-} - d_{4}^{+} = 1,039 \end{array}

Cost of Water Jetty Projects

\begin{array}{c} 7,913 b_{1} + 4,372 b_{2} + 4,372 b_{3} + 6,257 b_{4} + 6,257 b_{5} + 4,372 b_{6} + 4,372 b_{7} + 6,257 b_{8} \\ + 6,257 b_{9} + 6,041 b_{10} + 4,156 b_{11} + 6,041 b_{12} + 7,083 b_{13} + 6,537 b_{14} + 6,537 b_{15} \\ + 6,257 b_{16} + 8,230 b_{17} + 18,108 b_{18} + 7,125 b_{19} + 6,340 b_{20} + 6,340 b_{21} + 18,324 b_{22} \\ + 4,987 b_{23} + 6,340 b_{24} + 7,688 b_{25} + 7,477 b_{26} + 6,936 b_{27} + 7,135 b_{28} + 6,257 b_{29} \\ + 6,257 b_{30} + 6,041 b_{31} + 6,257 b_{32} + 12,683 b_{33} + 13,098 b_{34} + 9,391 b_{35} + 7,911 b_{36} \\ + 7,082 b_{37} + 9,272 b_{38} + 8,526 b_{39} + 8,526 b_{40} + 9,193 b_{41} + 8,893 b_{42} + 24,144 \\ + 14,741 b_{44} + 14,570 b_{45} + 18,324 b_{46} + 7,298 b_{47} + 15,513 b_{48} + 9,279 b_{49} + 10,084 b_{50} \\ + 14,703 b_{51} + 12,288 b_{52} + 5,184 b_{53} + 6,257 b_{54} + 7,683 b_{55} + 12,893 b_{56} + 4,446 b_{57} \\ + 27,233 b_{58} + 4,245 b_{59} + 3,735 b_{60} + 4,132 b_{61} + 6,128 b_{62} + 4,672 b_{63} + 6,281 b_{64} \\ + 7,789 b_{65} + 5,092 b_{66} + 8,320 b_{67} + 6,281 b_{68} + 6,281 b_{69} + 17,186 b_{70} + 7,484 b_{71} \\ + 15,908 b_{72} + 13,308 b_{73} + 24,636 b_{74} + 15,283 b_{75} + 7,323 b_{76} + 5,108 b_{77} + 17,300 b_{78} \\ + 4,644 b_{79} + 4,649 b_{80} + 5,920 b_{81} + 7,247 b_{82} + 15,303 b_{83} + 8,924 b_{84} + 7,660 b_{85} \\ + 6,939 b_{86} + 4,741 b_{87} + d_{5}^{-} - d_{5}^{+} = 774,648 \end{array}

Cost of Housing Projects

\begin{array}{c} 8,606 b_{1} + 8,606 b_{2} + 8,606 b_{3} + 8,606 b_{4} + 8,606 b_{5} + 8,606 b_{6} + 8,606 b_{7} + 8,606 b_{8} \\ + 8,376 b_{9} + 8,376 b_{10} + 8,376 b_{11} + 8,376 b_{12} + 8,376 b_{13} + 8,376 b_{14} + 8,376 b_{15} \\ + 8,376 b_{16} + 8,376 b_{17} + 8,376 b_{18} + 8,376 b_{19} + 8,376 b_{20} + 8,376 b_{21} + 8,376 b_{22} \\ + 8,146 b_{23} + 8,146 b_{24} + 8,146 b_{25} + 8,146 b_{26} + 12,882 b_{27} + 12,882 b_{28} + 12,882 b_{29} \\ + 12,882 b_{30} + 8,376 b_{31} + 8,376 b_{32} + 8,376 b_{33} + 8,376 b_{34} + 12,882 b_{35} + 12,882 b_{36} \\ + 12,882 b_{37} + 12,882 b_{38} + 12,882 b_{39} + 12,882 b_{40} + 12,882 b_{41} + 12,882 b_{42} \\ + 12,882 b_{43} + 12,882 b_{44} + 12,882 b_{45} + 12,882 b_{46} + 12,882 b_{47} + 12,882 b_{48} \\ + 12,882 b_{49} + 12,882 b_{50} + 12,882 b_{51} + 12,882 b_{52} + 12,882 b_{53} + 12,882 b_{54} \\ + 12,882 b_{55} + 12,882 b_{56} + 12,882 b_{57} + 12,882 b_{58} + 12,882 b_{59} + 12,882 b_{60} \\ + 12,882 b_{61} + 12,882 b_{62} + 12,882 b_{63} + 12,882 b_{64} + 12,882 b_{65} + 12,882 b_{66} \\ + 12,882 b_{67} + 12,882 b_{68} + 12,882 b_{68} + 12,882 b_{70} + 12,882 b_{71} + 12,882 b_{72} \\ + 12,882 b_{73} + 12,882 b_{74} + 12,882 b_{75} + 12,882 b_{76} + 12,882 b_{77} + 12,882 b_{78} \\ + 12,882 b_{79} + 12,882 b_{80} + 12,882 b_{81} + 12,882 b_{82} + 12,882 b_{83} + 8,606 b_{84} \\ + 12,882 b_{85} + 12,882 b_{86} + 12,882 b_{87} + 8,376 b_{88} + 8,376 b_{89} + 8,376 b_{90} + 8,376 b_{91} \\ + 8,376 b_{92} + 8,376 b_{93} + 8,376 b_{94} + 8,376 b_{95} + 8,376 b_{96} + 8,376 b_{97} + 8,376 b_{98} \\ + 8,376 b_{99} + 8,376 b_{100} + d_{6}^{-} - d_{6}^{+} = 1,091,086 \end{array}

Priority 3

Maximize number of jobs created for selected projects

$[M a x i m i z e (d_{7}^{-} + d_{8}^{-} + d_{9}^{-})]$

School Projects

\begin{array}{c} 14 b_{1} + 14 b_{2} + 14 b_{3} + 14 b_{4} + 14 b_{5} + 14 b_{6} + 14 b_{7} + 14 b_{8} + 14 b_{9} + 14 b_{10} + 14 b_{11} \\ + 14 b_{12} + 14 b_{13} + 14 b_{14} + 14 b_{15} + 14 b_{16} + 14 b_{17} + 14 b_{18} + 14 b_{19} + 14 b_{20} + 14 b_{21} \\ + 14 b_{22} + 14 b_{23} + 14 b_{24} + 14 b_{25} + 14 b_{26} + 14 b_{27} + 14 b_{28} + 14 b_{29} + 14 b_{30} + 14 b_{31} \\ + 14 b_{32} + 14 b_{33} + 14 b_{34} + 14 b_{35} + 14 b_{36} + 14 b_{37} + 14 b_{38} + 14 b_{39} + 14 b_{40} + 14 b_{41} \\ + 14 b_{42} + 14 b_{43} + 14 b_{44} + 14 b_{45} + 14 b_{46} + 14 b_{47} + 14 b_{48} + 14 b_{49} + 14 b_{50} + 14 b_{51} \\ + 14 b_{52} + 14 b_{53} + 14 b_{54} + 14 b_{55} + 14 b_{56} + 14 b_{57} + 14 b_{58} + 14 b_{59} + 14 b_{60} + 14 b_{61} \\ + 14 b_{62} + 14 b_{63} + 14 b_{64} + 14 b_{65} + 14 b_{66} + 14 b_{67} + 14 b_{68} + 14 b_{69} + 14 b_{70} + 14 b_{71} \\ + 14 b_{72} + 14 b_{73} + 14 b_{74} + 14 b_{75} + 14 b_{76} + 14 b_{77} + d_{7}^{-} - d_{7}^{+} = 1078 \end{array}

Water Jetty Projects

\begin{array}{c} 87 b_{1} + 87 b_{2} + 87 b_{3} + 87 b_{4} + 87 b_{5} + 87 b_{6} + 87 b_{7} + 87 b_{8} + 87 b_{9} + 87 b_{10} + 87 b_{11} \\ + 87 b_{12} + 87 b_{13} + 87 b_{14} + 87 b_{15} + 87 b_{16} + 87 b_{17} + 87 b_{18} + 87 b_{19} + 87 b_{20} + 87 b_{21} \\ + 87 b_{22} + 87 b_{23} + 87 b_{24} + 87 b_{25} + 87 b_{26} + 87 b_{27} + 87 b_{28} + 87 b_{29} + 87 b_{30} + 87 b_{31} \\ + 87 b_{32} + 87 b_{33} + 87 b_{34} + 87 b_{35} + 87 b_{36} + 87 b_{37} + 87 b_{38} + 87 b_{39} + 87 b_{40} + 87 b_{41} \\ + 87 b_{42} + 87 b_{43} + 87 b_{44} + 87 b_{45} + 87 b_{46} + 87 b_{47} + 87 b_{48} + 87 b_{49} + 87 b_{50} + 87 b_{51} \\ + 87 b_{52} + 87 b_{53} + 87 b_{54} + 87 b_{55} + 87 b_{56} + 87 b_{57} + 87 b_{58} + 87 b_{59} + 87 b_{60} + 87 b_{61} \\ + 87 b_{62} + 87 b_{63} + 87 b_{64} + 87 b_{65} + 87 b_{66} + 87 b_{67} + 87 b_{68} + 87 b_{68} + 87 b_{70} + 87 b_{71} \\ + 87 b_{72} + 87 b_{73} + 87 b_{74} + 87 b_{75} + 87 b_{76} + 87 b_{77} + 87 b_{78} + 87 b_{79} + 87 b_{80} + 87 b_{81} \\ + 87 b_{82} + 87 b_{83} + 87 b_{84} + 87 b_{85} + 87 b_{86} + 87 b_{87} + d_{8}^{-} - d_{8}^{+} = 7569 \end{array}

