A rectilinear distance location–relocation problem with a probabilistic restriction: mathematical modelling and solution approaches

Abstract

In this study, we have considered a multi-period centre facility location–relocation problem in the presence of a probabilistic polyhedral barrier uniformly distributed on a horizontal barrier route in rectilinear plane. The objective function of this location–relocation problem is the minimisation of the cost of maximum expected rectilinear barrier distance from demand points to the new facility plus the relocation cost (i.e. a changeover cost at the beginning of each period) in the form of a mixed integer quadratic-constrained mathematical programming. The computational results show that the non-linear solver of commercial software LINGO is only effective in solving small-sized problems. A linear approximation for the system constraints is proposed so that a new mixed integer linear programming model is generated which is solvable via CPLEX optimisation software. Moreover, we proposed a problem decomposition procedure that reduces the multi-period problem into a number of single-period problems with some modifications. To show the efficiency of the model and solution methodologies, a broad range of numerical examples are performed. Results indicate that the developed problem decomposition procedure obtains the near-optimal solution comparatively with the results obtained from the non-linear solver of LINGO, and that the lower bound problem can be useful for large-sized problems in a reasonable time. Moreover, a practical case example to show the model validity in real world is solved and to reality check from practice, results are compared with the problem without barrier.

Keywords:

• location–relocation problem
• probabilistic polyhedral barrier
• linear approximation
• lower bound