Location-routing problem with time-dependent demands

This study, by considering the time-dependent demand (TDD) characteristic, investigates the location-routing problem with time-dependent demands (LRPTDD) as an extension of the location-routing problem (LRP). The demand in each customer site is represented by a constant demand rate over a known production period. In the LRPTDD, the locations are selected, and the routes are constructed to pick up all the demands and minimize the total distance. The picked load depends on the vehicle arrival time at the site; thus, the ``time-dependency'' characteristic of the LRPTDD is based on the vehicle arrival time. A mixed-integer nonlinear programming (MINLP) formulation is presented. A simulated annealing (SA) algorithm for the LRPTDD is developed. The computational study demonstrates the competitiveness of the proposed SA heuristic against other well-known algorithms for LRPs, and most importantly, its effectiveness for the LRPTDD.