A class of random algorithms for inventory cycle offsetting

Abstract

The inventory cycle offsetting problem (ICP) is a strongly NPcomplete problem. We study this problem from the view of probability theory, and rigorously analyze the performance of a specific random algorithm for this problem; furthermore, we present a "local search" algorithm, and a modified local search, which give much better results (the modified local search gives better results than plain local search), and leads to good solutions to certain practical instances of ICP, as we demonstrate with some numerical data. The regime where the random algorithm is rigorously proved to work is when the number of items is large, while the time horizon and unit volumes are not too large. Under such natural hypotheses, the Law of Large Numbers, and various quantitative refinements (such as Bernstein's inequality) 1 come into play, and we use these results to show that there always exist good solutions, not merely that good solutions holds with high probability.

The Replenishment Schedule to Minimize Peak Storage Problem: The Gap Between the Continuous and Discrete Versions of the Problem

“…Studies of multi-cycle RSP with more than two items have been focused on the development of heuristics. These include genetic algorithms (Moon et al 2008, Yao and, a smoothing procedure utilizing a Boltzmann function , local search procedures (Croot and Huang 2013), a simulated annealing algorithm (Boctor 2010), hybrid heuristics (Boctor 2010, Russell andUrban 2016), and an evolutionary algorithm (Boctor and Bolduc 2015). None of these heuristics were shown to deliver a guaranteed approximation bound.…”

A Fully Polynomial Time Approximation Scheme for the Replenishment Storage Problem

“…Studies of algorithmic results for the multi-cycle RSP with more than two items have been focused on the development of heuristics. These include genetic algorithms [5,8]), a smoothing procedure utilizing a Boltzmann function [9], local-search procedures [2], a simulated-annealing algorithm [1] and a hybrid heuristic [1,7]. No algorithm with guaranteed approximation bound has been known for the multi-cycle RSP.…”