Metin Orbay, Necati Aras, Kuban Altınel · 2008
Abstract: In this paper, we study the capacitated squared Euclidean distance and general ℓp distance location-allocation problem in the continuous space which seeks the optimum locations of facilities and the allocation of their products to customers. We propose a mixed-integer programming formulation for the problem. The proposed formulation gives the optimum solution for the rectilinear distance version and approximate solutions for the general ℓp case for the original problem. While formulating the problem we use a cell based approach which uses a two-phase heuristic to discretise the continuous space. Computational results are provided for some test problems.
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Cristina Mora · AMS Campus - AlmaDL · 2017
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Naile Gulcan Yesilkokcen · MacSphere (McMaster University) · 1997
This study introduces a new model for a location distribution system, which is called the Supply Connected Location Allocation Problem (SCLAP). The problem involves locating p facilities with respect to n demand points and a supply plant. The supply plant originates all material in the system and distributes it to facilities along a route to be determined. Facilities then distribute the material to demand points via direct shipments. The problem minimizes the cost of shipping material from supply plant to all demand points via facilities. A description of the model is given and its subproblems are discussed in relation to well-known models in the literature. The problem is then investigated in three avenues: First, some special cases on which the problem is efficiently solvable are identified. For this, simple structured networks (e.g. a line and a tree) are considered. A dynamic programming solution procedure with polynomial time complexity is developed for the case on a line and it is extended to a special case of tree networks. Second, the problem is considered on general networks and a single assignment branch-and-bound algorithm is proposed to solve it. The algorithm is tested on randomly generated networks for relatively small sizes of problem instances. Discussions on the computational results are given with respect to computation time and the size of the branch and bound tree. Next, local search type heuristics are discussed briefly and two heuristic approaches are developed. Two versions of algorithms are constructed for each of those heuristics and they are tested on randomly generated networks, with respect to computation time and closeness to optimality (when optimal solutions were available) or to closeness to the best solution found. Finally, the study is concluded with recommendations for future research.
Cited by 0Open access
Gülcan N. Yesilkökcen · 1997
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Henrik Juel · Journal of Regional Science · 1981
Cited by 9
Anis D. Sherali, C. M. Shetty · A I I E Transactions · 1977
Abstract A convergent cutting plane algorithm is developed for the rectilinear distance location-allocation problem which is basically a nonconvex problem. The method is illustrated by a numerical example. Computational times are given both for small and large sized problems, and are compared with results reported in the literature.
Cited by 32
Dijin Gong, Mitsuo Gen, Genji Yamazaki et al. · 2002
We discuss an extension of the planar location-allocation model where obstacles exist and propose a hybrid evolutionary approach to solve this complex problem. We formulate the problem as a tri-level nonlinear mixed programming model. The hybrid evolutionary approach which hybridize evolutionary computing and traditional optimization techniques is shown effective in finding better solutions which may be regarded as global or near global solution by a case study problem.
Cited by 4
Wei Wang, Shuaian Wang, Lu Zhen et al. · Transportation Research Part E Logistics and Transportation Review · 2022
Cited by 24Open access
2008
One of the important logistic tasks is transfer of finished products from producers to customers. If there is a need to supply a large–scale area with large number of customers, it is disadvantageous to deliver products from the only central warehouse or direct from producers. It is suitable to build up local distribution warehouses. The promptitude and quality of customer services improve as the number of warehouses increases. Transport cost created by transfer of products from producers to customers is reduced too. On the other hand, both the fixed costs caused by the warehouse operation and cost of maintenance of greater current, buffer and protective stocks increase all at once. The contribution is concerned with a common case of a location-allocation problem, which involves both the location of distribution centres or warehouses and an allocation of customers to warehouses. Warehouses receive products from production plants and distribute them to customers such as retail or wholesale outlets. The well-known Weiszfeld algorithm [1] was adapted for sequentially increasing number of warehouses until adding another warehouse is advantageous from transport cost standpoint. The basic criterion for decision is minimization of freight cost, but increasing expenses of product stocks are considered as well. Distances between warehouses and customers are given by a suitable two-dimensional metric corresponding to the network of routes. Location of customers is given by means of either geographical information systems or GPS system. Key words. Multifacility location, location-allocation problem, conversion of coordinates AMS subject classifications. 90B05, 90B06, 90B80, 49M05 1. Introduction. Optimum
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Ted Eschenbach, Robert Carlson · Defense Technical Information Center (DTIC) · 1975
The problem is that of locating capacitated plants at some of a number of potential locations, so as to minimize the discounted sum of fixed costs incurred for open plants and variable supply costs. Both the costs and demands may vary arbitrarily over time. The results of optimal LIFO branch-and-bound and of heuristic algorithms using various branching variable selection rules and some new bounds are presented. (Author)
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Jack Brimberg, Zvi Drezner · IIE Transactions · 2015
We consider a continuous location problem for p concentric circles serving a given set of demand points. Each demand point is serviced by the closest circle. The objective is to minimize the sum of weighted distances between demand points and their closest circle. We analyze and solve the problem when demand is uniformly and continuously distributed in a disk and when a finite number of demand points are located in the plane. Heuristic and exact algorithms are proposed for the solution of the discrete demand problem. A much faster heuristic version of the exact algorithm is also proposed and tested. The exact algorithm solves the largest tested problem with 1000 demand points in about 3.5 hours. The faster heuristic version solves it in about 2 minutes.