Housing Projects

\begin{array}{c} 100 b_{1} + 100 b_{2} + 100 b_{3} + 100 b_{4} + 100 b_{5} + 100 b_{6} + 100 b_{7} + 100 b_{8} + 100 b_{9} \\ + 100 b_{10} + 100 b_{11} + 100 b_{12} + 100 b_{13} + 100 b_{14} + 100 b_{15} + 100 b_{16} + 100 b_{17} \\ + 100 b_{18} + 100 b_{19} + 100 b_{20} + 100 b_{21} + 100 b_{22} + 100 b_{23} + 100 b_{24} + 100 b_{25} \\ + 100 b_{26} + 100 b_{27} + 100 b_{28} + 100 b_{29} + 100 b_{30} + 100 b_{31} + 100 b_{32} + 100 b_{33} \\ + 100 b_{34} + 100 b_{35} + 100 b_{36} + 100 b_{37} + 100 b_{38} + 100 b_{39} + 100 b_{40} + 100 b_{41} \\ + 100 b_{42} + 100 b_{43} + 100 b_{44} + 100 b_{45} + 100 b_{46} + 100 b_{47} + 100 b_{48} + 100 b_{49} \\ + 100 b_{50} + 100 b_{51} + 100 b_{52} + 100 b_{53} + 100 b_{54} + 100 b_{55} + 100 b_{56} + 100 b_{57} \\ + 100 b_{50} + 100 b_{51} + 100 b_{52} + 100 b_{53} + 100 b_{54} + 100 b_{55} + 100 b_{56} + 100 b_{57} \\ + 100 b_{58} + 100 b_{59} + 100 b_{60} + 100 b_{61} + 100 b_{62} + 100 b_{63} + 100 b_{64} + 100 b_{65} \\ + 100 b_{66} + 100 b_{67} + 100 b_{68} + 10 b_{68} + 100 b_{70} + 100 b_{71} + 100 b_{72} + 100 b_{73} \\ + 100 b_{74} + 100 b_{75} + 100 b_{76} + 100 b_{77} + 100 b_{78} + 100 b_{79} + 100 b_{80} + 100 b_{81} \\ + 100 b_{82} + 100 b_{83} + 100 b_{84} + 100 b_{85} + 100 b_{86} + 100 b_{87} + 100 b_{88} + 100 b_{89} \\ + 100 b_{90} + 100 b_{91} + 100 b_{92} + 100 b_{93} + 100 b_{94} + 100 b_{95} + 100 b_{96} + 100 b_{97} \\ + 100 b_{98} + 100 b_{99} + 100 b_{100} + d_{9}^{-} - d_{9}^{+} = 10000 \\ b_{i} = 0 o r 1 \end{array}

4.3. Comparison of optimization results between the integrated (AHP-GP) and GP models

Table 7 below compares the optimization results between the proposed (AHP-GP) and GP models.

Table 7.

Optimization Results for GP and AHP-GP models.

Town	School	Water Jetty	Housing	GP Solution (Value)	AHP-GP Solution (Value)	No. of Jobs	Remarks
Town	School	Water Jetty	Housing	GP Solution (Value)	AHP-GP Solution (Value)	No. of Jobs	GP	AHP-GP
1.	Classrooms block (6B₁)	Water Jetty (B₁)	Housing unit (3B₁)	0	1	14,87 &100	NS	S
2.	Classrooms block (6B₂)	Water Jetty (B₂)	Housing unit (3B₂)	1	1	14,87 &100	S	S
3.	Classrooms block (6B₃)	Water Jetty (B₃)	Housing unit (3B₃)	1	1	14,87 &100	S	S
4.	Classrooms block (6B₄)	Water Jetty (B₄)	Housing unit (3B₄)	0	1	14,87 &100	NS	S
5.	Classrooms block (6B₅)	Water Jetty (B₅)	Housing unit (3B₅)	0	1	14,87 &100	NS	S
6.	Classrooms block (6B₆)	Water Jetty (B₆)	Housing unit (3B₆)	1	1	14,87 &100	S	S
7.	Classrooms block (6B₇)	Water Jetty (B₇)	Housing unit (3B₇)	1	1	14,87 &100	S	S
8.	Classrooms block (6B₈)	Water Jetty (B₈)	Housing unit (3B₈)	0	1	14,87 &100	NS	S
9.	Classrooms block (6B₉)	Water Jetty (B₉)	Housing unit (3B₉)	0	1	14,87 &100	NS	S
10.	Classrooms block (6B₁₀)	Water Jetty (B₁₀)	Housing unit (3B₁₀)	0	1	14,87 &100	NS	S
11.	Classrooms block (6B₁₁)	Water Jetty (B₁₁)	Housing unit (3B₁₁)	1	1	14,87 &100	S	S
12.	Classrooms block (6B₁₂)	Water Jetty (B₁₂)	Housing unit (3B₁₂)	0	1	14,87 &100	NS	S
13.	Classrooms block (6B₁₃)	Water Jetty (B₁₃)	Housing unit (3B₁₃)	0	1	14,87 &100	NS	S
14.	Classrooms block (6B₁₄)	Water Jetty (B₁₄)	Housing unit (3B₁₄)	0	1	14,87 &100	NS	S
15.	Classrooms block (6B₁₅)	Water Jetty (B₁₅)	Housing unit (3B₁₅)	0	1	14,87 &100	NS	S
16.	Classrooms block (6B₁₆)	Water Jetty (B₁₆)	Housing unit (3B₁₆)	0	1	14,87 &100	NS	S
17.	Classrooms block (6B₁₇)	Water Jetty (B₁₇)	Housing unit (3B₁₇)	0	1	14,87 &100	NS	S
18.	Classrooms block (6B₁₈)	Water Jetty (B₁₈)	Housing unit (3B₁₈)	0	0	14,87 &100	NS	NS
19.	Classrooms block (6B₁₉)	Water Jetty (B₁₉)	Housing unit (3B₁₉)	0	1	14,87 &100	NS	S
20.	Classrooms block (6B₂₀)	Water Jetty (B20)	Housing unit (3B₂₀)	0	1	14,87 &100	NS	S
21.	Classrooms block (6B₂₁)	Water Jetty (B₂₁)	Housing unit (3B₂₁)	0	1	14,87 &100	NS	S
22.	Classrooms block (6B₂₂)	Water Jetty (B₂₂)	Housing unit (3B₂₂)	0	0	14,87 &100	NS	NS
23.	Classrooms block (6B₂₃)	Water Jetty (B₂₃)	Housing unit (3B₂₃)	1	1	14,87 &100	S	S
24.	Classrooms block (6B₂₄)	Water Jetty (B₂₄)	Housing unit (3B₂₄)	0	1	14,87 &100	NS	S
25.	Classrooms block (6B₂₅)	Water Jetty (B₂₅)	Housing unit (3B₂₅)	0	1	14,87 &100	NS	S
26.	Classrooms block (6B₂₆)	Water Jetty (B₂₆)	Housing unit (3B₂₆)	0	1	14,87 &100	NS	S
27.	Classrooms block (6B₂₇)	Water Jetty (B₂₇)	Housing unit (3B₂₇)	0	1	14,87 &100	NS	S
28.	Classrooms block (6B₂₈)	Water Jetty (B28)	Housing unit (3B₂₈)	0	1	14,87 &100	NS	S
29.	Classrooms block (6B₂₉)	Water Jetty (B₂₉)	Housing unit (3B₁₂₉)	0	1	14,87 &100	NS	S
30.	Classrooms block (6B₃₀)	Water Jetty (B₃₀)	Housing unit (3B₃₀)	0	1	14,87 &100	NS	S
31.	Classrooms block (6B₃₁)	Water Jetty (B₃₁)	Housing unit (3B₃₁)	0	1	14,87 &100	NS	S
32.	Classrooms block (6B₃₂)	Water Jetty (B₃₂)	Housing unit (3B₃₂)	0	1	14,87 &100	NS	S
33.	Classrooms block (6B₃₃)	Water Jetty (B₃₃)	Housing unit (3B₃₃)	0	1	14,87 &100	NS	S
34.	Classrooms block (6B₃₄)	Water Jetty (B₃₄)	Housing unit (3B₃₄)	0	1	14,87 &100	NS	S
35.	Classrooms block (6B₃₅)	Water Jetty (B₃₅)	Housing unit (3B₃₅)	0	1	14,87 &100	NS	S
36.	Classrooms block (6B₃₆)	Water Jetty (B₃₆)	Housing unit (3B₃₆)	0	1	14,87 &100	NS	S
37.	Classrooms block (6B₃₇)	Water Jetty (B₃₇)	Housing unit (3B₃₇)	0	1	14,87 &100	NS	S
38.	Classrooms block (6B₃₈)	Water Jetty (B₃₈)	Housing unit (3B₃₈)	0	1	14,87 &100	NS	S
39.	Classrooms block (6B₃₉)	Water Jetty (B₃₉)	Housing unit (3B₃₉)	0	1	14,87 &100	NS	S
40.	Classrooms block (6B₄₀)	Water Jetty (B₄₀)	Housing unit (3B₄₀)	0	1	14,87 &100	NS	S
41.	Classrooms block (6B₄₁)	Water Jetty (B₄₁)	Housing unit (3B₄₁)	0	1	14,87 &100	NS	S
42.	Classrooms block (6B₄₂)	Water Jetty (B₄₂)	Housing unit (3B₄₂)	0	1	14,87 &100	NS	S
43.	Classrooms block (6B₄₃)	Water Jetty (B₄₃)	Housing unit (3B₄₃)	0	0	14,87 &100	NS	NS
44.	Classrooms block (6B₄₄)	Water Jetty (B₄₄)	Housing unit (3B₄₄)	0	1	14,87 &100	NS	S
45.	Classrooms block (6B₄₅)	Water Jetty (B₄₅)	Housing unit (3B₄₅)	0	1	14,87 &100	NS	S
46.	Classrooms block (6B₄₆)	Water Jetty (B₄₆)	Housing unit (3B₄₆)	0	0	14,87 &100	NS	NS
47.	Classrooms block (6B₄₇)	Water Jetty (B₄₇)	Housing unit (3B₄₇)	0	1	14,87 &100	NS	S
48.	Classrooms block (6B₄₈)	Water Jetty (B₄₈)	Housing unit (3B₄₈)	0	1	14,87 &100	NS	S
49.	Classrooms block (6B₄₉)	Water Jetty (B₄₉)	Housing unit (3B₄₉)	0	1	14,87 &100	NS	S
50.	Classrooms block (6B₅₀)	Water Jetty (B₅₀)	Housing unit (3B₅₀)	0	1	14,87 &100	NS	S
51.	Classrooms block (6B₅₁)	Water Jetty (B₅₁)	Housing unit (3B₅₁)	0	1	14,87 &100	NS	S
52.	Classrooms block (6B₅₂)	Water Jetty (B₅₂)	Housing unit (3B₅₂)	0	1	14,87 &100	NS	S
53.	Classrooms block (6B₅₃)	Water Jetty (B₅₃)	Housing unit (3B₅₃)	1	1	14,87 &100	S	S
54.	Classrooms block (6B₅₄)	Water Jetty (B₅₄)	Housing unit (3B₅₄)	0	1	14,87 &100	NS	S
55.	Classrooms block (6B₅₅)	Water Jetty (B₅₅)	Housing unit (3B₅₅)	0	1	14,87 &100	NS	S
56.	Classrooms block (6B₅₆)	Water Jetty (B₅₆)	Housing unit (3B₅₆)	0	1	14,87 &100	NS	S
57.	Classrooms block (3B₅₇)	Water Jetty (B₅₇)	Housing unit (3B₅₇)	1	1	14,87 &100	S	S
58.	Classrooms block (6B₅₈)	Water Jetty (B₅₈)	Housing unit (3B₅₈)	0	0	14,87 &100	NS	NS
59.	Classrooms block (3B₅₉)	Water Jetty (B₅₉)	Housing unit (3B₅₉)	1	1	14,87 &100	S	S
60.	Classrooms block (B₆₀)	Water Jetty (B₆₀)	Housing unit (3B₆₀)	1	1	14,87 &100	S	S
61.	Classrooms block (6B₆₁)	Water Jetty (B₆₁)	Housing unit (3B₆₁)	1	1	14,87 &100	S	S
62.	Classrooms block (6B₆₂)	Water Jetty (B₆₂)	Housing unit (3B₆₂)	0	1	14,87 &100	NS	S
63.	Classrooms block (6B₆₃)	Water Jetty (B₆₃)	Housing unit (3B₆₃)	1	1	14,87 &100	S	S
64.	Classrooms block (6B₆₄)	Water Jetty (B₆₄)	Housing unit (3B₆₄)	0	1	14,87 &100	NS	S
65.	Classrooms block (6B₆₅)	Water Jetty (B₆₅)	Housing unit (3B₆₅)	0	1	14,87 &100	NS	S
66.	Classrooms block (6B₆₆)	Water Jetty (B₆₆)	Housing unit (3B₆₆)	1	1	14,87 &100	S	S
67.	Classrooms block (6B₆₇)	Water Jetty (B₆₇)	Housing unit (3B₆₇)	0	1	14,87 &100	NS	S
68.	Classrooms block (6B₆₈)	Water Jetty (B₆₈)	Housing unit (3B₆₈)	0	1	14,87 &100	NS	S
69.	Classrooms block (6B₆₉)	Water Jetty (B₆₉)	Housing unit (3B₆₉)	0	1	14,87 &100	NS	S
70.	Classrooms block (6B₇₀)	Water Jetty (B₇₀)	Housing unit (3B₇₀)	0	0	14,87 &100	NS	NS
71.	Classrooms block (6B₇₁)	Water Jetty (B₇₁)	Housing unit (3B₇₁)	0	1	14,87 &100	NS	S
72.	Classrooms block (6B₇₂)	Water Jetty (B₇₂)	Housing unit (3B₇₂)	0	1	14,87 &100	NS	S
73.	Classrooms block (6B₇₃)	Water Jetty (B₇₃)	Housing unit (3B₇₃)	0	1	14,87 &100	NS	S
74.	Classrooms block (3B₇₄)	Water Jetty (B₇₄)	Housing unit (3B₇₄)	0	0	14,87 &100	NS	NS
75.	Classrooms block (6B₇₅)	Water Jetty (B₇₅)	Housing unit (3B₇₅)	0	1	14,87 &100	NS	S
76.	Classrooms block (3B₇₆)	Water Jetty (B₇₆)	Housing unit (3B₇₆)	0	1	14,87 &100	NS	S
77.	Classrooms block (6B₇₇)	Water Jetty (B₇₇)	Housing unit (3B₇₇)	1	1	14,87 &100	S	S
78.		Water Jetty (B₇₈)	Housing unit (3B₇₈)	0	0	14,87 &100	NS	NS
79.		Water Jetty (B₇₉)	Housing unit (3B₇₉)	1	1	14,87 &100	S	S
80.		Water Jetty (B₈₀)	Housing unit (3B₈₀)	1	1	14,87 &100	S	S
81.		Water Jetty (B₈₁)	Housing unit (3B₈₁)	0	1	14,87 &100	NS	S
82.		Water Jetty (B₈₂)	Housing unit (3B₈₂)	0	1	14,87 &100	NS	S
83.		Water Jetty (B₈₃)	Housing unit (3B₈₃)	0	1	14,87 &100	NS	S
84.		Water Jetty (B₈₄)	Housing unit (3B₈₄)	0	1	14,87 &100	NS	S
85.		Water Jetty (B₈₅)	Housing unit (3B₈₅)	0	1	14,87 &100	NS	S
86.		Water Jetty (B₈₆)	Housing unit (3B₈₆)	0	1	14,87 &100	NS	S
87.		Water Jetty (B₈₇)	Housing unit (3B₈₇)	1	1	14,87 &100	S	S
88.			Housing unit (3B₈₈)	1	1	14,87 &100	S	S
89.			Housing unit (3B₈₉)	1	1	14,87 &100	S	S
90.			Housing unit (3B₉₀)	1	1	14,87 &100	S	S
91.			Housing unit (3B₉₁)	1	1	14,87 &100	S	S
92.			Housing unit (3B₉₂)	1	1	14,87 &100	S	S
93.			Housing unit (3B₉₃)	1	1	14,87 &100	S	S
94.			Housing unit (3B₉₄)	1	1	14,87 &100	S	S
95.			Housing unit (3B₉₅)	1	1	14,87 &100	S	S
96.			Housing unit (3B₉₆)	1	1	14,87 &100	S	S
97.			Housing unit (3B₉₇)	1	1	14,87 &100	S	S
98.			Housing unit (3B₉₈)	1	1	14,87 &100	S	S
99.			Housing unit (3B₉₉)	1	1	14,87 &100	S	S
100.			Housing unit (3B₁₀₀)	1	1	14,87 &100	S	S
Total	454	87	300			980,6873 & 9200

