Single Allocation Hub Location with Heterogeneous Economies of Scale

2021 ◽  
Author(s):  
Borzou Rostami ◽  
Masoud Chitsaz ◽  
Okan Arslan ◽  
Gilbert Laporte ◽  
Andrea Lodi
Keyword(s):  
Large Scale ◽  
Economies Of Scale ◽  
Piecewise Linear ◽  
Distance Matrix ◽  
Linear Functions ◽  
Mixed Integer ◽  
Hub Location ◽  
Solution Methods ◽  
Problem Instances ◽  
Single Allocation

The economies of scale in hub location is usually modeled by a constant parameter, which captures the benefits companies obtain through consolidation. In their article “Single allocation hub location with heterogeneous economies of scale,” Rostami et al. relax this assumption and consider hub-hub connection costs as piecewise linear functions of the flow amounts. This spoils the triangular inequality property of the distance matrix, making the classical flow-based model invalid and further complicates the problem. The authors tackle the challenge by building a mixed-integer quadratically constrained program and by developing a methodology based on constructing Lagrangian function, linear dual functions, and specialized polynomial-time algorithms to generate enhanced cuts. The developed method offers a new strategy in Benders-type decomposition through relaxing a set of complicating constraints in subproblems when such relaxation is tight. The results confirm the efficacy of the solution methods in solving large-scale problem instances.

scholarly journals Hub location problem in round-trip service applications

2020 ◽  
Author(s):  
Omar Kemmar ◽  
Karim Bouamrane ◽  
Shahin Gelareh
Keyword(s):  
Economies Of Scale ◽  
Location Problem ◽  
Service Providers ◽  
Real Life ◽  
Mixed Integer ◽  
Neighborhood Search ◽  
Hub Location ◽  
Service Networks ◽  
Hub Location Problem ◽  
Hub And Spoke

In this paper, we introduce a new hub-and-spoke structure for service networks based on round-trips as practiced by some transport service providers. This problem is a variant of Uncapacitated Hub Location Problem wherein the spoke nodes allocated to a hub node form round-trips (cycles) starting from and ending to the hub node. This problem is motivated by two real-life practices in logistics wherein  runaway  nodes and  runaway  connections with their associated economies of scale were foreseen to increase redundancy in the network. We propose a mixed integer linear programming mathematical model with exponential number of constraints. In addition to the separation routines for separating from among exponential constraints, we propose a hyper-heuristic based on reinforcement learning and its comparable counterpart as a variable neighborhood search. Our extensive computational experiments confirm efficiency of the proposed approaches.In this paper, we introduce a new hub-and-spoke structure for service networks based on round-trips as practiced by some transport service providers. This problem is a variant of Uncapacitated Hub Location Problem wherein the spoke nodes allocated to a hub node form round-trips (cycles) starting from and ending to the hub node. This problem is motivated by two real-life practices in logistics wherein  runaway  nodes and  runaway  connections with their associated economies of scale were foreseen to increase redundancy in the network. We propose a mixed integer linear programming mathematical model with exponential number of constraints. In addition to the separation routines for separating from among exponential constraints, we propose a hyper-heuristic based on reinforcement learning and its comparable counterpart as a variable neighborhood search. Our extensive computational experiments confirm efficiency of the proposed approaches.

scholarly journals A Combinatorial Approach for Small and Strong Formulations of Disjunctive Constraints

2019 ◽  
Vol 44 (3) ◽  
pp. 793-820 ◽  
Author(s):  
Joey Huchette ◽  
Juan Pablo Vielma
Keyword(s):  
Piecewise Linear ◽  
Expressive Power ◽  
Complete Characterization ◽  
Linear Functions ◽  
Mixed Integer ◽  
Ordered Sets ◽  
Special Ordered Sets ◽  
Disjunctive Constraints

A framework is presented for constructing strong mixed-integer programming formulations for logical disjunctive constraints. This approach is a generalization of the logarithmically sized formulations of Vielma and Nemhauser for special ordered sets of type 2 (SOS2) constraints, and a complete characterization of its expressive power is offered. The framework is applied to a variety of disjunctive constraints, producing novel small and strong formulations for outer approximations of multilinear terms, generalizations of special ordered sets, piecewise linear functions over a variety of domains, and obstacle avoidance constraints.

scholarly journals Designing a Supply Chain Network under the Risk of Disruptions

