The Quadratic Multiknapsack Problem with Conflicts and Balance Constraints

2020 ◽  
Author(s):  
Philippe Olivier ◽  
Andrea Lodi ◽  
Gilles Pesant
Keyword(s):  
Integer Programming ◽  
Constraint Programming ◽  
Operations Research ◽  
Solution Process ◽  
Exact Method ◽  
The Core ◽  
Computational Evaluation ◽  
Operations Research Applications

The quadratic multiknapsack problem consists of packing a set of items of various weights into knapsacks of limited capacities with profits being associated with pairs of items packed into the same knapsack. This problem has been solved by various heuristics since its inception, and more recently it has also been solved with an exact method. We introduce a generalization of this problem that includes pairwise conflicts as well as balance constraints, among other particularities. We present and compare constraint programming and integer programming approaches for solving this generalized problem. Summary of Contribution: The quadratic multiknapsack problem consists of packing a set of items of various weights into knapsacks of limited capacities -- with profits being associated with pairs of items packed into the same knapsack. This problem has been solved by various heuristics since its inception, and more recently it has also been solved with an exact method. We introduce a generalization of this problem which includes pairwise conflicts as well as balance constraints, among other particularities. We present and compare constraint programming and integer programming approaches for solving this generalized problem. The problem we address is clearly in the core of the operations research applications in which subsets have to be built and, in particular, we add the concept of fairness to the modeling and solution process by computationally evaluating techniques to take fairness into account. This is clearly at the core of computational evaluation of algorithms.

scholarly journals Reshuffle minimisation to improve storage yard operations efficiency

2021 ◽  
Vol 15 ◽  
pp. 174830262199401
Author(s):  
Hammed Bisira ◽  
Abdellah Salhi
Keyword(s):  
Integer Programming ◽  
Programming Model ◽  
Heuristic Approach ◽  
Container Terminals ◽  
Exact Method ◽  
Computational Results ◽  
Binary Integer Programming ◽  
Integer Programming Model ◽  
Compatibility Test ◽  
Storage Area

There are many ways to measure the efficiency of the storage area management in container terminals. These include minimising the need for container reshuffle especially at the yard level. In this paper, we consider the container reshuffle problem for stacking and retrieving containers. The problem was represented as a binary integer programming model and solved exactly. However, the exact method was not able to return results for large instances. We therefore considered a heuristic approach. A number of heuristics were implemented and compared on static and dynamic reshuffle problems including four new heuristics introduced here. Since heuristics are known to be instance dependent, we proposed a compatibility test to evaluate how well they work when combined to solve a reshuffle problem. Computational results of our methods on realistic instances are reported to be competitive and satisfactory.

scholarly journals Implementasi Integer Programming dengan Algoritma Branch and Bound Menggunakan QM for Windows dalam Memaksimalkan Keuntungan di PT XYZ

2021 ◽  
Vol 5 (1) ◽  
pp. 14-18
Author(s):  
Nintia Litano Buyung ◽  
Endang Suhendar
Keyword(s):  
United States ◽  
Integer Programming ◽  
Production Planning ◽  
Branch And Bound ◽  
Operations Research ◽  
United States Of America ◽  
Applied Mathematics ◽  
Branch And Bound Algorithm ◽  
Theory Of Constraints ◽  
Engineering System

