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A Conic Integer Programming Approach to Stochastic Joint Location-Inventory Problems

Alper Atamtürk, Gemma Berenguer, Zuo-Jun (Max) Shen
2012 Operations Research  
Valid inequalities, including extended polymatroid and extended cover cuts, are added to strengthen the formulations and improve the computational results.  ...  We show how to formulate these problems as conic quadratic mixed-integer problems.  ...  They are also grateful to the anonymous referees and the associate editor for their insightful comments. This research was partially supported by the National Science Foundation [Grant CMMI 1068862].  ... 
doi:10.1287/opre.1110.1037 fatcat:wyhldjrvpbeupdjk2z4ftzmixe

Classification, models and exact algorithms for multi-compartment delivery problems

Leandro C. Coelho, Gilbert Laporte
2015 European Journal of Operational Research  
Extended logical inequalities We propose the following sets of constraints, which we call extended logical inequalities because they further enforce logical relationships between integer variables of the  ...  It extends the classical vehicle routing formulations [23] in which a relaxed problem is first solved and subtour elimination constraints are added dynamically as they are found to be violated.  ... 
doi:10.1016/j.ejor.2014.10.059 fatcat:pu75noj7gzgrppp6ysnwrf72su

A branch-and-cut algorithm for the multi-product multi-vehicle inventory-routing problem

Leandro C. Coelho, Gilbert Laporte
2013 International Journal of Production Research  
In this paper, we propose a branch-andcut algorithm for the solution of IRPs with multiple products and multiple vehicles. We formally define and model the problem, and we solve it exactly.  ...  While most IRP research deals with a single product, there are often several products involved in distribution activities.  ...  Third, we propose a large set of benchmark instances in order to evaluate our algorithm. These are made publicly available to the research community to allow the assessment of future algorithms.  ... 
doi:10.1080/00207543.2012.757668 fatcat:qdgaa3ga65evxppah7ni4tpmum

A survey on benders decomposition applied to fixed-charge network design problems

Alysson M. Costa
2005 Computers & Operations Research  
The basic idea behind this method is to decompose the problem into two simpler parts: the first part, called master problem, solves a relaxed version of the problem and obtain values for a subset of the  ...  The second part, called auxiliary problem (or subproblem), obtains the values for the remaining variables while keeping the first ones fixed, and uses these to generate cuts for the master problem.  ...  Acknowledgements The author is grateful to Jean-François Cordeau and Bernard Gendron for their valuable comments which improved both the content as well as the presentation of the paper.  ... 
doi:10.1016/j.cor.2003.11.012 fatcat:kcsfk336wvbjbdr5zbvsbhcjnq

A Decomposition Algorithm for Local Access Telecommunications Network Expansion Planning

Anantaram Balakrishnan, Thomas L. Magnanti, Richard T. Wong
1995 Operations Research  
By exploiting the special tree and routing structure of the expansion planning problem, our solution method integrates two major algorithmic strategies from mathematical programming-the use of valid inequalities  ...  The computational results for three actual test networks demonstrate that this enhanced dynamic programming algorithm, when embedded in a Lagrangian relaxation scheme (with problem preprocessing and local  ...  Acknowledgments: We wish to thank Marcia Helme, Jeffrey Musser, and Alexander Shulman for their valuable insights and modeling contributions, and for providing the linkage with network planners in the  ... 
doi:10.1287/opre.43.1.58 fatcat:isgxlp7hbnbmpmzozef33ralva

Achieving MILP feasibility quickly using general disjunctions

Hanan Mahmoud, John W. Chinneck
2013 Computers & Operations Research  
Branch and bound algorithms for Mixed-Integer Linear Programming (MILP) almost universally branch on a single variable to create disjunctions.  ...  General linear expressions involving multiple variables are another option for branching disjunctions, but are not used for two main reasons: (i) descendent LPs tend to solve more slowly because of the  ...  variable, one of the fastest algorithms for reaching integer feasibility quickly.  ... 
doi:10.1016/j.cor.2013.03.001 fatcat:o6pexk3lh5g23hatfdpoj5o5wy

Mixed Integer Optimization in the Chemical Process Industry

J. Kallrath
2000 Chemical engineering research & design  
This tutorial paper addresses two groups.  ...  Typical additional problems in the chemical industry suitable to optimization are process design, process synthesis and multi-component blended-flow problems leading to nonlinear or even mixed integer  ...  Acknowledgments: Thanks is directed to G. DeBeuckelaer, T. Maindl, K. Plitzko, P. Schmitt (BASF Corp., Mt.  ... 
doi:10.1205/026387600528012 fatcat:4a3kin2dcbc73p3j4gps3ygl6m

On the Undirected Rural Postman Problem: Tight Bounds Based on a New Formulation

Elena Fernández, Oscar Meza, Robert Garfinkel, Maruja Ortega
2003 Operations Research  
A rudimentary algorithm that yields lower bounds via cutting planes and upper bounds via heuristics is developed and tested for a variation of that formulation.  ...  Computational results are encouraging, especially in terms of the relatively small number of added inequalities needed to get good lower bounds, and the fact that the vast majority of these have efficient  ...  The authors also want to thank Angel Corberán and Alain Hertz for providing us their 33 problem sets.  ... 
doi:10.1287/opre.51.2.281.12790 fatcat:hdy64zeqovfjpmmyxvj4lcsb2i