2012 ◽  
Vol 2012 ◽  
pp. 1-23 ◽  
Author(s):  
Armin Jabbarzadeh ◽  
Seyed Gholamreza Jalali Naini ◽  
Hamid Davoudpour ◽  
Nader Azad
Keyword(s):  
Supply Chain ◽  
Supply Chain Design ◽  
Mixed Integer ◽  
Nonlinear Program ◽  
Supply Chain Network ◽  
Large Problem ◽  
Solution Methods ◽  
Total Profit ◽  
Order Quantities ◽  
Problem Instances

This paper studies a supply chain design problem with the risk of disruptions at facilities. At any point of time, the facilities are subject to various types of disruptions caused by natural disasters, man-made defections, and equipment breakdowns. We formulate the problem as a mixed-integer nonlinear program which maximizes the total profit for the whole system. The model simultaneously determines the number and location of facilities, the subset of customers to serve, the assignment of customers to facilities, and the cycle-order quantities at facilities. In order to obtain near-optimal solutions with reasonable computational requirements for large problem instances, two solution methods based on Lagrangian relaxation and genetic algorithm are developed. The effectiveness of the proposed solution approaches is shown using numerical experiments. The computational results, in addition, demonstrate that the benefits of considering disruptions in the supply chain design model can be significant.

scholarly journals The Unit Re-Balancing Problem

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3205
Author(s):  
Robin Dee ◽  
Armin Fügenschuh ◽  
George Kaimakamis
Keyword(s):  
Numerical Solutions ◽  
Piecewise Linear ◽  
Geographic Area ◽  
Piecewise Linear Function ◽  
Linear Functions ◽  
Mixed Integer ◽  
Mixed Integer Linear Program ◽  
Commodity Flow ◽  
The Status ◽  
Status Assessment

We describe the problem of re-balancing a number of units distributed over a geographic area. Each unit consists of a number of components. A value between 0 and 1 describes the current rating of each component. By a piecewise linear function, this value is converted into a nominal status assessment. The lowest of the statuses determines the efficiency of a unit, and the highest status its cost. An unbalanced unit has a gap between these two. To re-balance the units, components can be transferred. The goal is to maximize the efficiency of all units. On a secondary level, the cost for the re-balancing should be minimal. We present a mixed-integer nonlinear programming formulation for this problem, which describes the potential movement of components as a multi-commodity flow. The piecewise linear functions needed to obtain the status values are reformulated using inequalities and binary variables. This results in a mixed-integer linear program, and numerical standard solvers are able to compute proven optimal solutions for instances with up to 100 units. We present numerical solutions for a set of open test instances and a bi-criteria objective function, and discuss the trade-off between cost and efficiency.

scholarly journals Solving balanced multi-weighted attribute set partitioning problem with variable neighborhood search

Filomat ◽  
2019 ◽  
Vol 33 (9) ◽  
pp. 2875-2891
Author(s):  
Dusan Dzamic ◽  
Bojana Cendic ◽  
Miroslav Maric ◽  
Aleksandar Djenic
Keyword(s):  
Local Search ◽  
Large Scale ◽  
Variable Neighborhood Search ◽  
Heuristic Method ◽  
Set Partitioning ◽  
Mixed Integer ◽  
Neighborhood Search ◽  
Computationally Efficient ◽  
Local Search Procedure ◽  
Problem Instances

This paper considers the Balanced Multi-Weighted Attribute Set Partitioning (BMWASP) problem which requires finding a partition of a given set of objects with multiple weighted attributes into a certain number of groups so that each attribute is evenly distributed amongst the groups. Our approach is to define an appropriate criterion allowing to compare the degree of deviation from the ?perfect balance? for different partitions and then produce the partition that minimizes this criterion. We have proposed a mathematical model for the BMWASP and its mixed-integer linear reformulation. We evaluated its efficiency through a set of computational experiments. To solve instances of larger problem dimensions, we have developed a heuristic method based on a Variable Neighborhood Search (VNS). A local search procedure with efficient fast swap-based local search is implemented in the proposed VNS-based approach. Presented computational results show that the proposed VNS is computationally efficient and quickly reaches all optimal solutions for smaller dimension instances obtained by exact solver and provide high-quality solutions on large-scale problem instances in short CPU times.

scholarly journals Analysis of limited-memory BFGS on a class of nonsmooth convex functions

