Table 2.

Parameters and notations

Parameters
$T$	Length of replenishment cycle
$A$	Potential market demand
$c_i$	Production cost for ith manufacturer
${\theta }_0$	Deterioration rate for NOP at all,${0<\mathit{\theta }}_0<1$
${\theta }_i$	Deterioration rate for ith manufacturer product,${0<\mathit{\theta }}_{\mathit{i}}<1$
$\alpha$	Percentage of potential market demand for OPs
$\beta$	Coefficient of the price of the products on its market demand
$\rho$	Coefficient of organicity effect on deterioration rate
$c_d$	Deterioration cost of the products for the retailer
$h$	Cost of maintaining a unit of any product in a period in the retail warehouse
$w_i$	Wholesale price for ith manufacturer product
$\lambda$	Coefficient of the retailer price of similar product effect on the other manufacturer product demand
$\gamma$	Coefficient of organic level on OP demand
$\phi$	Coefficient of sales effort level on NOP demand
$\xi$	Coefficient of influence of the organic level of the OM on the demand of NOM
$\eta$	Coefficient of influence of the level of sales effort of the NOM on the demand of OM
$\vartheta$	Coefficient of the influence of organic investment cost on manufacturer cost
$k$	Coefficient of sales effort on the production cost of NOP
$y$	Percentage of OPs selling price, which is less than the selling price of NOP
$z$	Percentage of NOPs selling price, which is considered as its wholesale price
$p_2$	Retailer price for NOP
$D_{\mathit{ri}}$	Demand function of retailer for ith manufacturer product per cycle
$Q_{\mathit{ri}}$	Order amount by the retailer for ith manufacturer product per cycle
$B_i$	Amount of deterioration for ith manufacturer product in the retailer store per cycle
$I_{\mathit{ri}}\left(t\right)$	The retailer’s stock level at period t byith manufacturer product
$I_{\mathit{ri}}$	The total amount of inventory carried by the retailer per cycle
${\pi }_{m1}^d,{\pi }_{m1}^c,{\pi }_{m1/rs}^c,{\pi }_{m1/cs}^c$	Total profit of OM in the decentralized, centralized, revenue-sharing contract, and cost-sharing contract conditions respectively per cycle
${\pi }_{m2}^d,{\pi }_{m2}^c$	Total profit of NOM in the decentralized and centralized conditions respectively per cycle
${\pi }_r^d,{\pi }_r^c,{\pi }_{r/rs}^c,{\pi }_{r/cs}^c$	Total profit of retailer in the decentralized, centralized, revenue-sharing contract, and cost-sharing contract conditions respectively per cycle
${\pi }^c$	Total profit of OM and retailer in centralized condition per cycle
Decision variables
$o_d,o_c$	Organic level of products for OM in decentralized and centralized conditions respectively
${p_1}_d,{p_1}_c$	Retailer price for OP in decentralized and centralized conditions respectively
$s_d,s_c$	Sales effort level for NOM in decentralized and centralized conditions respectively