Cited by 4
Xiaolan Xie, Vincent Augusto, Rodriguez-Verjan Carlos, Fernando et al. · HAL (Le Centre pour la Communication Scientifique Directe) · 2012
International audience
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Ricardo Ernst, David F. Pyke · RePEc: Research Papers in Economics
This article is concerned with the analysis of a squared‐Euclidean distance location‐allocation problem with balanced transportation constraints, where the costs are directly proportional to distances and the amount shipped. The problem is shown to be equivalent to maximizing a convex quadratic function subject to transportation constraints. A branch‐and‐bound algorithm is developed that utilizes a specialized, tight, linear programming representation to compute strong upper bounds via a Lagrangian relaxation scheme. These bounds are shown to substantially dominate several other upper bounds that are derived using standard techniques as problem size increases. The special structure of the transportation constraints is used to derive a partitioning scheme, and this structure is further exploited to devise suitable logical tests that tighten the bounds implied by the branching restrictions on the transportation flows. The transportation structure is also used to generate additional cut‐set inequalities based on a cycle prevention method which preserves a forest graph for any partial solution. Results of the computational experiments, and a discussion on possible extensions, are also presented.
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María Beatríz Bernábe Loranca, Rogelio González Velázquez, Martín Estrada Analco et al. · Applied Mathematics · 2014
The allocation of facilities and customers is a key problem in the design of supply chains of companies. In this paper, this issue is approached by partitioning the territory in areas where the distribution points are allocated. The demand is modelled through a set of continuous functions based on the population density of the geographic units of the territory. Because the partitioning problem is NP hard, it is necessary to use heuristic methods to obtain reliable solutions in terms of quality and response time. The Neighborhood Variable Search and Simulated Annealing heuristics have been selected for the study because of their proven efficiency in difficult combinatorial optimization problems. The execution time is the variable chosen for a factorial experimental design to determine the best-performing heuristics in the problem. In order to compare the quality of the solutions in the territorial partition, we have chosen the execution time as the common parameter to compare the two heuristics. At this point, we have developed a factorial statistical experimental design to select the best heuristic approaches to this problem. Thus, we generate a territorial partition with the best performing heuristics for this problem and proceed to the application of the location-allocation model, where the demand is modelled by a set of continuous functions based on the population density of the geographical units of the territory.
Cited by 2Open access
Hanif D. Sherali, Cihan H. Tuncbilek · Naval Research Logistics (NRL) · 1992
This article is concerned with the analysis of a squared-Euclidean distance location-allocation problem with balanced transportation constraints, where the costs are directly proportional to distances and the amount shipped. The problem is shown to be equivalent to maximizing a convex quadratic function subject to transportation constraints. A branch-and-bound algorithm is developed that utilizes a specialized, tight, linear programming representation to compute strong upper bounds via a Lagrangian relaxation scheme. These bounds are shown to substantially dominate several other upper bounds that are derived using standard techniques as problem size increases. The special structure of the transportation constraints is used to derive a partitioning scheme, and this structure is further exploited to devise suitable logical tests that tighten the bounds implied by the branching restrictions on the transportation flows. The transportation structure is also used to generate additional cut-set inequalities based on a cycle prevention method which preserves a forest graph for any partial solution. Results of the computational experiments, and a discussion on possible extensions, are also presented.
Cited by 58Open access
Non Linear Costs, Federico Malucelli, Patrick Soriano et al. · 2003
This paper deals with a planning problem arising in large logistics companies. The problem consists in defining the optimal number of depots, their location, and their size as well as the routing decisions. Economies of scale are present both in the transportation and in the depots operations. The paper proposes an exact algorithm and an e#cient heuristic based on the integration of tabu search and variable neighborhood search principles. Computational results obtained with real-life data and randomly generated but realistic instances prove the validity of the approaches.
Cited by 0
Masoud Mirzaei, Mahdi Bashiri · 2010
Hub networks are used to connect supply and demand nodes without establishing direct connections between any origin-destination nodes. The issue is to find optimum hub locations and allocate non-hub nods to them at minimum cost and/or travel time. Multiple allocation hub location problems deal with network in which non-hub nodes can be allocated to more than one hub. In this paper we use a multiple objective approach for hub location to minimize total cost of the networks regarding minimizing maximum travel time between nodes. There are capacity restrictions on hub facilities and arcs connecting the nodes. Finally the comparison between the proposed model and existing ones has been illustrated.
Cited by 4
Boliang Lin, Siqi Liu, Ruixi Lin et al. · Transportation Research Part E Logistics and Transportation Review · 2018
Cited by 19
Mahdi Bashiri, Khosro Hamidian · SHILAP Revista de lepidopterología · 2014
Hub location problem is further used in transportation and telecommunication networks (airlines, post delivery services, etc.) so origin-destination pairs, receive or send commodities via special facilities called Hub. Hub median problem with multiple allocation is an NP-hard problem which includes both locating hub facilities and allocating non-hub nodes to hubs as minimizes total transportation and location costs. In this paper, the hub median problem is considered in an environment which network flow varies during the time periods and the capacities of hubs and arcs are unlimited. Also opening and closing hubs in different periods of planning horizon are permitted. The model and the proposed algorithm for this problem were considered to Iran airlines network using real passenger flows data. Computational results state that the dynamic network compared with static model has lower cost and whatever the number of time periods in dynamic case increases, the cost will be reduced as well.
Cited by 1Open access
Dijin Gong, Mitsuo Gen, Genji Yamazaki et al. · Computers & Industrial Engineering · 1997
Cited by 69