https://motivection.imeirs.org/index.php/motivection/issue/feed 2026-10-30T06:49:10+00:00 Wawan Purwanto wawan5527@gmail.com Open Journal Systems https://motivection.imeirs.org/index.php/motivection/article/view/643 2026-10-30T06:49:10+00:00 Eri Wirdianto eri_wirdianto@eng.unand.ac.id

<p>Distributors that serve many customers with strict delivery time windows over several days must decide which vehicle serves each customer, on which trip, and on which day. This study formulates a mixed-integer linear programming (MILP) model for the multi-trip multi-period vehicle routing problem with hard time windows (MTMPVRPTW) by integrating multi-trip and multi-period formulations to minimize transportation cost under vehicle-capacity, route-duration, and time-window constraints. The model was validated conceptually against the operations of a snack distributor in Padang, Indonesia, verified through dimensional analysis, and tested in LINGO on three reduced instances with five, eight, and ten customers served by two 50-bale vehicles. It generated one route in one day, three routes including a second trip within one day, and four routes over two days, respectively, with every route within capacity. Computation time rose from 2 s to 30 min 11 s, indicating that larger instances require heuristic solution approaches.</p>

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