Consistent Time Window Assignments for Stochastic Multi-Depot Multi-Commodity Pickup and Delivery

We present the problem of assigning consistent time windows (TWs) for the collection of multiple fresh products from local farmers and delivering them to distribution centers for consolidation and further distribution in a short agri-food supply chain. TWs are assigned for a longer horizon in which daily demand is uncertain. Consequently, we formulate the problem as a two-stage stochastic program. In the first stage, the TWs are assigned from a set of discrete TWs to farmers. In the second stage, which represents a daily realization of demand, the collection routes are planned by solving yet a newly introduced multi-depot, multi-commodity team orienteering problem with soft TWs. The objective is to minimize the overall travel time and the TW violations. To solve our problem, we combine scenario reduction techniques with a (heuristic) progressive hedging algorithm to decompose the deterministic equivalent problem into scenario subproblems and guide the scenario solutions toward consensus TWs. We show the value of considering demand uncertainty over solving the deterministic expected value problem and the superiority of our approach over benchmarks when it comes to reducing the routing cost as well as the inconvenience for farmers. Funding: This work was supported by Deutsche Forschungsgemeinschaft [Grant 444657906]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2024.0720 .