Vehicle Routing Problem with Time Windows in Agricultural Food Sector: Mathematical Modeling Example on Taşköprü Garlic

Abstract

Logistics plays a critically important role in establishing a sustainable supply chain in the agricultural food sector. This study examines the logistical optimization problem faced by a garlic-producing company in Taşköprü district of Kastamonu for the monthly distribution of 24 tons of products to 18 different cities. In the research, a detailed mathematical model was developed for the time-windowed vehicle routing problem (TWVRP) and this model was solved using GAMS Studio (49.6.1) software. The developed model simultaneously optimizes different acceptance hours at each delivery point, 4-ton vehicle capacity constraints, and multi-point distribution requirements. The model solution reached the optimal result after a computation time of 14 hours and 38 minutes, determining a total of 7 different routes. According to the obtained findings, the total distribution cost was determined as 161.612,88 TL. This means that the average distribution cost per kilogram is 6,73 TL. In terms of effective vehicle capacity utilization, 100% capacity was achieved on 57% of the routes, while 87.5% capacity utilization was achieved on 3 routes, and 25% capacity utilization was achieved on the remaining 1 route.These routes, covering a total distance of 10.802 km, meet all time window constraints, and with the longest route being 2,154 km, they remain within legal working time limits with two drivers. When examining the cost structure, driver costs constitute 40.1% of the total cost (64.818 TL), fuel expenses account for 38.5% (62.225,28 TL), and vehicle depreciation costs represent 21.4% (34.569,60 TL). It has been determined that the proposed model provides an applicable solution for systematic planning of time-critical deliveries in the agricultural food sector and offers a scalable optimization tool for similar enterprises.