Table 1.
Notation.
| Symbolizations | Explanation |
|---|---|
| C 0 | Replenishment cost per order in dollars |
| a | Fixed demand rate (a > 0) |
| b | Price scale in the demand (b > 0) |
| C p | Purchase price ($/unit) |
| p | Price of the item ($/unit) |
| θ(t) | Weibull distributed decay rate (0 < θ(t) ≪ 1) |
| A | The number of advertisement |
| γ | Advertising elasticity |
| G | Cost per advertisement ($) |
| h | Holding cost ($/unit time/unit) |
| C s | Shortage cost ($/unit) |
| δ | Backlogging parameter (δ > 0) |
| S | Initial stock |
| R | Highest number of backorders |
| Q | Order amount (unit/order) |
| C l | Opportunity cost ($/unit) |
| t 1 | Time period of physical stock in the warehouse (time unit) |
| T | Cycle length (time unit) |
| Z1(A, p, T) | The practitioner's profit under the first inventory procedure ($/time unit) |
| Z2(A, p, t1, T) | The practitioner's profit of the inventory procedure with backorders ($/time unit) |
| Decision variable | |
| A | Number of advertisements |
| p | Price of the item ($/unit) |
| t 1 | Time period of physical stock in the warehouse (time unit) |
| T | Cycle length (time unit) |