A Nonlinear Transformation Based Hybrid Evolutionary Method for MINLP Solution

S.A. Munawar, R.D. Gudi
2005 Chemical engineering research & design  
The handling of discrete variables has been quite ad hoc; for instance in DE, the algorithm works assuming them as continuous variables during all the steps but only for the objective function evaluation  ...  A nonlinear transformation proposed in the literature for representing the discrete variables as continuous variables has been explored for alternate ways of solving MINLP problems to global optimality  ...  Figure 2 . 2 Objective function and the inequality constraint for Example 1. Figure 3 . 3 Objective function and the constraints for Example 1a.  ... 
doi:10.1205/cherd.04286 fatcat:62rs6ov5lvaorj63zygrkpael4

An improved branch-cut-and-price algorithm for the two-echelon capacitated vehicle routing problem

Guillaume Marques, Ruslan Sadykov, Jean-Christophe Deschamps, Rémy Dupas
2019 Computers & Operations Research  
Acknowledgments We are grateful to François Vanderbeck whose efforts contributed to obtaining the Ph.D. studentship for the first author.  ...  Experiments presented in this paper were carried out using the PlaFRIM (Federative Platform for Research in Computer Science and Mathematics), created under the Inria PlaFRIM development action with support  ...  Our BCP algorithm could be extended to the two-echelon locationrouting problem [Contardo et al., 2012] in which satellites have predefined capacities and fixed opening costs.  ... 
doi:10.1016/j.cor.2019.104833 fatcat:srmscujsqbd4diflcxsp2xe5la

Logical Processing for Integer Programming

Monique Guignard, Ellis L. Johnson, Kurt Spielberg
2005 Annals of Operations Research  
Concepts which are likely to be specially important for (0,1) MIP are pointed out.  ...  This paper reviews tools which have great potential for reducing the difficulty of solving IP (and also MIP) problems, if well implemented in solvers.  ...  Acknowledgments We would like to thank three anonymous referees for their careful reading of the paper, and for numerous suggestions for improvement.  ... 
doi:10.1007/s10479-005-3974-4 fatcat:dmkynm4bd5codncb3bo45xkj6y

The production routing problem: A review of formulations and solution algorithms

Yossiri Adulyasak, Jean-François Cordeau, Raf Jans
2015 Computers & Operations Research  
We attempt to provide an in-depth summary and discussion of different formulation schemes and of algorithmic and computational issues.  ...  Finally, we point out interesting research directions for further developments in production routing.  ...  The facility location reformulation provides better computational performance when adding the valid inequalities for the routing problem (including the subtour elimination constraints) and solving the  ... 
doi:10.1016/j.cor.2014.01.011 fatcat:sugkfwaterg5lornhe3mfdyuoi

A Combinatorial Approach to Orthogonal Placement Problems [chapter]

Gunnar W. Klau
2003 Operations Research Proceedings 2002  
The reformulation allows us to develop exact algorithms for the original problems.  ...  Extensive computational studies on real-world benchmarks show that our linear programming-based algorithms are able to solve large instances of the placement problems to provable optimality within short  ...  Then the integer linear program reduces to computing two separate ¤ -minimal assignments; the consistency constraints can be either eliminated (if the corresponding variable The result follows with Theorem  ... 
doi:10.1007/978-3-642-55537-4_4 dblp:conf/or/Klau02 fatcat:jgxvmhcijbdibafixism7iami4

Duality and Sensitivity Analysis for Fractional Programs

Gabriel R. Bitran, Thomas L. Magnanti
1976 Operations Research  
In this paper, we consider algorithms, duality and sensitivity analysis for optimization problems, called fractional, whose objective function is the ratio of two real valued functions.  ...  We discuss a procedure suggested by Dinkelbach for solving the problem, its relationship to certain approaches via variable transformations, and a variant of the procedure which has convenient convergence  ...  Acknowledgment: The authors would like to thank Professor Daniel Granot for pointing out corollary 4.2 for linear fractional programs and two referees who have provided several references.  ... 
doi:10.1287/opre.24.4.675 fatcat:zcm34gq3unebhhs3gtd63uqo4m

The Ring Spur Assignment Problem: New formulation, valid inequalities and a branch-and-cut approach

Rahimeh Neamatian Monemi, Shahin Gelareh
2017 Computers & Operations Research  
We report optimal solutions for all SNDLib instances including those that have not previously been solved to optimality.  ...  Several classes of valid inequalities and corresponding separation procedures are presented giving rise to an efficient branch-and-cut solution algorithm.  ...  Acknowledgement The authors would like to give their warm thanks to Paula Carroll from University College of Dublin for sharing elements facilitating the comparison between the models.  ... 
doi:10.1016/j.cor.2017.06.016 fatcat:6ksf36p2ffgjlexontciqgxgyy
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