2020 ◽  
Author(s):  
Azam Asl ◽  
Michael L Overton
Keyword(s):  
Gradient Method ◽  
Large Scale ◽  
Line Search ◽  
Piecewise Linear ◽  
Fixed Number ◽  
Linear Functions ◽  
Limited Memory ◽  
Nonsmooth Problems ◽  
Wolfe Line Search ◽  
Large Scale Unconstrained Optimization

Abstract The limited-memory BFGS (Broyden-Fletcher-Goldfarb-Shanno) method is widely used for large-scale unconstrained optimization, but its behavior on nonsmooth problems has received little attention. L-BFGS (limited memory BFGS) can be used with or without ‘scaling’; the use of scaling is normally recommended. A simple special case, when just one BFGS update is stored and used at every iteration, is sometimes also known as memoryless BFGS. We analyze memoryless BFGS with scaling, using any Armijo–Wolfe line search, on the function $f(x) = a|x^{(1)}| + \sum _{i=2}^{n} x^{(i)}$, initiated at any point $x_0$ with $x_0^{(1)}\not = 0$. We show that if $a\ge 2\sqrt{n-1}$, the absolute value of the normalized search direction generated by this method converges to a constant vector, and if, in addition, $a$ is larger than a quantity that depends on the Armijo parameter, then the iterates converge to a nonoptimal point $\bar x$ with $\bar x^{(1)}=0$, although $f$ is unbounded below. As we showed in previous work, the gradient method with any Armijo–Wolfe line search also fails on the same function if $a\geq \sqrt{n-1}$ and $a$ is larger than another quantity depending on the Armijo parameter, but scaled memoryless BFGS fails under a weaker condition relating $a$ to the Armijo parameter than that implying failure of the gradient method. Furthermore, in sharp contrast to the gradient method, if a specific standard Armijo–Wolfe bracketing line search is used, scaled memoryless BFGS fails when $a\ge 2 \sqrt{n-1}$regardless of the Armijo parameter. Finally, numerical experiments indicate that the results may extend to scaled L-BFGS with any fixed number of updates $m$, and to more general piecewise linear functions.

scholarly journals Finding p-Hub Median Locations: An Empirical Study on Problems and Solution Techniques

2017 ◽  
Vol 2017 ◽  
pp. 1-23 ◽  
Author(s):  
Xiaoqian Sun ◽  
Weibin Dai ◽  
Yu Zhang ◽  
Sebastian Wandelt
Keyword(s):  
Genetic Algorithms ◽  
Empirical Study ◽  
Low Complexity ◽  
Location Problems ◽  
Hub Location ◽  
Allocation Problems ◽  
Solution Methods ◽  
Problem Formulations ◽  
Single Allocation ◽  
Solution Techniques

Hub location problems have been studied by many researchers for almost 30 years, and, accordingly, various solution methods have been proposed. In this paper, we implement and evaluate several widely used methods for solving five standard hub location problems. To assess the scalability and solution qualities of these methods, three well-known datasets are used as case studies: Turkish Postal System, Australia Post, and Civil Aeronautics Board. Classical problems in small networks can be solved efficiently using CPLEX because of their low complexity. Genetic algorithms perform well for solving three types of single allocation problems, since the problem formulations can be neatly encoded with chromosomes of reasonable size. Lagrangian relaxation is the only technique that solves reliable multiple allocation problems in large networks. We believe that our work helps other researchers to get an overview on the best solution techniques for the problems investigated in our study and also stipulates further interest on cross-comparing solution techniques for more expressive problem formulations.

scholarly journals Selecting Large Portfolios of Social Projects in Public Organizations

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Igor Litvinchev ◽  
Fernando Lopez-Irarragorri ◽  
Nancy Maribel Arratia-Martínez ◽  
José Antonio Marmolejo
Keyword(s):  
Mixed Integer Linear Programming ◽  
Large Scale ◽  
Programming Model ◽  
Public Organizations ◽  
Mixed Integer ◽  
Scale Problem ◽  
Integer Linear Programming Model ◽  
Problem Instances ◽  
Funding Resource ◽  
Selection Of

We address the portfolio selection of social projects in public organizations considering interdependencies (synergies) affecting project funds requirements and tasks. A mixed integer linear programming model is proposed incorporating the most relevant aspects of the problem found in the literature. The model supports both complete (all or nothing) and partial (a certain amount from a given interval of funding) resource allocation policies. Numerical results for large-scale problem instances are presented.

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