Notes on the single route lateral transhipment problem

Abstract

Previous research has analyzed deterministic and stochastic models of lateral transhipments between different retailers in a supply chain. In these models the analysis assumes given fixed transhipment costs and determines under which situations (magnitudes of excess supply and demand at various retailers) the transhipment is profitable. However, in reality, these depend on aspects like the distance between retailers or the transportation mode chosen. In many situations, combining the transhipments may save transportation costs. For instance, one or more vehicle routes may be used to redistribute the inventory of the potential pickup and delivery stations. This can be done in any sequence as long as the vehicle capacity is not violated and there is enough load on the vehicle to satisfy demand. The corresponding problem is an extension of the one-commodity pickup and delivery traveling salesman and the pickup and delivery vehicle routing problem. When ignoring the routing aspect and assuming given fixed costs, transhipment is only profitable if the quantities are higher than a certain threshold. In contrast to that, the selection of visited retailers is dependent on the transportation costs of the tour and therefore the selected retailers are interrelated. Hence the problem also has aspects of a (team) orienteering problem. The main contribution is the discussion of the tour planning aspects for lateral transhipments which may be valuable for in-house planning but also for price negotiations with external contractors. A mixed integer linear program for the single route and single commodity version is presented and an improved LNS framework to heuristically solve the problem is introduced. Furthermore, the effect of very small load capacity on the structure of optimal solutions is discussed.