International Journal of Industrial Engineering & Production Research

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Discrete facility location,   Distribution center,   Logistics,   Inventory policy,   Queueing theory,   Markov processes,

The distribution center location problem is a crucial question for logistics decision makers. The optimization of these decisions needs careful attention to the fixed facility costs, inventory costs, transportation costs and customer responsiveness. In this paper we study the location selection of a distribution center which satisfies demands with a M/M/1 finite queueing system plus balking and reneging. The distribution center uses one for one inventory policy, where each arrival demand orders a unit of product to the distribution center and the distribution center refers this demand to its supplier. The matrix geometric method is applied to model the queueing system in order to obtain the steady-state probabilities and evaluate some performance measures. A cost model is developed to determine the best location for the distribution center and its optimal storage capacity and a numerical example is presented to determine the computability of the results derived in this study .

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Network location models comprise one of the main categories of location models. These models have various applications in regional and urban planning as well as in transportation, distribution, and energy management. In a network location problem, nodes represent demand points and candidate locations to locate the facilities. If the links network is unchangeably determined, the problem will be an FLP (Facility Location Problem). However, if links can be added to the network at a reasonable cost, the problem will then be a combination of facility location and NDP (Network Design Problem) hence, called FLNDP (Facility Location Network Design Problem), a more general variant of FLP. In previous studies of this problem, capacity of facilities was considered to be a constraint while capacity of links was not considered at all. The proposed MIP model considers capacity of facilities and links as decision variables. This approach increases the utilization of facilities and links, and prevents the construction of links and location of facilities with low utilization. Furthermore, facility location cost (link construction cost) in the proposed model is supposed to be a function of the associated facility (link) capacity. Computational experiments as well as sensitivity analyses performed indicate the efficiency of the model.

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Location-allocation of facilities in service systems is an essential factor of their performance. One of the considerable situations which less addressed in the relevant literature is to balance service among customers in addition to minimize location-allocation costs. This is an important issue, especially in the public sector. Reviewing the recent researches in this field shows that most of them allocated demand customer to the closest facility. While, using probability rules to predict customer behavior when they select the desired facility is more appropriate. In this research, equitable facility location problem based on the gravity rule was investigated. The objective function has been defined as a combination of balancing and cost minimization, keeping in mind some system constraints. To estimate demand volume among facilities, utility function(attraction function) added to model as one constraint. The research problem is modeled as one mixed integer linear programming. Due to the model complexity, two heuristic and genetic algorithms have been developed and compared by exact solutions of small dimension problems. The results of numerical examples show the heuristic approach effectiveness with good-quality solutions in reasonable run time.

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This paper addresses a reliable facility location problem with considering facility capacity constraints. In reliable facility location problem some facilities may become unavailable from time to time. If a facility fails, its clients should refer to other facilities by paying the cost of retransfer to these facilities. Hence, the fail of facilities leads to disruptions in facility location decisions and this problem is an attempt to reducing the impact of these disruptions. In order to formulate the problem, a new mixed-integer nonlinear programming (MINLP) model with the objective of minimizing total investment and operational costs is presented. Due to complexity of MINLP model, two different heuristic procedures based on mathematical model are developed. Finally, the performance of the proposed heuristic methods is evaluated through executive numerical example. The numerical results show that the proposed heuristic methods are efficient and provide suitable solutions.