Computationally Efficient Problem Reformulations for Capacitated Lot Sizing Problem

Renduchintala Raghavendra Kumar Sharma,Priyank Sinha,Mananjay Kumar Verma

doi:10.4236/ajor.2018.84018

Renduchintala Raghavendra Kumar Sharma, Priyank Sinha + Show 1 more

Open Access

https://doi.org/10.4236/ajor.2018.84018

Copy DOI

Abstract

In this article, we propose novel reformulations for capacitated lot sizing problem. These reformulations are the result of reducing the number of variables (by eliminating the backorder variable) or increasing the number of constraints (time capacity constraints) in the standard problem formulation. These reformulations are expected to reduce the computational time complexity of the problem. Their computational efficiency is evaluated later in this article through numerical analysis on randomly generated problems.

Highlights

Lot sizing problem aims to optimally utilize the available production resources while meeting the demand targets
We propose novel reformulations for capacitated lot sizing problem
These reformulations are the result of reducing the number of variables or increasing the number of constraints in the standard problem formulation

Summary

Introduction

Lot sizing problem aims to optimally utilize the available production resources while meeting the demand targets. We restrict our discussion to general dynamic multi-level capacitated lot sizing problem This problem was first proposed by Billington et al [1]. Formulations given in this article belongs to inventory and lot-size (I & L) formulations category, which are among the most popular in the literature due to their computational efficiency These formulations use production quantity and inventory levels as the variables. We state the standard problem formulation and derive three reformulations of the problem by eliminating the backordering variable or/and adding two capacity constraints.

Research Methodology

Model A4

Numerical Experiments

Data Analysis

Conclusion