This paper considers finite horizon, multiperiod, sequential, minisum location-allocation problems on chain graphs and tree networks. The demand has both deterministic and probabilistic components, and increases dynamically from period to period. The problem is to locate one additional capacitated facility in each of the p specified periods, and to determine the service allocations of the facilities, in order to optimally satisfy the demand on the network. In this context, two types of objective criteria or location strategies are addressed. The first is a myopic strategy in which the present period cost is minimized sequentially for each period, and the second is a discounted present worth strategy. For the chain graph, a p-facility problem is analyzed under both these criteria, while for the tree graph, a 3-facility myopic problem, and a 2-facility discounted present worth problem are analyzed. All these problems are nonconvex, and a finite set of candidate solutions is specified which may be compared in order to deterime a global optimal solution.