AbstractIn maximizing the profits to be obtained the company needs optimal production planning. The plan considers the resources of the company. PT XYZ is a furniture company. This research focuses on optimizing production planning on the manufacture of door products at PT. XYZ. There are several types of products issued in: D1 type door, D2 type door, D3 type door, and D4 type door. Production planning at PT. XYZ can be seen as an integer program model, which is a method related to optimizing resources to increase profits. Optimization is done by determining the amount of production for each type and each calculating existing resources. The solution search for this model is done by the Branch and Bound algorithm. Based on the calculation results using QM software for Windows, the amount corresponding to production is obtained by using Branches and Bound giving an increase of 36.5% compared to the acquisition of PT. XYZ before. Keywords: Branch and Bound Algorithms, Integer Programming,Optimization  AbstrakDalam memaksimalkan keuntungan yang akan diperoleh perusahaan perlu adanya perencanaan produksi yang optimal. Perencanaan tersebut mempertimbangkan ketersediaan sumber daya pada perusahaan. PT XYZ merupakan perusahaan yang bergerak di bidang furniture. Penelitian ini fokus kepada pengoptimalan perencanaan produksi pada pembuatan produk pintu di PT.XYZ. Terdapat beberapa jenis produk yang diproduksi di antaranya: Pintu tipe D1, Pintu tipe D2, Pintu tipe D3, dan Pintu tipe D4. Perencanaan produksi di PT.XYZ ini dapat dikatakan sebagai model program integer, karena semua variabel menghendaki hasilnya berupa bilangan bulat. Program tersebut berhubungan dengan pengoptimalan ketersediaan sumber daya bertujuan untuk memaksimalkan keuntungan. Pengoptimalan yang dilakukan yaitu dengan menentukan jumlah produksi untuk masing-masing tipe serta mempertimbangkan semua ketersediaan sumber daya yang ada. Pencarian solusi untuk model ini dilakukan dengan algoritma Branch and Bound. Berdasarkan hasil perhitungan menggunakan software QM for Windows, diketahui bahwa penentuan jumlah produksi dengan menggunakan algoritma Branch and Bound memberikan peningkatan keuntungan sebesar 36.5% dibandingkan dengan keuntungan PT.XYZ sebelumnya. Kata kunci: Optimasi, program integer, algoritma Branch and BoundReferensi[1]     Sofyan Assauri. Manajemen Produksi dan Operasi. Lembaga Penerbit FakultasEkonomi Universitas Indonesia. Jakarta. 2008.[2]      Winston, W. L. Operations Research: Applications and Algorithms. Edisi Keempat.Canada: Brooks/Cole-Thomson Learning. 2004.[3]      Akram, S. A., dan Jaya, A. I. Optimalisasi Produksi Roti dengan Menggunakan Metode Branch and Bound (Studi Kasus Pada Pabrik Roti Syariah Bakery, Jl. Maleo, Lrg.VIII No. 68 Palu). Jurnal Ilmiah Matematika dan Terapan, 13(2): 98-107. 2016.[4]      Jiao, H. W., dkk. An Effective Branch and Bound Algorithm for MinimaxLinear Fractional Programming. Journal of Applied Mathematics, Volume 2014: 8. 2014.[5]      Williams, H. P. The Problem with Integer Programming. Journal of Management Mathematics, 22(3): 213-230. 2011.[6]      Falani, I. Penentuan Nilai Parameter Metode Exponential Smoothing dengan Algoritma Genetik dalam Meningkatkan Akurasi Forecasting. Journal of Computer Engineering System and Science, 3(1): 14–16. 2018.[7]      Mehdizadeh, E., dan Jalili, S. An Algorithm Based on Theory of Constraints and Branch and Bound for Solving Integrated Product-Mix-Outsourcing Problem. Journal of Optimization in Industrial Engineering, 12(1): 167-172. 2019.[8]      Taylor, B. W. Introduction to Management Science. Edisi ke-11. United States of America: Prentice-Hall International, INC. 2013[9]      Puryani., dan Ristono, A. Penelitian Operasional. Yogyakarta: Graha Ilmu. 2012.[10]    Yusrah N. dkk. Implementasi Algoritma Branch and Bound Dalam Penentuan Jumlah Produksi Untuk Memaksimalkan Keuntungan. Jurnal String Vol. 3 No. 1 Agustus 2018. ISSN: 2527-9661[11]    Taha, H. A. Operations Research: An Introduction. Edisi ke-8. United States of America: Prentice-Hall International, INC. 2007.

scholarly journals Exact and Heuristic Approaches to the Maximum Capacity Representatives Problem