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NB: NS = NOT SELECTED; S = SELECTED.

The deviational variables of AHP-GP model are: $d_{1}^{-}$ = 39.0; $d_{2}^{-}$ = 8.0; $d_{3}^{-}$ = 24; $d_{4}^{-}$ = 87; $d_{5}^{-}$ = 165255; $d_{6}^{-}$ = 94044; $d_{7}^{-}$ = 98.0; $d_{8}^{-}$ = 696; $d_{9}^{-}$ = 800. The objective value of AHP-GP is 1596.579.

While the deviational variables of GP model are: $d_{1}^{-}$ = 372; $d_{2}^{-}$ = 70; $d_{3}^{-}$ = 210; $d_{4}^{-}$ = 836000; $d_{5}^{-}$ = 697369; $d_{6}^{-}$ = 787550; $d_{7}^{-}$ = 882; $d_{8}^{-}$ = 6090; $d_{9}^{-}$ = 7000. The objective value of GP is 14615.96.

5. Discussion

The AHP method was employed through the use of Spice Logic software. Table 1 shows the project selection criteria and the scores scale. Table 2, Table 3, Table 4, Table 5 show the pairwise comparison matrix of each sub-criteria including their relative priorities which indicates project criteria that will improve community developments and Table 6 also shows the final weight of the projects that indicated projects with the highest priorities for the communities. The hybrid model in Equation (4) was solved using LINGO 18.0 software package within a few seconds. The optimization results in Table 7 show that the projects with solution values of (1) were eligible for selection while projects with solution values of (0) were not eligible for selection. The projects considered for various communities are school, wooden jetty and housing. In school projects, 68 out of 74 projects, meaning 415 classrooms from 454 classrooms were selected, that created 980 jobs for the citizens of the communities. In wooden jetty projects, 79 projects were selected from 87 projects that created 6873 jobs. In housing scheme projects, 92 out of 100 schemes were selected that translated into 276 housing units out of 300 units, that generated 92 000 jobs for the communities. The total cost saving from projects not selected is ₦346 million. Thus, $d_{4}^{-}$ = 87; $d_{5}^{-}$ = 165255; $d_{6}^{-}$ = 94044.

To prove the efficiency of the integrated approach (AHP-GP) for project portfolio selection, the optimization results of AHP-GP and GP were compared in Table 7. The AHP-GP model selected more school, wooden jetty and housing projects compared to the GP model, that translated into more classrooms and more jobs to the host communities. The AHP-GP model had a lower objective value of 1596.578 compared to 14615.96 of the GP model and also had 0.08 s elapsed time compared to 0.11 s for the GP model. The integrated AHP-GP approach also showed the decision makers the project criteria that were more important to enhance or improve the projects to be selected as opposed to the GP model that selected projects without considering project criteria. The AHP-GP model highlighted school and housing projects with high priorities to be given appropriate attention. The results confirmed the validity of the approach. Therefore, the AHP-GP integrated model enhanced the decisions to select the right, or appropriate projects for community developments.

