The Multi-Period Inventory Management Study Under Uncertain Environment

The fast changing market makes the demand and cost parameters fluctuate from time to time. How to form an optimal production/ordering plan under such a complex environment becomes a key issue for industrial mangers. We consider two important extensions of stochastic lot-sizing problem:quantity discounts and machine breakdown.For the stochastic lot-sizing problem with quantity discounts, we assume that the demand and the cost parameters in each period are random and discrete. The unsatisfied demand can be backlogged. The objective is to minimize the total cost including ordering cost, holding cost and backlogging cost. We characterize the properties of the optimal policy. By defining an objective function and analyzing the continuity and the breakpoints of the objective function, we propose an O(n3L) algorithm for the problem when the discount level is one and there are at least two children at each node of the scenario tree, where n is the number of nodes in the scenario tree and L is the total number of leaf nodes. Then we extend our analysis to general stochastic lot-sizing problem with multi-discount levels and propose a polynomial time algorithm for it. Numerical experiments are conducted to study the impact of parameters on the efficiency of the algorithm.Next, we discussed the stochastic lot-sizing problem under machine breakdown. In the preempt-resume case, the breakdown merely act as an interruption, which means the prior work can be resumed as long as the machine is back in operation. Through analyzing the continuity of objective functions, we find that the turning points can be used to represent the objective function. Then, an O(n2logβ2+1 log n) polynomial time algorithm is proposed to solve the model. Later, we use an empirical case to study the effect of breakdown parameters on the optimal production policy.We develop and enrich the theory research about the stochastic lot-sizing problem. In addition, in terms of application, we provide decision suggestions for the managers of industrial manufacturers.