scholarly journals Scenario Grouping and Decomposition Algorithms for Chance-Constrained Programs

2020 ◽  
Author(s):  
Yan Deng ◽  
Huiwen Jia ◽  
Shabbir Ahmed ◽  
Jon Lee ◽  
Siqian Shen
Keyword(s):  
Operations Research ◽  
Branch And Cut ◽  
Mixed Integer ◽  
Decomposition Algorithms ◽  
Linear Programs ◽  
Solution Quality ◽  
Bilevel Program ◽  
Research Problems ◽  
Optimal Grouping

A lower bound for a finite-scenario-based chance-constrained program is the quantile value corresponding to the sorted optimal objective values of scenario subproblems. This quantile bound can be improved by grouping subsets of scenarios at the expense of solving larger subproblems. The quality of the bound depends on how the scenarios are grouped. In this paper, we formulate a mixed-integer bilevel program that optimally groups scenarios to tighten the quantile bounds. For general chance-constrained programs, we propose a branch-and-cut algorithm to optimize the bilevel program, and for chance-constrained linear programs, a mixed-integer linear-programming reformulation is derived. We also propose several heuristics for grouping similar or dissimilar scenarios. Our computational results demonstrate that optimal grouping bounds are much tighter than heuristic bounds, resulting in smaller root-node gaps and better performance of scenario decomposition for solving chance-constrained 0-1 programs. Also, the optimal grouping bounds can be greatly strengthened using larger group size. Summary of Contribution: Chance-constrained programs are in general NP-hard but widely used in practice for lowering the risk of undesirable outcomes during decision making under uncertainty. Assuming finite scenarios of uncertain parameter, chance-constrained programs can be reformulated as mixed-integer linear programs with binary variables representing whether or not the constraints are satisfied in corresponding scenarios. A useful quantile bound for solving chance-constrained programs can be improved by grouping subsets of scenarios at the expense of solving larger subproblems. In this paper, we develop algorithms for optimally and heuristically grouping scenarios to tighten the quantile bounds. We aim to improve both the computation and solution quality of a variety of chance-constrained programs formulated for different Operations Research problems.

scholarly journals Operations Research Problems and Data Envelopment Analysis in Agricultural Land Processing – A Review

2020 ◽  
Author(s):  
Bisera Andrić Gušavac ◽  
Gordana Savić
Keyword(s):  
Data Envelopment Analysis ◽  
Operations Research ◽  
Agricultural Land ◽  
Linear Optimization ◽  
Specific Area ◽  
Mixed Integer ◽  
Data Envelopment ◽  
Detailed Review ◽  
Methods And Techniques ◽  
Research Problems

Research Question: This paper aims at specifying the contribution of operations research (OR) methods and techniques to agricultural land processing. Motivation: Agricultural production is performed on an agricultural land, which has to be exploited in the best possible way, given the increasing human population and the limited availability of the land. Considering the importance of this issue, a large number of research studies dealing with problems in agriculture can be found in the literature, and many of these problems are solved by OR methods and techniques. However, to our knowledge, there are no review papers that deal with this specific area, so the main motivation is to provide a detailed review of selected OR methods application in the agricultural land processing area. Idea: The core idea behind this research is to perceive a real impact of OR methods and techniques implementation in the agricultural land processing. The research is based on detailed literature review for the period 2014-2019 and performed statistics involving publication by year, publication by journal and statistics involving keywords in articles. Data: The review was conducted using online repositories of the papers published in SCI and SCIe journals with impact factors in the period from 2014-2019. Tools: Analyzed papers are divided into three groups according to the OR method applied: linear optimization problems, DEA method and other OR methods (non linear, multicriteria, mixed integer programming, dynamic programming). Papers within the groups are analyzed according to the type of problems solved. Statistical analyses of all collected data were used to get a good insight into the applications of operations research problems and data envelopment analysis in agricultural land processing. Findings: The number of published papers in this specific area has a growing trend over the observed years (with some minor decrease in 2016 and 2019 in comparison with the previous year). All of the articles are related to specific application of the given methods to solving problems in the agricultural land processing, and this is the reason for many different keywords appearing in the articles. Some very important keywords such as “operations research” or “OR” does not appear in any article as a keyword. Inclusion of such common keywords may result in a faster search in repositories of all articles. Contribution: The primary contribution of this paper is a detailed review of application of linear optimization, data envelopment analysis and other OR methods in agricultural land processing in the period 2014-2019.

scholarly journals Consistency Cuts for Dantzig-Wolfe Reformulations

2022 ◽  
Author(s):  
Jens Vinther Clausen ◽  
Richard Lusby ◽  
Stefan Ropke
Keyword(s):  
Valid Inequalities ◽  
Branch And Cut ◽  
Mixed Integer ◽  
Linear Programming Relaxation ◽  
Linear Programs ◽  
Integer Programs ◽  
New Family ◽  
Integer Linear Programs ◽  
Integer Solutions ◽  
Online Library

