https://motivection.imeirs.org/index.php/motivection en-US wawan5527@gmail.com (Wawan Purwanto) agusbaharudin99@gmail.com (Agus Baharudin, M.Sc.) Fri, 30 Oct 2026 06:43:34 +0000 OJS 3.1.1.4 http://blogs.law.harvard.edu/tech/rss 60 https://motivection.imeirs.org/index.php/motivection/article/view/643 <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> Eri Wirdianto ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 https://motivection.imeirs.org/index.php/motivection/article/view/643 Fri, 30 Oct 2026 06:49:10 +0000