A New Branching Rule to Solve the Capacitated Lot Sizing and Scheduling Problem with Sequence Dependent Setups

Willy Alves De Oliveira,Maristela Oliveira Dos Santos

doi:10.5540/tema.2017.018.03.515

Abstract

In this paper, we deal with the Capacitated Lot Sizing and Scheduling Problem with sequencedependent setup times and costs - CLSD model. More specifically, we propose a simple reformulation for the CLSD model that enables us to define a new branching rule to be used in Branch-and-Bound (or Branch-and-Cut) algorithms to solve this NP-hard problem. Our branching rule can be easily implemented in commercial solvers. Computational tests performed in 240 test instances from the literature show that our approach can significantly reduce the running time to solve this problem using a Branch-and-Cut algorithm of a commercial MIP solver.Therefore, our approach can also improve the performance of other approaches that need to solve partial sub problems of the CLSD model in each iteration, such as Lagrangian approaches and heuristics based on the mathematical formulation of the problem.

Highlights

In most production environments, companies need to decide on the size of production lots in order to obtain efficient inventory management and reduce costs
The traditional branch-and-bound algorithm consumed around 56 seconds to solve the CLSD model to optimality, while the branch-and-bound algorithm with the branching rule introduced in this paper consumed only around 6 seconds to solve the CLSDw model
We deal with the lot sizing and scheduling problem with sequence dependent setup costs and times

Summary

INTRODUCTION

Companies need to decide on the size of production lots in order to obtain efficient inventory management and reduce costs. If we can identify that item j is not produced in one period, we can fix directly the value of 2 J + 1 binary variables on zero This fact motivated us to introduce the binary variables w jt in the CLSD model, obtaining the CLSDw model, and performing a branch-and-bound algorithm with a priority of branching for these variables. In this test instance, the traditional branch-and-bound algorithm consumed around 56 seconds to solve the CLSD model to optimality, while the branch-and-bound algorithm with the branching rule introduced in this paper consumed only around 6 seconds to solve the CLSDw model.

Test environment

Test instance features and computational results

Impact of the proposed branching rule

CONCLUSIONS AND FUTURE STUDIES