A New Family of Valid-Inequalities for Dantzig-Wolfe Reformulation of Mixed Integer Linear Programs In “Consistency Cuts for Dantzig-Wolfe Reformulation,” Jens Vinther Clausen, Richard Lusby, and Stefan Ropke present a new family of valid inequalities to be applied to Dantzig-Wolfe reformulations with binary linking variables. They show that, for Dantzig-Wolfe reformulations of mixed integer linear programs that satisfy certain properties, it is enough to solve the linear programming relaxation of the Dantzig-Wolfe reformulation with all consistency cuts to obtain integer solutions. An example of this is the temporal knapsack problem; the effectiveness of the cuts is tested on a set of 200 instances of this problem, and the results are state-of-the-art solution times. For problems that do not satisfy these conditions, the cuts can still be used in a branch-and-cut-and-price framework. In order to show this, the cuts are applied to a set of generic mixed linear integer programs from the online library MIPLIB. These tests show the applicability of the cuts in general.

Operations Research on the Female Village-Based Family Planning Worker Program of Pakistan

1998 ◽  
Vol 18 (3) ◽  
pp. 283-305
Author(s):  
Louisiana Lush ◽  
George P. Cernada ◽  
A. K. Ubaidur Rob ◽  
Mohammed Shafiq Arif ◽  
Minhaj Ul Haque ◽  
...  
Keyword(s):  
Family Planning ◽  
Operations Research ◽  
Technical Assistance ◽  
Field Studies ◽  
Family Planning Services ◽  
Training And Supervision ◽  
The Government ◽  
And Training ◽  
Broad Program

This article presents the results of a number of operations research studies (OR) of family planning services provided by a new cadre of female village-based family planning workers in Punjab Province, Pakistan. This cadre of workers, recruited nationwide, have been trained to visit women in their villages to provide information and family planning services. The studies were conducted as part of a broad program of technical assistance to the Government of Pakistan. Surveys investigated the quality of their training as well as attitudes among clients to the new program. They found that the program is developing well but there is room for improvement, particularly in counseling and training. Additional field studies are ongoing and recommendations for change have been incorporated in training and supervision. The program is expanding on a national scale.

scholarly journals Joint optimization of computing ratio and access points’ density for mixed mobile edge/cloud computing

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Tianqi Jing ◽  
Shiwen He ◽  
Fei Yu ◽  
Yongming Huang ◽  
Luxi Yang ◽  
...  
Keyword(s):  
Cloud Computing ◽  
Coverage Probability ◽  
Optimization Problem ◽  
Mobile Cloud Computing ◽  
Low Complexity ◽  
Mixed Integer ◽  
Joint Optimization ◽  
Mobile Cloud ◽  
Convex Problem

AbstractCooperation between the mobile edge computing (MEC) and the mobile cloud computing (MCC) in offloading computing could improve quality of service (QoS) of user equipments (UEs) with computation-intensive tasks. In this paper, in order to minimize the expect charge, we focus on the problem of how to offload the computation-intensive task from the resource-scarce UE to access point’s (AP) and the cloud, and the density allocation of APs’ at mobile edge. We consider three offloading computing modes and focus on the coverage probability of each mode and corresponding ergodic rates. The resulting optimization problem is a mixed-integer and non-convex problem in the objective function and constraints. We propose a low-complexity suboptimal algorithm called Iteration of Convex Optimization and Nonlinear Programming (ICONP) to solve it. Numerical results verify the better performance of our proposed algorithm. Optimal computing ratios and APs’ density allocation contribute to the charge saving.

scholarly journals Bi-objective design-for-control of water distribution networks with global bounds

2021 ◽  
Author(s):  
Aly-Joy Ulusoy ◽  
Filippo Pecci ◽  
Ivan Stoianov
Keyword(s):  
Water Distribution ◽  
Distribution Networks ◽  
Water Distribution Networks ◽  
Mixed Integer ◽  
Global Optimality ◽  
Linear Programs ◽  
Design For Control ◽  
Non Linear ◽  
Feasible Solutions

AbstractThis manuscript investigates the design-for-control (DfC) problem of minimizing pressure induced leakage and maximizing resilience in existing water distribution networks. The problem consists in simultaneously selecting locations for the installation of new valves and/or pipes, and optimizing valve control settings. This results in a challenging optimization problem belonging to the class of non-convex bi-objective mixed-integer non-linear programs (BOMINLP). In this manuscript, we propose and investigate a method to approximate the non-dominated set of the DfC problem with guarantees of global non-dominance. The BOMINLP is first scalarized using the method of $$\epsilon $$ ϵ -constraints. Feasible solutions with global optimality bounds are then computed for the resulting sequence of single-objective mixed-integer non-linear programs, using a tailored spatial branch-and-bound (sBB) method. In particular, we propose an equivalent reformulation of the non-linear resilience objective function to enable the computation of global optimality bounds. We show that our approach returns a set of potentially non-dominated solutions along with guarantees of their non-dominance in the form of a superset of the true non-dominated set of the BOMINLP. Finally, we evaluate the method on two case study networks and show that the tailored sBB method outperforms state-of-the-art global optimization solvers.