6. Conclusion

Project portfolio selection methods are expedient because they help organizations in choosing the most appropriate projects to be successful and efficient in their resource allocation. An integrated approach called analytic hierarchy process (AHP) and goal programming (GP) was used to select projects for community developments and needs. The school projects will provide education for the children of the community and reduce the problem of getting access to education. The goals of the wooden jetty projects are to connect the land to deep water further away from the coast for the purpose of docking ships and unloading cargo and improving the safety of pedestrians. Furthermore, the housing projects will provide affordable, or social housing for the community and reduce community concerns and reduce the [financial] burden for the construction of affordable housing projects. In the interim, employment opportunities will be created for the citizens of each community in terms of jobs and small businesses for the economic development of the communities and the entire region, and which will also improve their quality of life. In the study of [49] less than 50 projects have been proposed using goal programming in project portfolio selection problems. However, following conclusions were made from this study by using AHP integrated with GP model:

1.)
The Analytic hierarchy process (AHP) and Goal programming (GP) model could be used to plan project selection according to priorities.
2.)
Using the integrated approach could generate some financial saving from proposed projects that are not selected which could be used for other projects.
3.)
Applying the goal programming model to a large number of 100 projects is a novel approach.

For further research, the proposed approach should be extended or integrated with a meta-heuristic algorithm to solve complex large-scale optimization project portfolio selection problems. For example, the possibility of investigating a pareto set of optimal project selection via integration of a Genetic algorithm into the mix should be explored. The approach could also be applied in private organizations and other fields. In the interim, the projects selected, and the jobs created during the project's activities, will be most beneficial to the community's development and the citizens themselves.

Production notes

Author contribution statement

Akinlo Olorunju Mogbojuri & Oludolapo Akanni Olanrewaju: Conceived and designed the experiments; Performed the experiments; Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data; Wrote the paper.

Data availability statement

The authors do not have permission to share data.

Funding statement

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

We acknowledge Dr Azunna Agwo Eze of Department of Chemical, Metallurgy and Materials Engineering, Institute for Nano-Engineering Research (INER), Tshwane University of Technology, Pretoria, South Africa, and also Mr Olatunde Joseph Oloyede for their supports.

Appendix A. Primary Data

Table A.1.

School Projects

Project	Project Description (b)	Town	Duration (Months)	Cost (x10⁶)	Estimated % completion
1.	Construction of 6 Classrooms block (6b₁)	1	12	17	100
2.	Construction of 6 Classrooms block (6b₂)	2	12	17	100
3.	Construction of 6 Classrooms block (6b₃)	3	12	17	100
4.	Construction of 6 Classrooms block (6b₄)	4	12	17	100
5.	Construction of 6 Classrooms block (6b₅)	5	12	17	100
6.	Construction of 6 Classrooms block (6b₆)	6	12	17	100
7.	Construction of 6 Classrooms block (6b₇)	7	12	17	100
8.	Construction of 6 Classrooms block (6b₈)	8	12	17	100
9.	Construction of 6 Classrooms block (6b₉)	9	12	13	100
10.	Construction of 6 Classrooms block (6b₁₀)	10	12	13	100
11.	Construction of 6 Classrooms block (6b₁₁)	11	12	13	100
12.	Construction of 6 Classrooms block (6b₁₂)	12	12	17	100
13.	Construction of 3 Classrooms block (6b₁₃)	13	7	7	95
14.	Construction of 6 Classrooms block (6b₁₄)	14	12	17	95
15.	Construction of 6 Classrooms block (6b₁₅)	15	12	13	100
16.	Construction of 6 Classrooms block (6b₁₆)	16	12	13	100
17.	Construction of 16 classroom blocks (6b₁₇)	17	12	13	100
18.	Construction of 6 Classrooms block (6b₁₈)	18	12	17	100
19.	Construction of 6 Classrooms block (6b₁₉)	19	12	17	100
20.	Construction of a Classroom block (6b₂₀)	20	7	3	100
21.	Construction of 6 Classrooms block (6b₂₁)	21	12	13	100
22.	Construction of 6 Classrooms block (6b₂₂)	22	12	13	100
23.	Construction of 6 Classroom block (6b₂₃)	23	12	13	100
24.	Construction of 6 Classrooms block (6b₂₄)	24	12	13	100
25.	Construction of 6 Classrooms block (6b₂₅)	25	12	13	100
26.	Construction of 6 Classrooms block (6b₂₆)	26	12	13	100
27.	Reconstruction of 6 Classrooms block (6b₂₇)	27	12	13	100
28.	Reconstruction of 6 Classrooms block (6b₂₈)	28	12	13	100
29.	Reconstruction of 6 Classrooms block (6b₂₉)	29	12	13	100
30.	Reconstruction of 6 Classrooms block (6b₃₀)	30	12	13	100
31.	Reconstruction of 6 Classrooms block (6b₃₁)	31	12	13	100
32.	Reconstruction of 6 Classrooms block (6b₃₂)	32	12	13	100
33.	Reconstruction of 6 Classrooms block (6b₃₃)	33	12	13	100
34.	Reconstruction of 6 Classrooms block (6b₃₄)	34	12	13	100
35.	Reconstruction of 6 Classrooms block (6b₃₅)	35	12	13	100
36.	Reconstruction of 6 Classrooms block (6b₃₆)	36	12	13	100
37.	Reconstruction of 6 Classrooms block (6b₃₇)	37	12	13	100
38.	Reconstruction of 6 Classrooms block (6b₃₈)	38	12	13	100
39.	Reconstruction of 6 Classrooms block (6b₃₉)	39	12	13	100
40.	Reconstruction of 6 Classrooms block (6b₄₀)	40	12	13	100
41.	Reconstruction of 6 Classrooms block (6b₄₁)	41	12	13	100
42.	Reconstruction of 6 Classrooms block (6b₄₂)	42	12	13	100
43.	Renovation of 6 Classrooms block (6b₄₃)	43	12	13	100
44.	Rehabilitation of 6 Classrooms school (6b₄₄)	44	12	13	100
45.	Construction of 6 classroom block (6b₄₅)	45	12	17	100
46.	Construction of 6 classroom block (6b₄₆)	46	12	17	100
47.	Construction of 6 classroom block (6b₄₇)	47	12	13	100
48.	Construction of 6 classroom block (6b₄₈)	48	12	13	100
49.	Construction of 6 classroom block (6b₄₉)	49	12	13	100
50.	Construction of 6 classroom block (6b₅₀)	50	12	13	100
51.	Construction of 3 classroom block (3b₅₁)	51	7	7	100
52.	Construction of 3 classroom block (3b₅₂)	52	7	7	100
53.	Construction of 6 classroom block (6b₅₃)	53	12	13	100
54.	Construction of 6 classroom block (6b₅₄)	54	12	13	100
55.	Construction of 6 classroom block (6b₅₅)	55	12	13	100
56.	Construction of 6 classroom block (6b₅₆)	56	12	13	100
57.	Construction of 6 classroom block (6b₅₇)	57	12	13	100
58.	Construction of 6 classroom block (6b₅₈)	58	12	13	100
59.	Construction of 3 classroom block (3b₅₉)	59	12	13	100
60.	Construction of laboratory block (b₆₀)	60	7	7	100
61.	Construction of 6 classroom block (6b₆₁)	61	12	13	100
62.	Construction of 6 classroom block (6b₆₂)	62	12	13	100
63.	Construction of 6 classroom block (6b₆₃)	63	12	13	100
64.	Construction of 6 classroom block (6b₆₄)	64	12	13	100
65.	Construction of 6 classroom block (6b₆₅)	65	12	13	100
66.	Construction of 12 classroom block (12b₆₆)	66	17	34	100
67.	Construction of 12 classroom block (12b₆₇)	67	17	26	100
68.	Construction of 6 classroom blocks (6b₆₈)	68	12	13	100
69.	Construction of 6 classroom blocks (6b₆₉)	69	12	13	100
70.	Construction of 6 classroom blocks (6b₇₀)	70	12	7	100
71.	Construction of 6 classroom blocks (6b₇₁)	71	12	13	100
72.	Construction of 6 classroom blocks (6b₇₂)	72	12	13	100
73.	Construction of 6 classroom blocks (6b₇₃)	73	12	13	100
74.	Construction of 3 classroom blocks (3b₇₄)	74	7	7	100
75.	Construction of 6 classroom blocks (6b₇₅)	75	12	13	100
76.	Construction of 3 classroom blocks (3b₇₆)	76	7	7	100
77.	Construction of 6 classroom blocks (6b₇₇)	77	12	13	100
	Total cost			1,039

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Table A.2.

