A restricted dynamic model for refuse collection network design in reverse logistics

• We define a restricted dynamic refuse collection network design problem in reverse logistics.
• A mathematical programming model is suggested for the new class of the network design problem.
• Two heuristics are developed, together with their performances, according to the characteristics of the problem.

This study considers the problem of determining the locations of collection points as well as the allocations of refuses at demand points to collection points while satisfying the capacity and the maximum allowable collection distance constraints at each collection point. To consider fluctuating demands commonly occurred in refuse collection systems, we consider a restricted dynamic version of the problem in which the locations are fixed, but the allocations are changed over a given planning horizon. The problem is formulated as an integer programming model for the objective of minimizing the sum of fixed costs to open collection points and variable costs to transport refuses between demand and collection points, and then, due to the complexity of the problem, two heuristic algorithms are suggested. The heuristics, called the multi-stage branch and bound and the modified drop heuristics in this paper, are based on the decomposition of the entire problem into the static location and the dynamic allocation sub-problems. Computational experiments were done on various test instances, and the results are reported.