Heuristics for Inventory Systems Based on Quadratic Approximation of L-Natural-Convex Value Functions

Abstract

We propose an approximation scheme for single-product periodic-review inventory systems with L-natural-convex structure. We lay out three well-studied inventory models, namely the lost-sales system, the perishable inventory system, and the joint inventory-pricing problem. We approximate the value functions for these models by the class of L-natural-convex quadratic functions, through the technique of linear programming approach to approximate dynamic programming. A series of heuristics are derived based on the quadratic approximation, and their performances are evaluated by comparison with existing heuristics. We present the numerical results and show that our heuristics outperform the benchmarks for majority of cases and scale well with long lead times. In this dissertation we also discuss the alternative strategies we have tried but with unsatisfactory result.