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# Forecast horizon of dynamic lot size model for perishable inventory with minimum order quantities

• * Corresponding author: Zirui Lan
• We consider the dynamic lot size problem for perishable inventory under minimum order quantities. The stock deterioration rates and inventory costs depend on both the age of the stocks and their periods of order. Based on two structural properties of the optimal solution, we develop a dynamic programming algorithm to solve the problem without backlogging. We also extend the model by considering backlogging. By establishing the regeneration set, we give a sufficient condition for obtaining forecast horizon under without and with backlogging. Finally, based on a detailed test bed of instance, we obtain useful managerial insights on the impact of minimum order quantities and perishability of product and the costs on the length of forecast horizon.

Mathematics Subject Classification: Primary: 90C39, 90C90; secondary: 90B05.

 Citation: • • Figure 1.  Median forecast horizon as a function of minimum order quantities

Figure 2.  Median forecast horizon as a function of lifetime

Figure 3.  Median forecast horizon as a function of backlogging cost

Figure 4.  Median forecast horizon as a function of inventory holding cost

Table 1.  Summary of Computations of Example 1

 $t$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $d_t$ $6$ $8$ $9$ $12$ $11$ $7$ $26$ $x_t^\ast$ $25$ $x_t^\ast$ $25$ $0$ $x_t^\ast$ $25$ $0$ $0$ $x_t^\ast$ $35$ $0$ $0$ $0$ $x_t^\ast$ $25$ $0$ $0$ $25$ $0$ $x_t^\ast$ $25$ $0$ $0$ $32$ $0$ $0$ $x_t^\ast$ $25$ $0$ $0$ $32$ $0$ $0$ $26$ $C(t)$ $263$ $285$ $289$ $399$ $544$ $607$ $837$
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