The continuous single-source capacitated multi-facility Weber problem with setup costs: formulation and solution methods
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The continuous single-source capacitated multi-facility Weber problem with setup costs: formulation and solution methods Chandra Ade Irawan1
· Said Salhi2 · Kusmaningrum Soemadi3
Received: 5 December 2018 / Accepted: 26 November 2019 © Springer Science+Business Media, LLC, part of Springer Nature 2019
Abstract The continuous single-source capacitated multi-facility Weber problem (SSCMFWP) where setup cost of opening facilities is taken into account is investigated. The aim is to locate a set of facilities on the plane, to define their respective capacities which can be linked to the configuration of the processing machines used, and to allocate customers to exactly one facility with the objective being the minimisation of the total transportation and setup costs. A new nonlinear mathematical model based on the SSCMFWP is introduced where Rectilinear and Euclidean distances are used. Efficient metaheuristic approaches based on Variable Neighbourhood Search and Simulated Annealing are also developed. The proposed metaheuristics incorporate an exact method and the commonly used Cooper’s alternate location-allocation method. We also constructed a new data set to reflect the characteristic of this particular location problem as no data set is available in the literature. Computational experiments show that the proposed metaheuristics generate interesting results for this class of continuous location problems. Keywords Location on the plane · Setup cost · Single-source · VNS · Simulated Annealing
1 Introduction The continuous single-source capacitated multi-facility Weber problem (SSCMFWP) is to seek the location of p facilities on the plane and the allocation of each customer to exactly
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Chandra Ade Irawan [email protected] Said Salhi [email protected] Kusmaningrum Soemadi [email protected]
1
Nottingham University Business School China, University of Nottingham Ningbo China, 199 Taikang East Road, Ningbo 315100, China
2
Centre for Logistics & Heuristic Optimization (CLHO), Kent Business School, University of Kent, Canterbury CT2 7FS, UK
3
Department of Industrial Engineering, Institut Teknologi Nasional, Bandung 40124, Indonesia
123
Journal of Global Optimization
one of the open facilities so that the sum of the total transportation costs is minimised. This problem is one of the variants of the Multi-facility Weber problem (MFWP) which is introduced by Cooper [1,2] who states that the objective function of MFWP is neither convex nor concave. Megiddo and Supowit [3] and Sherali and Nordai [4] reveal that the MFWP is NP-hard. The SSCMFWP is relatively more difficult to solve than its counterpart the MFWP. This is mainly due to the binary nature of the decision variables when allocating each customer to a single open facility. The SSCMFWP has several real life applications. For example, in a telecommunication network design, a user is assigned to a single base transceiver station while in the case of finding the location of oil drill platforms, each oil well has to be allocated to o
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