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Time minimization delivery planning with the time-quantity dependence

Kowalik Przemysław, Stopka Ondrej

Zeszyty Naukowe. Transport / Politechnika Śląska

2025

z. 128

95--114

One of the classical problems in transportation planning is represented minimizing the maximal delivery time of a uniform commodity between sources and destinations, known as the Bottleneck Transportation Problem (BTP). It assumes that a fixed transportation time – independent of the quantity of the transported commodity – is assigned to each source-to-destination route. In some cases, however, the quantity of the transported commodity may affect the transportation time, e.g., because of the duration of loading/unloading the commodity to/from the vehicle. Extensions of the BTP as well as the closely related Total Time Minimization Transportation Problem (TTMTP) which include the linear time-quantity dependence of the delivery time are considered. Whereas similar optimization problems known in the literature are nonlinear, linear programming is used in this research. Linear optimization provides better performance of the optimization software in comparison with nonlinear optimization. The above fact is illustrated by improving solutions to the problems known in the literature. A detailed insight into the issue of the existence of integer optimal solutions and interpretations of optimal solutions is also provided.