Wooden Jetty

S/N	PROJECT DESCIPTION (JETTY)	LOCATION	PROJECT COST (x10³)	DURATION (MONTHS)	% COMPLETION
1.	Wooden Jetty (B1)	1	7,913	9	100
2.	Wooden Jetty (B2)	2	4,372	9	100
3.	Wooden Jetty (B3)	3 ′	4,372	9	100
4.	Wooden Jetty (B4)	4	6,257	9	100
5.	Wooden Jetty (B5)	5	6,257	9	100
6.	Wooden Jetty (B6)	6	4,372	9	100
7.	Wooden Jetty (B7)	7	4,372	9	100
8.	Wooden Jetty (B8)	8	6,257	9	100
9.	Wooden Jetty (B9)	9	6,257	9	100
10.	Wooden Jetty (B10)	10	6,041	9	100
11.	Wooden Jetty (B11)	11	4,156	9	100
12.	Wooden Jetty (B12)	12	6,041	9	100
13.	Wooden Jetty (B13)	13	7,083	9	100
14.	Wooden Jetty (B14)	14	6,537	9	100
15.	Wooden Jetty (B15)	15	6,537	9	100
16.	Wooden Jetty (B16)	16	6,257	9	100
17.	Wooden Jetty (B17)	17	8,230	9	100
18.	Wooden Jetty (B18)	18	18,108	9	100
19.	Wooden Jetty (B19)	19	7,125	9	100
20.	Wooden Jetty (B20)	20	6,340	9	100
21.	Wooden Jetty (B21)	21	6,340	9	100
22.	Wooden Jetty (B22)	22	18,324	9	100
23.	Wooden Jetty (B23)	23	4,987	9	100
24.	Wooden Jetty (B24)	24	6,340	9	100
25.	Wooden Jetty (B25)	25	7,688	9	100
26.	Wooden Jetty (B26)	26	7,477	9	100
27.	Wooden Jetty (B27)	27	6,936	9	100
28.	Wooden Jetty (B28)	28	7,135	9	100
29.	Wooden Jetty (B29)	29	6,257	9	100
30.	Wooden Jetty (B30)	30	6,257	9	100
31.	Wooden Jetty (B31)	31	6,041	9	100
32.	Wooden Jetty (B32)	32	6,257	9	100
33.	Wooden Jetty (B33)	33	12,683	9	100
34.	Wooden Jetty (B34)	34	13,098	9	100
35.	Wooden Jetty (B35)	35	9,391	9	100
36.	Wooden Jetty (B36)	36	7,911	9	100
37.	Wooden Jetty (B37)	37	7,082	9	100
38.	Wooden Jetty (B38)	38	9,272	9	100
39.	Wooden Jetty (B39)	39	8,526	9	100
40.	Wooden Jetty (B40)	40	8,526	9	100
41.	Wooden Jetty (B41)	41	9,193	9	100
42.	Wooden Jetty (B42)	42	8,893	9	100
43.	Wooden Jetty (B43)	43	24,144	9	100
44.	Wooden Jetty (B44)	44	14,741	9	100
45.	Wooden Jetty (B45)	45	14,570	9	100
46.	Wooden Jetty (B46)	46	18,324	9	100
47.	Wooden Jetty (B47)	47	7,298	9	100
48.	Wooden Jetty (B49)	48	15,513	9	100
49.	Wooden Jetty (B49)	49	9,279	9	100
50.	Wooden Jetty (B50)	50	10,084	9	100
51.	Wooden Jetty (B51)	51	14,703	9	100
52.	Wooden Jetty (B52)	52	12,288	9	100
53.	Wooden Jetty (B53)	53	5,184	9	100
54.	Wooden Jetty (B54)	54	6,257	9	100
55.	Wooden Jetty (B55)	55	7,683	9	100
56.	Wooden Jetty (B56)	56	12,893	9	100
57.	Wooden Jetty (B57)	57	4,446	9	100
58.	Wooden Jetty (B58)	58	27,233	9	100
59.	Wooden Jetty (B59)	59	4,245	9	100
60.	Wooden Jetty (B60)	60	3,735	9	100
61.	Wooden Jetty (B61)	61	4,123	9	100
62.	Wooden Jetty (B62)	62	6,128	9	100
63.	Wooden Jetty (B63)	63	4,672	9	100
64.	Wooden Jetty (B64)	64	6,281	9	100
65.	Wooden Jetty (B65)	65	7,789	9	100
66.	Wooden Jetty (B66)	66	5,092	9	100
67.	Wooden Jetty (B67)	67	8,320	9	100
68.	Wooden Jetty (B68)	68	6,281	9	100
69.	Wooden Jetty (B69)	69	6,281	9	100
70.	Wooden Jetty (B70)	70	17,186	9	100
71.	Wooden Jetty (B71)	71	7,484	9	100
72.	Wooden Jetty (B72)	72	15,908	9	100
73.	Wooden Jetty (B73)	73	13,308	9	100
74.	Wooden Jetty (B74)	74	24,636	9	100
75.	Wooden Jetty (B75)	75	15,283	9	100
76.	Wooden Jetty (B76)	76	7,323	9	100
77.	Wooden Jetty (B77)	77	5,108	9	100
78.	Wooden Jetty (B78)	78	17,300	9	100
79.	Wooden Jetty (B79)	79	4,644	9	100
80.	Wooden Jetty (B80)	80	4,649	9	100
81.	Wooden Jetty (B81)	81	5,920	9	100
82.	Wooden Jetty (B82)	82	7,247	9	100
83.	Wooden Jetty (B83)	83	15,302	9	100
84.	Wooden Jetty (B84)	84	8,925	9	100
85.	Wooden Jetty (B85)	85	7,660	9	100
86.	Wooden Jetty (B86)	86	6,939	9	100
87.	Wooden Jetty (B87)	87	4,741	9	100
TOTAL			774,648

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Table A.3.

Housing Projects

S/N	PROJECT DESCIPTION (HOUSING)	LOCATION	PROJECT COST (x10³)	DURATION (MONTHS)	% COMPLETION
1.	Construction of 3-Bedroom Housing unit (3b₁)	1	8,606	12	100
2.	Construction of 3-Bedroom Housing unit (3b₂)	2	8,606	12	100
3.	Construction of 3-BedroomHousing unit (3b₃)	3	8,606	12	100
4.	Construction of 3-Bedroom Housing unit (3b₄)	4	8,606	12	100
5.	Construction of 3-Bedroom Housing unit (3b₅)	5	8,606	12	100
6.	Construction of 3-Bedroom Housing unit (3b₆)	6	8,606	12	100
7.	Construction of 3-Bedroom Housing unit (3b₇)	7	8,606	12	100
8.	Construction of 3-Bedroom Housing unit (3b₈)	8	8,606	12	100
9.	Construction of 3-Bedroom Housing unit (3b₉)	9	8,376	12	100
10.	Construction of 3-Bedroom Housing unit (3b₁₀)	10	8,376	12	100
11.	Construction of 3-Bedroom Housing unit (3b₁₁)	11	8,376	12	100
12.	Construction of 3-Bedroom Housing unit (3b₁₂)	12	8,376	12	100
13.	Construction of 3-Bedroom Housing unit (3b₁₃)	13	8,376	12	100
14.	Construction of 3-Bedroom Housing unit (3b₁₄)	14	8,376	12	100
15.	Construction of 3-Bedroom Housing unit (3b₁₅)	15	8,376	12	100
16.	Construction of 3-Bedroom Housing unit (3b₁₆)	16	8,376	12	100
17.	Construction of 3-Bedroom Housing unit (3b₁₆)	17	8,376	12	100
18.	Construction of 3-Bedroom Housing unit (3b₁₇)	18	8,376	12	100
19.	Construction of 3-Bedroom Housing unit (3b₁₈)	19	8,376	12	100
20.	Construction of 3-Bedroom Housing unit (3b₂₀)	20	8,376	12	100
21.	Construction of 3-Bedroom Housing unit (3b₂₁)	21	8,376	12	100
22.	Construction of 3-Bedroom Housing unit (3b₂₂)	22	8,376	12	100
23.	Construction of 3-Bedroom Housing unit (3b₂₃)	23	8,146	12	100
24.	Construction of 3-Bedroom Housing unit (3b₂₄)	24	8,146	12	100
25.	Construction of 3-Bedroom Housing unit (3b₂₅)	25	8,146	12	100
26.	Construction of 3-Bedroom Housing unit (3b₂₆)	26	8,146	12	100
27.	Construction of 3-Bedroom Housing unit (3b₂₇)	27	12,882	12	100
28.	Construction of 3-Bedroom Housing unit (3b₂₈)	28	12,882	12	100
29.	Construction of 3-Bedroom Housing unit (3b₂₉)	29	12,882	12	100
30.	Construction of 3-Bedroom Housing unit (3b₃₀)	30	12,882	12	100
31.	Construction of 3-Bedroom Housing unit (3b₃₁)	31	8,376	12	100
32.	Construction of 3-Bedroom Housing unit (3b₃₁)	32	8,376	12	100
33.	Construction of 3-Bedroom Housing unit (3b₃₃)	33	8,376	12	100
34.	Construction of 3-Bedroom Housing unit (3b₃₄)	34	8,376	12	100
35.	Construction of 3-Bedroom Housing unit (3b₃₅)	35	12,882	12	100
36.	Construction of 3-Bedroom Housing unit (3b₃₆)	36	12,882	12	100
37.	Construction of 3-Bedroom Housing unit (3b₃₇)	37	12,882	12	100
38.	Construction of 3-Bedroom Housing unit (3b₃₈)	38	12,882	12	100
39.	Construction of 3-Bedroom Housing unit (3b₃₉)	39	12,882	12	100
40.	Construction of 3-Bedroom Housing unit (3b₄₀)	40	12,882	12	100
41.	Construction of 3-Bedroom Housing unit (3b₄₁)	41	12,882	12	100
42.	Construction of 3-Bedroom Housing unit (3b₄₂)	42	12,882	12	100
43.	Construction of 3-Bedroom Housing unit (3b₄₃)	43	12,882	12	100
44.	Construction of 3-Bedroom Housing unit (3b₄₄)	44	12,882	12	100
45.	Construction of 3-Bedroom Housing unit (3b₄₅)	45	12,882	12	100
46.	Construction of 3-Bedroom Housing unit (3b₄₆)	46	12,882	12	100
47.	Construction of 3-Bedroom Housing unit (3b₄₇)	47	12,882	12	100
48.	Construction of 3-Bedroom Housing unit (3b₄₈)	48	12,882	12	100
49.	Construction of 3-Bedroom Housing unit (3b₄₉)	49	12,882	12	100
50.	Construction of 3-Bedroom Housing unit (3b₅₀)	50	12,882	12	100
51.	Construction of 3-Bedroom Housing unit (3b₅₁)	51	12,882	12	100
52.	Construction of 3-Bedroom Housing unit (3b₅₂)	52	12,882	12	100
53.	Construction of 3-Bedroom Housing unit (3b₅₃)	53	12,882	12	100
54.	Construction of 3-Bedroom Housing unit (3b₅₄)	54	12,882	12	100
55.	Construction of 3-Bedroom Housing unit (3b₅₅)	55	12,882	12	100
56.	Construction of 3-Bedroom Housing unit (3b₅₆)	56	12,882	12	100
57.	Construction of 3-Bedroom Housing unit (3b₅₇)	57	12,882	12	100
58.	Construction of 3-Bedroom Housing unit (3b₅₈)	58	12,882	12	100
59.	Construction of 3-Bedroom Housing unit (3b₅₉)	59	12,882	12	100
60.	Construction of 3-Bedroom Housing unit (3b₆₀)	60	12,882	12	100
61.	Construction of 3-Bedroom Housing unit (3b₆₁)	61	12,882	12	100
62.	Construction of 3-Bedroom Housing unit (3b₆₂)	62	12,882	12	100
63.	Construction of 3-Bedroom Housing unit (3b₆₃)	63	12,882	12	100
64.	Construction of 3-Bedroom Housing unit (3b₆₄)	64	12,882	12	100
65.	Construction of 3-Bedroom Housing unit (3b₆₅)	65	12,882	12	100
66.	Construction of 3-Bedroom Housing unit (3b₆₆)	66	12,882	12	100
67.	Construction of 3-Bedroom Housing unit (3b₆₇)	67	12,882	12	100
68.	Construction of 3-Bedroom Housing unit (3b₆₈)	68	12,882	12	100
69.	Construction of 3-Bedroom Housing unit (3b₆₉)	69	12,882	12	100
70.	Construction of 3-Bedroom Housing unit (3b₇₀)	70	12,882	12	100
71.	Construction of 3-Bedroom Housing unit (3b₇₁)	71	12,882	12	100
72.	Construction of 3-Bedroom Housing unit (3b₇₂)	72	12,882	12	100
73.	Construction of 3-Bedroom Housing unit (3b₇₃)	73	12,882	12	100
74.	Construction of 3-Bedroom Housing unit (3b₇₄)	74	12,882	12	100
75.	Construction of 3-Bedroom Housing unit (3b₇₅)	75	12,882	12	100
76.	Construction of 3-Bedroom Housing unit (3b₇₆)	76	12,882	12	100
77.	Construction of 3-Bedroom Housing unit (3b₇₇)	77	12,882	12	100
78.	Construction of 3-Bedroom Housing unit (3b₇₈)	78	12,882	12	100
79.	Construction of 3-Bedroom Housing unit (3b₇₉)	79	12,882	12	100
80.	Construction of 3-Bedroom Housing unit (3b₈₀)	80	12,882	12	100
81.	Construction of 3-Bedroom Housing unit (3b₈₁)	81	12,882	12	100
82.	Construction of 3-Bedroom Housing unit (3b₈₂)	82	12,882	12	100
83.	Construction of 3-Bedroom Housing unit (3b₈₃)	83	12,882	12	100
84.	Construction of 3-Bedroom Housing unit (3b₈₄)	84	8,606	12	100
85.	Construction of 3-Bedroom Housing unit (3b₈₅)	85	12,882	12	100
86.	Construction of 3-Bedroom Housing unit (3b₈₆)	86	12,882	12	100
87.	Construction of 3-Bedroom Housing unit (3b₈₇)	87	12,882	12	100
88.	Construction of 3-Bedroom Housing unit (3b₈₈)	88	8,376	12	100
89.	Construction of 3-Bedroom Housing unit (3b₈₉)	89	8,376	12	100
90.	Construction of 3-Bedroom Housing unit (3b₉₀)	90	8,376	12	100
91.	Construction of 3-Bedroom Housing unit (3b₉₁)	91	8,376	12	100
92.	Construction of 3-Bedroom Housing unit (3b₉₂)	92	8,376	12	100
93.	Construction of 3-Bedroom Housing unit (3b₉₃)	93	8,376	12	100
94.	Construction of 3-Bedroom Housing unit (3b₉₄)	94	8,376	12	100
95.	Construction of 3-Bedroom Housing unit (3b₉₅)	95	8,376	12	100
96.	Construction of 3-Bedroom Housing unit (3b₉₆)	96	8,376	12	100
97.	Construction of 3-Bedroom Housing unit (3b₉₇)	97	8,376	12	100
98.	Construction of 3-Bedroom Housing unit (3b₉₈)	98	8,376	12	100
99.	Construction of 3-Bedroom Housing unit (3b₉₉)	99	8,376	12	100
100.	Construction of 3-Bedroom Housing unit (3b₁₀₀)	100	8,376	12	100
TOTAL			1,091,086,000.00

