Minimum Number of Vehicles to Meet Dynamic Transportation Demand

The fundamental resources of a transportation network are channels, terminals, and vehicles. In practical situations, however, all of them do not always restrict flow volume, usually one of them constrains it. Channels restrict the flow in conventional network flow models. An example where terminal constraints are realized is a multistage inventory model. A new flow model is proposed where flow is limited by the number of vehicles. It is noted that the problem can be reduced to a minimum cost circulation problem when transportation demand is assumed to be time-independent. However, the minimum number of vehicles required to satisfy time-varying transportation demands is obtained. This problem is formulated as a transportation problem in linear programming. In the case where the number of terminals n = 2, however, the problem is not only solved analytically, but its solution also yields an interesting interpretation. Furthermore, the case of "compound operation" is investigated and discussed where vehicles are separated into two groups and operated among m terminals on a single path. The first group of vehicles shuttles between terminal 1 and terminal m. The second group shuttles between terminal p and terminal q, where 1 ≤ p < q ≤ m. Consequently, the minimum number of vehicles required for a compound operation is obtained.