A branch and price algorithm to minimize makespan on a single batch processing machine with non-identical job sizes

Authors:
N. Rafiee Parsa;B. Karimi;A. Husseinzadeh Kashan
Affiliations:
Department of Industrial Engineering, Amirkabir University of Technology, 424 Hafez Ave., Tehran 15916-34311, Iran;Department of Industrial Engineering, Amirkabir University of Technology, 424 Hafez Ave., Tehran 15916-34311, Iran;Department of Industrial Engineering, Amirkabir University of Technology, 424 Hafez Ave., Tehran 15916-34311, Iran
Venue:
Computers and Operations Research
Year:
2010

Citing 13
Cited 3

A note on bounding a class of linear programming problems, including cutting stock problems

Operations Research
A new optimization algorithm for the vehicle routing problem with time windows

Operations Research
Solving binary cutting stock problems by column generation and branch-and-bound

Computational Optimization and Applications
Lotsizing and Scheduling on Parallel Machines with Sequence-Dependent Setup Costs

Management Science
Scheduling a batch processing machine with incompatible job families

Computers and Industrial Engineering
Minimizing the makespan on a batch machine with non-identical job sizes: an exact procedure

Computers and Operations Research
Branch-And-Price: Column Generation for Solving Huge Integer Programs

Operations Research
Solving Parallel Machine Scheduling Problems by Column Generation

INFORMS Journal on Computing
Time-Indexed Formulations for Machine Scheduling Problems: Column Generation

INFORMS Journal on Computing
A Set-Covering-Based Heuristic Approach for Bin-Packing Problems

INFORMS Journal on Computing
A hybrid genetic heuristic for scheduling parallel batch processing machines with arbitrary job sizes

Computers and Operations Research
An exact algorithm for IP column generation

Operations Research Letters
Minimizing makespan on a single batching machine with release times and non-identical job sizes

Operations Research Letters

The train delivery problem: vehicle routing meets bin packing

WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
An improved ant colony optimization for scheduling identical parallel batching machines with arbitrary job sizes

Applied Soft Computing
Tactical fixed job scheduling with spread-time constraints

Computers and Operations Research

Quantified Score

Hi-index	0.01

Visualization

Abstract

In this paper, we consider the scheduling problem on a single batch processing machine with non-identical job sizes; in which the machine has a limited capacity and can process a group of jobs simultaneously as a batch. The processing time of a batch is the longest processing time of all jobs in the batch. The objective is to minimize the makespan. We formulate the problem using Dantzig-Wolfe decomposition as a set partitioning problem. Based on the set partitioning formulation, we present a tight lower bound using column generation method. A heuristic algorithm is also developed to generate the basic solution in the column generation method. A branch and price algorithm which combines the column generation technique with branch and bound method is then presented to obtain the optimal solution of the problem. The efficiency of the proposed branch and price algorithm is ultimately compared to the branch and bound algorithm from the literature, based on the generated sample problems.