Open in a new tab

References

1.Brown E.D. 2008. Project Selection Using Decision Support Optimization Tools: Aligning Technology, Strategy, People and Projects; pp. 1–14.http://ericbrown.com Chicago. [Online]. Available: [Google Scholar]
2.Tavana M., Khosrojerdi G., Mina H., Rahman A. A hybrid mathematical programming model for optimal project portfolio selection using fuzzy inference system and analytic hierarchy process. Eval. Progr. Plann. 2019;77 doi: 10.1016/j.evalprogplan.2019.101703. July. [DOI] [PubMed] [Google Scholar]
3.Asadujjaman M., Rahman H.F., Chakrabortty R.K., Ryan M.J. An immune genetic algorithm for solving NPV-based resource constrained project scheduling problem. IEEE Access. 2021;9:26177–26195. doi: 10.1109/ACCESS.2021.3057366. [DOI] [Google Scholar]
4.Bai L., Sun Y., Shi H., Shi C., Bai J., Han X. Dynamic assessment modelling for project portfolio benefits. J. Oper. Res. Soc. 2021;0(0):1–24. doi: 10.1080/01605682.2021.1915193. [DOI] [Google Scholar]
5.Saiz M., Lostumbo M.A., Juan A.A., Lopez-Lopez D. A clustering-based review on project portfolio optimization methods. Int. Trans. Oper. Res. 2022;29(1):172–199. doi: 10.1111/itor.12933. [DOI] [Google Scholar]
6.Pinto J.K. second ed. Pearson Education, Inc. Prentice Hall; New York: 2010. Project Management: Achieving Competitive Advantage. [Google Scholar]
7.Zdravkovic J., Bogdanovic D. Developing an mcda model for choosing criteria used in project ranking. Econ. Comput. Econ. Cybern. Stud. Res. 2022;56(3):219–233. doi: 10.24818/18423264/56.3.22.14. [DOI] [Google Scholar]
8.Hamurcu M., Alagas H.M., Eren T. Selection of rail system projects with analytic hierarchy process and goal programming. Sigma J. Eng. Nat. Sci. Muhendis. Ve Fen Bilim. Derg. 2017;8(4):291–302. SI. [Google Scholar]
9.Zhang X., Fang L., Hipel K.W., Ding S., Tan Y. A hybrid project portfolio selection procedure with historical performance consideration. Expert Syst. Appl. 2020;142 doi: 10.1016/j.eswa.2019.113003. [DOI] [Google Scholar]
10.Iranmanesh S.H., Shakhsi-Niaei M., Rastegar H. A multi-objective optimization model for project portfolio selection considering aggregate complexity : a case study. Int. J. Optim. Civ. Eng. 2019;9(2):291–311. [Google Scholar]
11.Khalili-Damghani K., Sadi-Nezhad S., Lotfi F.H., Tavana M. A hybrid fuzzy rule-based multi-criteria framework for sustainable project portfolio selection. Inf. Sci. 2013;220:442–462. doi: 10.1016/j.ins.2012.07.024. [DOI] [Google Scholar]
12.Chávez R. IT project portfolio selection using analytic hierarchy process. Ind. Data. 2008;11(2):59–62. [Google Scholar]
13.Keskin F.D. A two-stage fuzzy approach for Industry 4.0 project portfolio selection within criteria and project interdependencies context. J. Multi-Criteria Decis. Anal. 2020;27(1–2):65–83. doi: 10.1002/mcda.1691. [DOI] [Google Scholar]
14.Radulescu C., Radulescu M. Project portfolio selection models and decision support. Stud. Inf. Control. 2001;10(4):275–286. [Google Scholar]
15.Etgar R., Cohen Y. Roadmap optimization: multi-annual project portfolio selection method. Mathematics. 2022;10(1601):1–23. doi: 10.3390/math10091601. [DOI] [Google Scholar]
16.Rouyendegh B.D. Evaluating projects based on intuitionistic fuzzy group decision making. J. Appl. Math. 2012;2012(824265):1–17. doi: 10.1155/2012/824265. [DOI] [Google Scholar]
17.Sadi-Nezhad S. A state-of-art survey on project selection using MCDM techniques. J. Proj. Manag. 2017;2:1–10. doi: 10.5267/j.jpm.2017.6.001. [DOI] [Google Scholar]
18.Pariz M.C., Carvalho C.M.F., Rebelo P.C.A., Colmenero J.C. Treatment of the uncertainties in prioritization of information technology projects: a hybrid multicriteria approach. J. Multi-Criteria Decis. Anal. 2022;29(5–6):327–340. doi: 10.1002/mcda.1777. [DOI] [Google Scholar]
19.Kandakoglu M., Alther G.W., Ben Amor S. 2020. The Use Of Multi-Criteria Decision-Making Methods In Project Portfolio Selection: A Literature Review And Future Research Directions; pp. 1–14. no. 1. [Online]. Available: url: http://www.optimization-online.org/DB_HTML/2020/06/7836.html. [Google Scholar]
20.Kim G.C., Emery J. An application of zero-one goal programming in project selection and resource planning - a case study from the Woodward Governor Company. Comput. Oper. Res. 2000;27(14):1389–1408. doi: 10.1016/S0305-0548(99)00080-5. [DOI] [Google Scholar]
21.Badri M.A., Davis D., Davis D. A comprehensive 0–1 goal programming model for project selection. Int. J. Proj. Manag. 2001;19(4):243–252. doi: 10.1016/s0263-7863(99)00078-2. [DOI] [Google Scholar]
22.Eldrandaly K. GIS software selection: a multi-criteria decision making approach. Appl. GIS. 2007;3(5):1–17. [Google Scholar]
23.Liao C. A zero-one goal programming model for marketing project selection. J. China Inst. Tech. 2009;40:77–88. [Google Scholar]
24.Liang T.F. Applying fuzzy goal programming to project management decisions with multiple goals in uncertain environments. Expert Syst. Appl. 2010;37(12):8499–8507. doi: 10.1016/j.eswa.2010.05.026. [DOI] [Google Scholar]
25.Mohamad F.B. Othman Yeop Abdullah Graduate School of Business; Sintok: 2015. Project Selection for Group Decision Making Using Analytical Hierarchy Process : a Private College Perspective. [Google Scholar]
26.Sharma A., Batra R.K. Application of the analytical hierarchy process (AHP) in the selection of contractors/consultants. Int. J. Curr. Eng. Sci. Res. 2016;3(1):128–134. [Google Scholar]
27.Chatterjee K., Hossain S.A., Kar S. Prioritization of project proposals in portfolio management using fuzzy AHP. Opsearch. 2018;55(2):478–501. doi: 10.1007/s12597-018-0331-3. [DOI] [Google Scholar]
28.Li P. Project selection of government guarantee in BOT/PPP project finance. Am. J. Ind. Bus. Manag. 2020;10(6):1107–1120. doi: 10.4236/ajibm.2020.106073. [DOI] [Google Scholar]
29.Razi P.Z., Ramli N.I., Ali M.I., Ramadhansyah P.J. Selection of contractor by using analytical hierarchy process (AHP) IOP Conf. Ser. Mater. Sci. Eng. 2020;712(1) doi: 10.1088/1757-899X/712/1/012014. [DOI] [Google Scholar]
30.Alyamani R., Long S. The application of fuzzy analytic hierarchy process in sustainable project selection. Sustain. Times. 2020;12(20):1–16. doi: 10.3390/su12208314. [DOI] [Google Scholar]
31.Bellahcene M., Benamar F.Z., Mekidiche M. Ahp and wafgp hybrid model for information system project selection. Int. J. Anal. Hierarchy Process. 2020;12(2):228–253. doi: 10.13033/ijahp.v12i2.761. [DOI] [Google Scholar]
32.Wu Y.J., Chen J. A structured method for smart city project selection. Int. J. Inf. Manag. 2021;56(31) doi: 10.1016/j.ijinfomgt.2019.07.007. [DOI] [Google Scholar]
33.Akbari N., Jones D., Arabikhan F. Goal programming models with interval coefficients for the sustainable selection of marine renewable energy projects in the UK. Eur. J. Oper. Res. 2021;293(2):748–760. doi: 10.1016/j.ejor.2020.12.038. [DOI] [Google Scholar]
34.Wiguna P.A.P., Sudiartha M.M. Determination of optimal warehouse location at PT . Sumber alfaria TrijayaTbk (bali branch) Am. J. Humanit. Soc. Sci. Res. 2021;5(1):664–671. [Google Scholar]
35.Baffoe G. Exploring the utility of Analytic Hierarchy Process (AHP) in ranking livelihood activities for effective and sustainable rural development interventions in developing countries. Eval. Progr. Plann. 2019;72:197–204. doi: 10.1016/j.evalprogplan.2018.10.017. [DOI] [PubMed] [Google Scholar]
36.De Marinis P., Sali G. Participatory analytic hierarchy process for resource allocation in agricultural development projects. Eval. Progr. Plann. 2020;80 doi: 10.1016/j.evalprogplan.2020.101793. [DOI] [PubMed] [Google Scholar]
37.Chaparro X.A.F., V Gomes L.A., Nascimento P.T.S. The evolution of project portfolio selection methods: from incremental to radical innovation. Rev. Gestão. 2019;26(3):212–236. doi: 10.1108/rege-10-2018-0096. [DOI] [Google Scholar]
38.Hamurcu M., Eren T. Transportation planning with analytic hierarchy process and goal programming. Int. Adv. Res. Eng. J. 2018;2(2):92–97. [Google Scholar]
39.Solangi Y.A., Longsheng C., Shah S.A.A. Assessing and overcoming the renewable energy barriers for sustainable development in Pakistan: an integrated AHP and fuzzy TOPSIS approach. Renew. Energy. 2021;173:209–222. doi: 10.1016/j.renene.2021.03.141. [DOI] [Google Scholar]
40.Azmi R., Tamiz M. vol. 638. 2010. A review of goal programming; pp. 15–33. (Lecture Notes in Economics and Mathematical Systems). September. [Google Scholar]
41.Chandra P. sixth ed. Tata McGraw-Hill Publishing Company Limited; New Delhi: 2008. Projects Planning, Analysis, Selection, Financing, Implementation and Review. [Google Scholar]
42.Kumar P.P. Goal programming through bakery production. Int. J. Sci. Technol. Res. 2019;8(10):3722–3725. [Google Scholar]
43.Wu Y., Xu C., Ke Y., Chen K., Sun X. An intuitionistic fuzzy multi-criteria framework for large-scale rooftop PV project portfolio selection: case study in Zhejiang, China. Energy. 2018;143(2018):295–309. doi: 10.1016/j.energy.2017.10.105. [DOI] [Google Scholar]
44.Huang C.C., Chu P.Y., Chiang Y.H. A fuzzy AHP application in government-sponsored R&D project selection. Omega. 2008;36(6):1038–1052. doi: 10.1016/j.omega.2006.05.003. [DOI] [Google Scholar]
45.Dutra C.C., Ribeiro J.L.D., De Carvalho M.M. An economic-probabilistic model for project selection and prioritization. Int. J. Proj. Manag. 2014;32(6):1042–1055. doi: 10.1016/j.ijproman.2013.12.004. [DOI] [Google Scholar]
46.Kaiser R., Futami A.H., Valentina L.V.O.D., De Oliveira M.A. Development of a managerial tool for prioritization and selection of portfolio projects using the analytic hierarchy process methodology in software companies. Gestão Produção. 2019;26(4) doi: 10.1590/0104-530X4267-19. [DOI] [Google Scholar]
47.Wu Y., Xu C., Ke Y., Li X., Li L. Portfolio selection of distributed energy generation projects considering uncertainty and project interaction under different enterprise strategic scenarios. Appl. Energy. 2019;236(October 2018):444–464. doi: 10.1016/j.apenergy.2018.12.009. [DOI] [Google Scholar]
48.De Souza L.P., Gomes C.F.S., De Barros A.P. Implementation of new hybrid AHP-TOPSIS-2N method in sorting and prioritizing of an it CAPEX project portfolio. Int. J. Inf. Technol. Decis. Making. 2018;17(4):977–1005. doi: 10.1142/S0219622018500207. [DOI] [Google Scholar]
49.Mogbojuri A.O., Olanrewaju O.A. Goal programming and genetic algorithm in multiple objective optimization model for project portfolio selection: a review. Niger. J. Tech. 2022;41(5):862–869. doi: 10.4314/njt.v41i5.6. [DOI] [Google Scholar]

Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Data Availability Statement

The authors do not have permission to share data.

[bib1] 1.Brown E.D. 2008. Project Selection Using Decision Support Optimization Tools: Aligning Technology, Strategy, People and Projects; pp. 1–14.http://ericbrown.com Chicago. [Online]. Available: [Google Scholar]

[bib2] 2.Tavana M., Khosrojerdi G., Mina H., Rahman A. A hybrid mathematical programming model for optimal project portfolio selection using fuzzy inference system and analytic hierarchy process. Eval. Progr. Plann. 2019;77 doi: 10.1016/j.evalprogplan.2019.101703. July. [DOI] [PubMed] [Google Scholar]

[bib3] 3.Asadujjaman M., Rahman H.F., Chakrabortty R.K., Ryan M.J. An immune genetic algorithm for solving NPV-based resource constrained project scheduling problem. IEEE Access. 2021;9:26177–26195. doi: 10.1109/ACCESS.2021.3057366. [DOI] [Google Scholar]

[bib4] 4.Bai L., Sun Y., Shi H., Shi C., Bai J., Han X. Dynamic assessment modelling for project portfolio benefits. J. Oper. Res. Soc. 2021;0(0):1–24. doi: 10.1080/01605682.2021.1915193. [DOI] [Google Scholar]

[bib5] 5.Saiz M., Lostumbo M.A., Juan A.A., Lopez-Lopez D. A clustering-based review on project portfolio optimization methods. Int. Trans. Oper. Res. 2022;29(1):172–199. doi: 10.1111/itor.12933. [DOI] [Google Scholar]

[bib6] 6.Pinto J.K. second ed. Pearson Education, Inc. Prentice Hall; New York: 2010. Project Management: Achieving Competitive Advantage. [Google Scholar]

[bib7] 7.Zdravkovic J., Bogdanovic D. Developing an mcda model for choosing criteria used in project ranking. Econ. Comput. Econ. Cybern. Stud. Res. 2022;56(3):219–233. doi: 10.24818/18423264/56.3.22.14. [DOI] [Google Scholar]

[bib8] 8.Hamurcu M., Alagas H.M., Eren T. Selection of rail system projects with analytic hierarchy process and goal programming. Sigma J. Eng. Nat. Sci. Muhendis. Ve Fen Bilim. Derg. 2017;8(4):291–302. SI. [Google Scholar]

[bib9] 9.Zhang X., Fang L., Hipel K.W., Ding S., Tan Y. A hybrid project portfolio selection procedure with historical performance consideration. Expert Syst. Appl. 2020;142 doi: 10.1016/j.eswa.2019.113003. [DOI] [Google Scholar]

[bib10] 10.Iranmanesh S.H., Shakhsi-Niaei M., Rastegar H. A multi-objective optimization model for project portfolio selection considering aggregate complexity : a case study. Int. J. Optim. Civ. Eng. 2019;9(2):291–311. [Google Scholar]

[bib11] 11.Khalili-Damghani K., Sadi-Nezhad S., Lotfi F.H., Tavana M. A hybrid fuzzy rule-based multi-criteria framework for sustainable project portfolio selection. Inf. Sci. 2013;220:442–462. doi: 10.1016/j.ins.2012.07.024. [DOI] [Google Scholar]

[bib12] 12.Chávez R. IT project portfolio selection using analytic hierarchy process. Ind. Data. 2008;11(2):59–62. [Google Scholar]

[bib13] 13.Keskin F.D. A two-stage fuzzy approach for Industry 4.0 project portfolio selection within criteria and project interdependencies context. J. Multi-Criteria Decis. Anal. 2020;27(1–2):65–83. doi: 10.1002/mcda.1691. [DOI] [Google Scholar]

[bib14] 14.Radulescu C., Radulescu M. Project portfolio selection models and decision support. Stud. Inf. Control. 2001;10(4):275–286. [Google Scholar]

[bib15] 15.Etgar R., Cohen Y. Roadmap optimization: multi-annual project portfolio selection method. Mathematics. 2022;10(1601):1–23. doi: 10.3390/math10091601. [DOI] [Google Scholar]

[bib16] 16.Rouyendegh B.D. Evaluating projects based on intuitionistic fuzzy group decision making. J. Appl. Math. 2012;2012(824265):1–17. doi: 10.1155/2012/824265. [DOI] [Google Scholar]

