Joint replenishment and pricing decisions in inventory systems with stochastically dependent supply capacity.

*(English)*Zbl 1144.90003Summary: We study a joint optimization problem of replenishment and pricing for a periodic-review inventory system with random supply capacity. When making replenishment and pricing decisions at the beginning of each period, the firm only knows the supplier’s available capacity in the current period, but does not know what will be the available capacity in future periods. The salient feature of our model is that the random supply capacities for different periods are dependent. Several stochastic dependency structures are considered for the supply capacity sequence, including the one-lag and the multi-lag dependency.

We show that the optimal inventory control policy is of the modified base-stock type and the base-stock level is decreasing in the available capacity of the current period and that the optimal pricing policy is a “list-price” coined with markdown and markup. This paper generalizes the work of A. Federgruen and P. Zipkin [Math. Oper. Res. 11, 193–207 (1986; Zbl 0602.90053); ibid. 11, 208–215 (1986; Zbl 0628.90017)] in which the supply capacity and selling price are assumed to be fixed constants, and the work of A. Federgruen and A. Heching [Oper. Res. 47, No. 3, 454–475 (1999; Zbl 0979.90004)] on joint optimization of replenishment and pricing with unlimited supply capacity.

We show that the optimal inventory control policy is of the modified base-stock type and the base-stock level is decreasing in the available capacity of the current period and that the optimal pricing policy is a “list-price” coined with markdown and markup. This paper generalizes the work of A. Federgruen and P. Zipkin [Math. Oper. Res. 11, 193–207 (1986; Zbl 0602.90053); ibid. 11, 208–215 (1986; Zbl 0628.90017)] in which the supply capacity and selling price are assumed to be fixed constants, and the work of A. Federgruen and A. Heching [Oper. Res. 47, No. 3, 454–475 (1999; Zbl 0979.90004)] on joint optimization of replenishment and pricing with unlimited supply capacity.

##### MSC:

90B05 | Inventory, storage, reservoirs |

##### Keywords:

inventory; pricing; dependent capacity; modified base-stock policy; list-price; markup; markdown
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\textit{X. Chao} et al., Eur. J. Oper. Res. 191, No. 1, 142--155 (2008; Zbl 1144.90003)

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