scholarly journals Quality and Operations Management in Food Supply Chains: A Literature Review

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Yong He ◽  
Hongfu Huang ◽  
Dong Li ◽  
Chunming Shi ◽  
Sarah J. Wu
Keyword(s):  
Literature Review ◽  
Supply Chains ◽  
Operations Research ◽  
Operations Management ◽  
Food Supply ◽  
Research Field ◽  
Food Supply Chains ◽  
The Past ◽  
Starting Point

We present a literature review on quality and operations management problems in food supply chains. In food industry, the quality of the food products declines over time and should be addressed in the supply chain operations management. Managing food supply chains with operations management methods not only generates economic benefit, but also contributes to environmental and social benefits. The literature on this topic has been burgeoning in the past few years. Since 2005, more than 100 articles have been published on this topic in major operations research and management science journals. In this literature review, we concentrate on the quantitative models in this research field and classify the related articles into four categories, that is, storage problems, distribution problems, marketing problems, and food traceability and safety problems. We hope that this review serves as a reference for interested researchers and a starting point for those who wish to explore it further.

Analysis of Solution Quality of Multiobjective Evolutionary Algorithms for Service Restoration in Distribution Systems

2017 ◽  
Vol 28 (6) ◽  
pp. 796-805
Author(s):  
Danilo Sipoli Sanches ◽  
Marcelo Favoretto Castoldi ◽  
João Bosco Augusto London ◽  
Alexandre Cláudio Botazzo Delbem
Keyword(s):  
Evolutionary Algorithms ◽  
Distribution Systems ◽  
Multiobjective Evolutionary Algorithms ◽  
Solution Quality ◽  
Service Restoration

Modeling and scheduling hybrid open shops for makespan minimization

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Kennedy Anderson Guimarães de Araújo ◽  
Tiberius Oliveira e Bonates ◽  
Bruno de Athayde Prata
Keyword(s):  
Programming Model ◽  
Computing Time ◽  
Iterated Local Search ◽  
Mixed Integer ◽  
Scheduling Problems ◽  
Priority Rules ◽  
Production Flow ◽  
Solution Quality ◽  
Content Type ◽  
Constructive Heuristics

Purpose This study aims to address the hybrid open shop problem (HOSP) with respect to the minimization of the overall finishing time or makespan. In the HOSP, we have to process n jobs in stages without preemption. Each job must be processed once in every stage, there is a set of mk identical machines in stage k and the production flow is immaterial. Design/methodology/approach Computational experiments carried out on a set of randomly generated instances showed that the minimal idleness heuristic (MIH) priority rule outperforms the longest processing time (LPT) rule proposed in the literature and the other proposed constructive methods on most instances. Findings The proposed mathematical model outperformed the existing model in the literature with respect to computing time, for small-sized instances, and solution quality within a time limit, for medium- and large-sized instances. The authors’ hybrid iterated local search (ILS) improved the solutions of the MIH rule, drastically outperforming the models on large-sized instances with respect to solution quality. Originality/value The authors formalize the HOSP, as well as argue its NP-hardness, and propose a mixed integer linear programming model to solve it. The authors propose several priority rules – constructive heuristics based on priority measures – for finding feasible solutions for the problem, consisting of adaptations of classical priority rules for scheduling problems. The authors also propose a hybrid ILS for improving the priority rules solutions.

scholarly journals ON SAMPLING BASED METHODS FOR THE DUBINS TRAVELING SALESMAN PROBLEM WITH NEIGHBORHOODS

2015 ◽  
Vol 2 (2) ◽  
pp. 57-61
Author(s):  
Petr Váňa ◽  
Jan Faigl
Keyword(s):  
Path Planning ◽  
Traveling Salesman Problem ◽  
Traveling Salesman ◽  
Computational Time ◽  
Solution Quality ◽  
Goal Region ◽  
Dubins Vehicle ◽  
Proposed Modification ◽  
Dubins Traveling Salesman Problem

In this paper, we address the problem of path planning to visit a set of regions by Dubins vehicle, which is also known as the Dubins Traveling Salesman Problem Neighborhoods (DTSPN). We propose a modification of the existing sampling-based approach to determine increasing number of samples per goal region and thus improve the solution quality if a more computational time is available. The proposed modification of the sampling-based algorithm has been compared with performance of existing approaches for the DTSPN and results of the quality of the found solutions and the required computational time are presented in the paper.

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