Loss of customer goodwill in the uncapacitated lot-sizing problem

Loss of customer goodwill in uncapacitated single level lot-sizing is studied with a mixed integer programming model extending the well-known Wagner-Whitin (WW) model. The objective is to maximize profit from production and sales of a single good over a finite planning horizon. Demand, costs, and prices vary with time. Unsatisfied demand cannot be backordered. It leads to the immediate loss of profit from sales. Previous models augment the total cost objective by this lost profit. The difference of the proposed model is that unsatisfied demand in a given period causes the demand in the next period to shrink due to the loss of customer goodwill. A neighborhood search and restoration heuristic is developed that tries to adjust the optimal lot sizes of the original no-goodwill-loss model to the situation with goodwill loss. Its performance is compared with the Wagner-Whitin solution, and with the commercial solver CPLEX 8.1 on 360 test problems of various period lengths.