International Journal of Industrial Engineering & Production Research

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An interactive heuristic approach can offer a practical solution to the problem of linear integer programming (LIP) by combining an optimization technique with the Decision Maker’s (DM) judgment and technical supervision. This is made possible using the concept of bicriterion linear programming (BLP) problem in an integer environment. This model proposes two bicriterion linear programs for identifying a feasible solution point when an initial infeasible solution point is provided by the decision maker or when the searching process leaves the region of feasibility seeking for a better pattern to improve the objective function. Instructions regarding the structure of such BLP problems are broadly discussed. This added property offers a great degree of flexibility to the decision making problem solving process.

The heuristic engine is comprised of four algorithms: Improve, Feasible, Leave, and Backtrack. In each iteration, when a selected algorithm has been terminated, the DM is presented with the results and asked to reevaluate the solution process by choosing an appropriate algorithm to follow. It is shown that the method converges to the optimal solution for most of the time. A solution technique for solving such a problem is introduced with sufficient details.

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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.