Abstract
The focus of this study is a stochastic inventory rationing problem. Requests to the warehouse are categorized into several classes based on different shortage costs. The higher the class, the higher the shortage cost. Under the stochastic problem in which the request arrivals are Poisson processes and quantity of each request is a random variable, this study investigates how to allocate the limited available inventory to requests with the objective of minimizing total shortage cost. A sampling expected cost gap decision procedure (SECG) is proposed to determinate whether to fulfill the current arrival request or to reject the current request for reserving the inventory for future requests. In addition, in SECG procedure, the inventory allocation problem in which the number of requests of various classes and the quantity of each request are known has to be solved. There are two solution methods of the problem are used in this study. One is an optimal solution method - 0-1 knapsack problem formulation. To improve the solution time, the other one, a heuristic algorithm, is proposed. The simulation experiments show that the total shortage costs of SECG with both allocation methods are very close the optimal decision under perfect information and the normalized gap are about 1%. The allocation method of knapsack formulation performs a little bit better than the heuristic method. However, the computation time of heuristic method is shorter than that of knapsack formulation. In addition, both methods are very robust under varying problem conditions.