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| Dynamic Production Policy with Fixed and Convex Variable Costs and Two Demand Sources |
| ZHAO Ling，LIU Zhixue |
| Huazhong University of Science and Technology, Wuhan, China |
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Abstract Consider a single-product manufacturer facing a periodically-reviewed inventory problem. The production cost includes a fixed cost and a convex variable cost. And the demand is classified into two types, a deterministic source and a random source, where the random source can be backlogged, but the deterministic source and the backorders from the previous period must be satisfied. The manufacturer needs to decide the production level in each period and the goal is to minimize the expected total cost over a planning horizon. We develop a stochastic dynamic programming model, show some convexity of optimal value functions and apply this property to characterize the optimal production policy. From this, we find that the produce-up-to level increases in the initial inventory level when the initial inventory level is below the deterministic demand, and producing nothing is optimal when the initial inventory level is high enough. Numerical study shows that the structure of the policy is obviously different with the optimal one when the constraint that the deterministic demand must be satisfied is ignored.
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Received: 17 May 2020
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