[bib17] 17.Sadi-Nezhad S. A state-of-art survey on project selection using MCDM techniques. J. Proj. Manag. 2017;2:1–10. doi: 10.5267/j.jpm.2017.6.001. [DOI] [Google Scholar]

[bib18] 18.Pariz M.C., Carvalho C.M.F., Rebelo P.C.A., Colmenero J.C. Treatment of the uncertainties in prioritization of information technology projects: a hybrid multicriteria approach. J. Multi-Criteria Decis. Anal. 2022;29(5–6):327–340. doi: 10.1002/mcda.1777. [DOI] [Google Scholar]

[bib19] 19.Kandakoglu M., Alther G.W., Ben Amor S. 2020. The Use Of Multi-Criteria Decision-Making Methods In Project Portfolio Selection: A Literature Review And Future Research Directions; pp. 1–14. no. 1. [Online]. Available: url: http://www.optimization-online.org/DB_HTML/2020/06/7836.html. [Google Scholar]

[bib20] 20.Kim G.C., Emery J. An application of zero-one goal programming in project selection and resource planning - a case study from the Woodward Governor Company. Comput. Oper. Res. 2000;27(14):1389–1408. doi: 10.1016/S0305-0548(99)00080-5. [DOI] [Google Scholar]

[bib21] 21.Badri M.A., Davis D., Davis D. A comprehensive 0–1 goal programming model for project selection. Int. J. Proj. Manag. 2001;19(4):243–252. doi: 10.1016/s0263-7863(99)00078-2. [DOI] [Google Scholar]

[bib22] 22.Eldrandaly K. GIS software selection: a multi-criteria decision making approach. Appl. GIS. 2007;3(5):1–17. [Google Scholar]

[bib23] 23.Liao C. A zero-one goal programming model for marketing project selection. J. China Inst. Tech. 2009;40:77–88. [Google Scholar]

[bib24] 24.Liang T.F. Applying fuzzy goal programming to project management decisions with multiple goals in uncertain environments. Expert Syst. Appl. 2010;37(12):8499–8507. doi: 10.1016/j.eswa.2010.05.026. [DOI] [Google Scholar]

[bib25] 25.Mohamad F.B. Othman Yeop Abdullah Graduate School of Business; Sintok: 2015. Project Selection for Group Decision Making Using Analytical Hierarchy Process : a Private College Perspective. [Google Scholar]

[bib26] 26.Sharma A., Batra R.K. Application of the analytical hierarchy process (AHP) in the selection of contractors/consultants. Int. J. Curr. Eng. Sci. Res. 2016;3(1):128–134. [Google Scholar]

[bib27] 27.Chatterjee K., Hossain S.A., Kar S. Prioritization of project proposals in portfolio management using fuzzy AHP. Opsearch. 2018;55(2):478–501. doi: 10.1007/s12597-018-0331-3. [DOI] [Google Scholar]

[bib28] 28.Li P. Project selection of government guarantee in BOT/PPP project finance. Am. J. Ind. Bus. Manag. 2020;10(6):1107–1120. doi: 10.4236/ajibm.2020.106073. [DOI] [Google Scholar]

[bib29] 29.Razi P.Z., Ramli N.I., Ali M.I., Ramadhansyah P.J. Selection of contractor by using analytical hierarchy process (AHP) IOP Conf. Ser. Mater. Sci. Eng. 2020;712(1) doi: 10.1088/1757-899X/712/1/012014. [DOI] [Google Scholar]

[bib30] 30.Alyamani R., Long S. The application of fuzzy analytic hierarchy process in sustainable project selection. Sustain. Times. 2020;12(20):1–16. doi: 10.3390/su12208314. [DOI] [Google Scholar]

[bib31] 31.Bellahcene M., Benamar F.Z., Mekidiche M. Ahp and wafgp hybrid model for information system project selection. Int. J. Anal. Hierarchy Process. 2020;12(2):228–253. doi: 10.13033/ijahp.v12i2.761. [DOI] [Google Scholar]

[bib32] 32.Wu Y.J., Chen J. A structured method for smart city project selection. Int. J. Inf. Manag. 2021;56(31) doi: 10.1016/j.ijinfomgt.2019.07.007. [DOI] [Google Scholar]

[bib33] 33.Akbari N., Jones D., Arabikhan F. Goal programming models with interval coefficients for the sustainable selection of marine renewable energy projects in the UK. Eur. J. Oper. Res. 2021;293(2):748–760. doi: 10.1016/j.ejor.2020.12.038. [DOI] [Google Scholar]

[bib34] 34.Wiguna P.A.P., Sudiartha M.M. Determination of optimal warehouse location at PT . Sumber alfaria TrijayaTbk (bali branch) Am. J. Humanit. Soc. Sci. Res. 2021;5(1):664–671. [Google Scholar]

[bib35] 35.Baffoe G. Exploring the utility of Analytic Hierarchy Process (AHP) in ranking livelihood activities for effective and sustainable rural development interventions in developing countries. Eval. Progr. Plann. 2019;72:197–204. doi: 10.1016/j.evalprogplan.2018.10.017. [DOI] [PubMed] [Google Scholar]

[bib36] 36.De Marinis P., Sali G. Participatory analytic hierarchy process for resource allocation in agricultural development projects. Eval. Progr. Plann. 2020;80 doi: 10.1016/j.evalprogplan.2020.101793. [DOI] [PubMed] [Google Scholar]

[bib37] 37.Chaparro X.A.F., V Gomes L.A., Nascimento P.T.S. The evolution of project portfolio selection methods: from incremental to radical innovation. Rev. Gestão. 2019;26(3):212–236. doi: 10.1108/rege-10-2018-0096. [DOI] [Google Scholar]

[bib38] 38.Hamurcu M., Eren T. Transportation planning with analytic hierarchy process and goal programming. Int. Adv. Res. Eng. J. 2018;2(2):92–97. [Google Scholar]

[bib39] 39.Solangi Y.A., Longsheng C., Shah S.A.A. Assessing and overcoming the renewable energy barriers for sustainable development in Pakistan: an integrated AHP and fuzzy TOPSIS approach. Renew. Energy. 2021;173:209–222. doi: 10.1016/j.renene.2021.03.141. [DOI] [Google Scholar]

[bib40] 40.Azmi R., Tamiz M. vol. 638. 2010. A review of goal programming; pp. 15–33. (Lecture Notes in Economics and Mathematical Systems). September. [Google Scholar]

[bib41] 41.Chandra P. sixth ed. Tata McGraw-Hill Publishing Company Limited; New Delhi: 2008. Projects Planning, Analysis, Selection, Financing, Implementation and Review. [Google Scholar]

[bib42] 42.Kumar P.P. Goal programming through bakery production. Int. J. Sci. Technol. Res. 2019;8(10):3722–3725. [Google Scholar]

[bib43] 43.Wu Y., Xu C., Ke Y., Chen K., Sun X. An intuitionistic fuzzy multi-criteria framework for large-scale rooftop PV project portfolio selection: case study in Zhejiang, China. Energy. 2018;143(2018):295–309. doi: 10.1016/j.energy.2017.10.105. [DOI] [Google Scholar]

[bib44] 44.Huang C.C., Chu P.Y., Chiang Y.H. A fuzzy AHP application in government-sponsored R&D project selection. Omega. 2008;36(6):1038–1052. doi: 10.1016/j.omega.2006.05.003. [DOI] [Google Scholar]

[bib45] 45.Dutra C.C., Ribeiro J.L.D., De Carvalho M.M. An economic-probabilistic model for project selection and prioritization. Int. J. Proj. Manag. 2014;32(6):1042–1055. doi: 10.1016/j.ijproman.2013.12.004. [DOI] [Google Scholar]

[bib46] 46.Kaiser R., Futami A.H., Valentina L.V.O.D., De Oliveira M.A. Development of a managerial tool for prioritization and selection of portfolio projects using the analytic hierarchy process methodology in software companies. Gestão Produção. 2019;26(4) doi: 10.1590/0104-530X4267-19. [DOI] [Google Scholar]

[bib47] 47.Wu Y., Xu C., Ke Y., Li X., Li L. Portfolio selection of distributed energy generation projects considering uncertainty and project interaction under different enterprise strategic scenarios. Appl. Energy. 2019;236(October 2018):444–464. doi: 10.1016/j.apenergy.2018.12.009. [DOI] [Google Scholar]

[bib48] 48.De Souza L.P., Gomes C.F.S., De Barros A.P. Implementation of new hybrid AHP-TOPSIS-2N method in sorting and prioritizing of an it CAPEX project portfolio. Int. J. Inf. Technol. Decis. Making. 2018;17(4):977–1005. doi: 10.1142/S0219622018500207. [DOI] [Google Scholar]

[bib49] 49.Mogbojuri A.O., Olanrewaju O.A. Goal programming and genetic algorithm in multiple objective optimization model for project portfolio selection: a review. Niger. J. Tech. 2022;41(5):862–869. doi: 10.4314/njt.v41i5.6. [DOI] [Google Scholar]

PERMALINK

Using the deterministic approach model for project portfolio selection problem (PPSP) solutions

AO Mogbojuri

OA Olanrewaju

Abstract

1. Introduction

2. Previous studies

3. Methodology

3.1. Analytic hierarchy process (AHP)

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

3.2. Goal programming model

3.3. Case study

4. Results

4.1. The AHP model steps are implemented as described in section 3.1

Table 1.

Table 2.

Table 3.

Table 4.

Table 5.

Table 6.

4.2. Goal programming model formulation from the final or global weight obtained from AHP

Priority 1

Priority 2

Priority 3

4.3. Comparison of optimization results between the integrated (AHP-GP) and GP models

Table 7.

5. Discussion

6. Conclusion

Production notes

Author contribution statement

Data availability statement

Funding statement

Declaration of competing interest

Acknowledgments

Appendix A. Primary Data

Table A.1.

Table A.2.

Table A.3.

References

Associated Data

Data Availability Statement

ACTIONS

PERMALINK

RESOURCES

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