Optimal ordering policy for newsvendor models with bidirectional changes in demand using expert judgment

Demand forecast is a critical determinant of order quantity under newsvendor problem (NVP) framework and warrants major revision in the event of changing circumstances or happening of some unforeseen events having potential to alter the demand. Retailers of single period products such as fashion apparels are required to pass their orders far ahead of selling seasons and apply preseason two-stage ordering procedure, where an initial order (first stage) is followed by a final confirmed order (second stage). The enterprise forecasting experts may get additional information related to the occurrence of some unforeseen events that may significantly impact the initial demand estimation. In this paper, the potential impact of such events is combined using a weight factor to obtain revised demand forecasts. In this context, this paper develops inventory models under NVP framework to determine the optimal order quantity and weight factor on the basis of revised forecasts. Considering the bidirectional changes in demand, we formulate a unique objective function that operates as a profit maximization function for the positive demand adjustment and turns into a cost minimization function for the negative demand adjustment. Models developed without constraints at first instance are extended subsequently by incorporating constraints of budget limits, storage space capacity and required service level. Near closed form expressions of decision variables for four demand distributions with multiplicative demand forms are presented. The results demonstrate economic benefits of using revised demand through models developed, negative impact of constraints, and role of demand distribution entropy in determining the order size and expected profit.