2018 ◽  
Author(s):  
Italos Estilon Da Silva De Souza ◽  
Mauro Roberto Costa Da Silva ◽  
Welverton Rodrigues Da Silva ◽  
Rafael C. S. Schoeury
Keyword(s):  
Integer Programming ◽  
Branch And Bound ◽  
Exact Method ◽  
Branch And Bound Algorithm ◽  
Maximum Capacity ◽  
Heuristic Approaches ◽  
Disjoint Sets

This paper approaches the problem of finding the system of representatives of a family of disjoint sets. To solve this problem, three methods were used: integer programming, branch-and-bound, and the BRKGA metaheuristic. We observed that, in randomly generated instances, the branch-and-bound algorithm was the best exact method but it was surpassed by BRKGA for large instances.

Imposing Contiguity Constraints in Political Districting Models

2021 ◽  
Author(s):  
Hamidreza Validi ◽  
Austin Buchanan ◽  
Eugene Lykhovyd
Keyword(s):  
Integer Programming ◽  
Operations Research ◽  
Programming Model ◽  
A Priori ◽  
Source Code ◽  
Branch And Cut ◽  
Computer Implementation ◽  
Census Tracts ◽  
Integer Programming Model ◽  
Political Districting

For nearly 60 years, operations research techniques have assisted in the creation of political districting plans, beginning with an integer programming model. This model, which seeks compactness as its objective, tends to generate districts that are contiguous, or nearly so, but provides no guarantee of contiguity. In the paper “Imposing contiguity constraints in political districting models” by Hamidreza Validi, Austin Buchanan, and Eugene Lykhovyd, the authors consider and analyze four different contiguity models (two old and two new). Their computer implementation can handle redistricting instances as large as Indiana (1,511 census tracts). Their fastest approach uses a branch-and-cut algorithm, where contiguity constraints are added in a callback. Critically, many variables can be fixed to zero a priori by Lagrangian arguments. All test instances and source code are publicly available.

Operations Research Problems for Airline Industry

2018 ◽  
pp. 163-176
Author(s):  
Mehmet Anil Sahin ◽  
Gulfem Tuzkaya
Keyword(s):  
Operations Research ◽  
Airline Industry ◽  
Network Models ◽  
Crew Scheduling ◽  
Fleet Assignment ◽  
Routing Problem ◽  
Aircraft Routing ◽  
Research Problems ◽  
Operations Research Applications

Maintenance routing is one of the most complicated problems of operations research applications for airline industry. In this study, airline industry operations' main applications and subjects are basically mentioned and literature is briefly reviewed. This study is conducted under the headings of; Fleet Assignment, Aircraft Routing, Maintenance Routing and Crew Scheduling. Additionally, network models are explained basically on an example flight program. This study's purpose is to be a guide for the new researchers of this area through operations research applications for airline industry and to introduce maintenance routing problem literature.

Latest Advances on Benders Decomposition

2018 ◽  
pp. 5411-5421 ◽  
Author(s):  
Antonios Fragkogios ◽  
Georgios K. D. Saharidis
Keyword(s):  
Mathematical Programming ◽  
Operations Research ◽  
Decomposition Method ◽  
Large Scale ◽  
Benders Decomposition ◽  
Information Science ◽  
Solution Process ◽  
Cpu Time ◽  
Mathematical Problems ◽  
Modern Economic

Operations Research and Mathematical Programming together with Information Science and Technology are tools used to solve various problems in the modern economic environment. This chapter addresses the Benders Decomposition method, which is used for the solution of problems of Operations Research. This method, applied to certain large-scale mathematical problems, can make their solution feasible (if they cannot be solved with another procedure) or can accelerate the solution process in terms of CPU time. The authors provide a thorough presentation of how the decomposition of a problem is made and the Benders algorithm is applied for its solution. Main purpose of this chapter is to analyze the recent studies that address the method's weaknesses and accelerate its application for the faster solution of mathematical problems. A large number of papers is presented and the contribution of each one of them to the improvement of the method is described.

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