Single Item Lot Sizing Models with Backlogging and Outsourcing and Non-decreasing Inventory Capacity
考虑延期交货、转包和非减库存能力约束的单产品批量模型

This paper addresses a dynamic single-item lot sizing problem with backlogging and outsourcing and non-decreasing inwentory capacity.By the means of the concept of sub-plan,the problem can be solved by first computing all possible sub-plans and then searching the best combination or concatenation of sub-plans using dynamic programming.All the sub-plans are described by a group of general mathematic formulae.The computation of the sub-plan can be decomposed into two sub-problems by relaxing the constraint that production level at production period of a sub-plan must be more than zero.Based on the properties of an optimal solution,two polynomial algorithms are devised to solve sub-problems and reintegrate the relaxed constraint.Finally,a dynamic programming algorithm with complexity O(T4) is developed to solve the global problem,where T is number of periods in planning horizon.The performance of the proposed algorithm is evaluated by numeric experiment.