Optimal Inventory Policies under a Hierarchy of Setup Costs

Abstract

This paper considers multi-product inventory problems which are subject to an order cost or setup cost hierarchy of the following form: all replenishment orders issued in any given scheduling period are filled in the next period, with the total setup cost of replenishing N different products in one period being S + s N. The values of N observed in the various periods, and therefore the expected setup cost per job, depend on the unknown lot sizes. This type of setup cost dependence can arise in simple inventory problems but is more commonly found in production environments in which the setup cost for a given job depends on the job immediately preceding it in the production schedule. Assuming demands to be random with known probability distributions, an iterative algorithm is presented for computing optimal lot sizes and reorder points for a set of heterogeneous products.

Optimization in simulation: Current issues and the future outlook

“…Therefore, whenever possible, analytical and algorithmic solutions are favored over simulation. For example, using an iterative algorithm, Simmons [78] has investigated optimal inventory policies under a hierarchy of setup costs. More recently, Curry and Hartfiel [25] and Hartfiel and Curry [37] have combined algorithmic techniques with simulation to obtain efficient solutions to the problems with partially known structures.…”

A simulation–optimization method: Its convergence and utility

“…An iterative algorithm was presented by Simmons [26] for a multiproduct continuously reviewed inventory system with joint replenishment of all products to be ordered in a scheduling period. The replenishment cost consists of a constant plus a variable cost for each product ordered.…”

“…Nolan and Sovereign [20], on the other hand, proposed a recursive linear programming-simulation scheme for the analysis of large-scale transportation system problems. The concepts of an iterative optimization-simulation scheme is not unique to their approach, having been proposed independently in at least three other articles [4, 25,26]. These iterative algorithms utilize the known structure of the system, with certain relationships still being treated as unknown or simulated, to generate highly efficient (in terms of the number of simulations) policy improvement schemes.…”