Planning horizon results from the dynamic warehouse location problem

This paper proposes a mixed integer linear programming model to determine which of a finite set of warehouse sites will be operating in each time period of a finite planning horizon. The model is general in the sense that it can reflect a number of acquisition alternatives-purchase, lease or rent. The principal assumptions of the model are: (a) Warehouses are assumed to have infinite capacity in meeting customer demand. (b) In each time period, any non-operating warehouse is a candidate for becoming operational, and likewise any operational warehouse is a candidate for disposal. (c) During a given time period, the fixed costs of becoming operational at a site are greater than the disposal value at that site to reflect the noncoverable costs involved in operating a warehouse. (d) During a time period the operation of a warehouse incurs overhead and maintenance costs as well as a depreciation in the disposal value. To solve the model, it is first simplified and a partial optimal solution is obtained by the iterative examination by both lower and upper bounds on the savings realized if a site is opened in a given time period. An attempt is made to fix each warehouse open or closed in each time period. The bounds are based on the delta and omega tests proposed by Efroymson and Ray and also by Khumawala with adjustment for changes in the value of the warehouse between the beginning and end of a time period. A complete optimal solution is obtained by solving the reduced model with Benders’ decomposition procedure. The optimal solution is then tested to determine which time periods contain ‘tentative’ decisions that may be affected by post horizon data by analyzing the relationship between the lower (or upper) bounds used in the model simplification time period. If the warehouse decisions made in a time period satisfy these relationships and are thus unaffected by data changes in subsequent time periods, then the decisions made in earlier time periods will also be unaffected by future changes.