DISPLAN: A multiproduct plant/warehouse location model with nonlinear inventory costs
Authors: Ballou Ronald H. 
Published: October 2002

DISPLAN is a large‐scale computer model used for the strategic planning of physical supply and distribution networks. This planning may involve the determination of the number, size, and location of plants, warehouses, inventories, terminals, and like facilities. Although a number of mathematical models exist to treat this problem, a unique feature of DISPLAN is its handling of nonlinear inventory costs.

The proper economic analysis of network designs requires that all relevant costs be balanced to achieve the minimum cost configuration of facilities. These costs include facility inbound and outbound transportation costs, warehouse storage and handling costs, order processing costs, facility fixed costs, and inventory carrying costs. Among these costs, it is vital that inventory carrying costs be accurately described since they are a major factor determining the number of facilities in a network. Due to the limitations of many solution methods, inventory carrying costs are neglected or they are treated as a linear function of the number of facilities in the network. However, if a company's inventory policy is based on the concept of the economic order quantity, then the relationship between the number of facilities and the total inventory in the network is nonlinear, commonly referred to as the inventory consolidation effect. Inaccurate representation of this effect through linear approximation can lead to an incorrect number of facilities in the network.

The methodology of DISPLAN is a heuristic procedure that uses the 3‐dimensional transportation algorithm of linear programming in an iterative fashion to converge on the minimum cost network configuration subject to facility capacity and customer service constraints. Warehouse fixed costs and inventory costs are recomputed on a per‐unit basis after each iteration, once the warehouse throughput has been established. These per‐unit costs can be added to the per‐unit transportation, handling, and order processing costs of the linear programming algorithm. The revised problem is resolved. The process is repeated until the best number, location, and size of warehouses are determined.

Because of the nonlinear inventory cost curve, the procedure may terminate at a local optimum on the total cost curve. The stopping rule that terminates the procedure when the change in total costs between successive iterations is less than a given percentage is not absolute. Additional iterations may be computed to help assure that the global optimum is realized.

Finally, a reconsideration routine is included in the computational procedure for those cases where fixed costs are a high proportion of total costs. The main heuristic may leave too many warehouses in the network and this routine explores a reduced number of warehouses. This assures that a substantial cost‐saving opportunity is not overlooked.

The DISPLAN methodology has been applied to many network configuration problems in a variety of industries. Typical of these are retailing, manufacturing, and spare parts distribution. The method has shown modest computer running times that are linear with problem size.