A Dynamic Lot-Size Model with Make-or-Buy Decisions
研究一个动态批量模型，每个时期的生产有容量限制但采购无限制，生产、采购和库存成本为凹函数，目标是找到T期内满足已知需求的最小成本生产和采购计划，并给出了O(T^5)算法。
This paper considers a dynamic lot-size model with make-or-buy decisions. In each period, the production level may not exceed a given capacity, but the purchase is unrestricted. The costs for production, purchase and inventory are concave. The problem is to find a minimum-cost production and purchase schedule that satisfies known demands over T periods. After characterizing the form of an optimal solution, we present an O(T 5 ) algorithm when the production capacities are stationary. The algorithm is extended to the case where the capacities are integer multiples of a constant. The results are further extended to the cases of backlogging, bounded inventory, and capacitated purchase.