We consider a class of location-allocation problems with immobile servers, stochastic demand and congestion that arises in several planning contexts: location of emergency medical clinics; preventive healthcare centers; refuse collection and disposal centers; stores and service centers; bank branches and automated teller machines; internet mirror sites; and distribution centers in supply chains. The problem seeks to simultaneously locate service facilities, equip them with appropriate capacities, and allocate customer demand to these facilities such that the total cost, which consists of the fixed cost of opening facilities with sufficient capacities, the access cost of users' travel to facilities, and the queuing delay cost, is minimized. Under Poisson user demand arrivals and general service time distributions, the problem is set up as a network of independent M/G/1 queues, whose locations, capacities and service zones need to be determined. The resulting mathematical model is a non-linear integer program. Using simple transformation and piecewise linear approximation, the model is linearized and solved to-optimality using a constraint generation method. Computational results are presented for instances up to 400 users, 25 potential service facilities, and 5 capacity levels with different coefficient of variation of service times and average queueing delay costs per customer. The results indicate that the proposed solution method is efficient in solving a wide range of problem instances.
The advent of Just-in-Time (JIT) and Group Technology philosophies has popularized Ushaped assembly lines, which help overcome many of the disadvantages, like line inflexibility, job monotony, large inventories, etc., typically associated with straight assembly lines. Although U-shaped layout has demonstrated it supremacy over the traditional straight layout, the problem of U-shaped assembly line balancing (ULB) is much more complex. The extant literature on ULB assumes that each assembly task requires a fixed (or no) equipment and a fixed number of workers. However, it is often desirable to reduce certain task times by assigning more workers or alternative equipments at a given workstation. The problem in such cases is to assign not only the task but also resource alternatives (number of workers and equipment type) to workstations. Research on such resource dependent U-shaped assembly line balancing (RDULB) is scarce. We address the problem of RDULB and propose a Simulated Annealing (SA) based metaheuristic, which gives optimal solution for most of the small-to-medium problem instances. For very large problems, while SA generates a good feasible solution within half an hour to 1.5 hours, Cplex is unable to find a single feasible solution even after 10 times the CPU time required by SA.
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Highlights• This paper studies a bilevel Hub Interdiction and trilevel Hub Protection Problem.• We study efficient methods to reduce the bilevel problem to single level.• We present different closest assignment constraints to enable this reduction.• We propose a Benders Decomposition method that solves large interdiction problems.
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