An exact method with variable fixing for solving the generalized assignment problem

Posta, Marius; Ferland, Jacques A.; Michelon, Philippe

doi:10.1007/s10589-011-9432-0

Cited by 48 publications

(49 citation statements)

References 12 publications

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“…; 4. Since the hospital has the first priority goal to pay as less overtime as possible, and this exactly matches with the first summation term in (12) which comprises minimizing both d þ 1 i f in (7) and d þ 1 i p in (8). Goal #2, implied by (9), is to regulate no more than two shifts a day, and this is the second summation term in (12).…”

Section: The Objective Functionsupporting

confidence: 60%

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Solving an outpatient nurse scheduling problem by binary goal programming

Wang

Hsieh

Zhuang

et al. 2014

Journal of Industrial and Production Engineering

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The cyclic scheduling for staffs in hospitals has been widely studied but none in the literature is about the nurse scheduling problem in the outpatient departments. Considering fairness and relevant constraints in scheduling outpatient nurses, this study formulates the nurse assignment problem as a binary goal programming model. An optimized and "fair" weekly schedule satisfying the stated hospital's policies and the outpatient nurses' preferences is solved. A "fair" schedule is in the sense that the number of due shifts and the shift patterns are assigned as same as possible for all the full-time nurses during the weekdays. A sensitivity analysis on the number of full-time nurses is also performed to answer the question about the best utilization in scheduling nurses. This study replaces the manual-made schedule with a computerized one and provides hospital managers insights in identifying the best human-resource portfolio in outpatient nurse scheduling.

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Section: The Objective Functionsupporting

confidence: 60%

“…For example, Gutjahr and Rauner [4] utilized the ant colony optimization in solving a nurse scheduling problem. Posta et al [12] proposed another heuristic algorithm to solve the generalized assignment problem.…”

Section: Introductionmentioning

confidence: 99%

Solving an outpatient nurse scheduling problem by binary goal programming

Wang

Hsieh

Zhuang

et al. 2014

Journal of Industrial and Production Engineering

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“…3.1 different variants of our approach are tested on the Generalized Assignment Problem (GAP) in order to find the best one. There is also comparison with CPLEX solver and the state-of-the-art approach proposed by Posta et al [24]. In the next subsection, the computational experiments on the Multilevel Generalized Assignment Problem, Capacited pMedian Problem and Capacitated Network Location Problem are presented.…”

Section: Computational Resultsmentioning

confidence: 99%

“…A short survey and comprehensive list of references concerning this problem can be found in some recent papers [4,24].…”

Section: Generalized Assignment Problemmentioning

confidence: 99%

“…the separation routing is used only in the root node of branch-and-bound tree) in columns C&B in comparison with CPLEX (CPX) and POSTA proposed by Posta et al [24], which consists in solving a series of decision problems by a lagrangean branch-and-bound algorithm with a few variable fixing rules, are presented in Table 5. OPT is an optimal value found and the computational time is given for two cases: Proof-when the methods are run with the given optimal values, i.e.…”

Section: Generalized Assignment Problemmentioning

confidence: 99%

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An implementation of exact knapsack separation

2015

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Cutting planes have been used with great success for solving mixed integer programs. In recent decades, many contributions have led to successive improvements in branch-and-cut methods which incorporate cutting planes in branch and bound algorithm. Using advances that have taken place over the years on 0-1 knapsack problem, we investigate an efficient approach for 0-1 programs with knapsack constraints as local structure. Our approach is based on an efficient implementation of knapsack separation problem which consists of the four phases: preprocessing, row generation, controlling numerical errors and sequential lifting. This approach can be used independently to improve formulations with cutting planes generated or incorporated in branch and cut to solve a problem. We show that this approach allows us to efficiently solve large-scale instances of generalized assignment problem, multilevel generalized assignment problem, capacitated p-median problem and capacitated network location problem to optimality.Keywords Knapsack problem · Cutting plane · Exact separation · Generalized assignment problem · Multilevel generalized assignment problem · Capacitated p-median problem · Capacitated network location problem B Igor Vasilyev

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A Generic Exact Solver for Vehicle Routing and Related Problems

Pessoa

Sadykov

Uchôa

et al. 2019

Lecture Notes in Computer Science

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Major advances were recently obtained in the exact solution of Vehicle Routing Problems (VRPs). Sophisticated Branch-Cutand-Price (BCP) algorithms for some of the most classical VRP variants now solve many instances with up to a few hundreds of customers. However, adapting and reimplementing those successful algorithms for other variants can be a very demanding task. This work proposes a BCP solver for a generic model that encompasses a wide class of VRPs. It incorporates the key elements found in the best recent VRP algorithms: ng-path relaxation, rank-1 cuts with limited memory, and route enumeration; all generalized through the new concept of "packing set". This concept is also used to derive a new branch rule based on accumulated resource consumption and to generalize the Ryan and Foster branch rule. Extensive experiments on several variants show that the generic solver has an excellent overall performance, in many problems being better than the best existing specific algorithms. Even some non-VRPs, like bin packing, vector packing and generalized assignment, can be modeled and effectively solved.

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An exact method with variable fixing for solving the generalized assignment problem

Cited by 48 publications

References 12 publications

Solving an outpatient nurse scheduling problem by binary goal programming

Solving an outpatient nurse scheduling problem by binary goal programming

An implementation of exact knapsack separation

A Generic Exact Solver for Vehicle Routing and Related Problems

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