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International Journal of Production Economics
Volume 112, Issue 1, March 2008, Pages 96-108
Special Section on Recent Developments in the Design, Control, Planning and Scheduling of Productive Systems
 
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doi:10.1016/j.ijpe.2006.08.030    How to Cite or Link Using DOI (Opens New Window)
Copyright © 2007 Elsevier B.V. All rights reserved.

Solving surgical cases assignment problem by a branch-and-price approachstar, open

H. Feia, b, Corresponding Author Contact Information, E-mail The Corresponding Author, C. Chub, N. Meskensa and A. Artibac

aProduction and Operations Management Department, Catholic University of Mons (FUCaM), Chaussée de Binche 151, 7000 Mons, Belgium bUniversity of Technology of Troyes (UTT), ISTIT—OSI, 12 Rue Marie Curie BP 2060, 10010 Troyes CEDEX, France cInstitut Supérieur de Mécanique de Paris (Supmeca), 3, rue Fernand Hainaut, 93407 Saint-Ouen, France

Received 6 December 2005; 
accepted 28 August 2006. 
Available online 14 April 2007.

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Abstract

In this paper, we study a surgical cases assignment problem (SCAP) of assigning a set of surgical cases to several multifunctional operating rooms with an objective of minimizing total operating cost. Firstly, we formulate this problem as an integer problem and then reformulate the integer program by using Dantzig–Wolf decomposition as a set partitioning problem. Based on this set partitioning formulation, a so-called branch-and-price exact solution algorithm, combining Branch-and-Bound procedure with column generation (CG) method, is designed for the proposed problem where each node is the linear relaxation problem of a set partitioning problem. This linear relaxation problem is solved by a CG approach in which each column represents a plan for one operating room and is generated by solving a sub-problem (SP) of single operating room planning problem. The computational results indicate that the decomposition approach is promising and capable of solving large problems.

Keywords: Surgical cases assignment problem; Dantzig–Wolfe decomposition; Column generation; Branch-and-price

Article Outline

1. Introduction
2. General integer programming
3. Framework of branch-and-price procedure
4. Set partitioning general problem (GP) corresponding to general integer problem (GIP)
5. Framework of heuristic procedure based on column generation
5.1. General description
5.2. Description of sub-problems
6. Selection strategy of node and branching variable
6.1. Node selection strategy
6.2. Branching variable selection strategy
7. Experimental results
7.1. Data
7.2. Computational results
8. Conclusion and perspective
References



International Journal of Production Economics
Volume 112, Issue 1, March 2008, Pages 96-108
Special Section on Recent Developments in the Design, Control, Planning and Scheduling of Productive Systems
 
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