Solving the optimal order quantity with unknown parameters for products with stock-dependent demand and variable holding cost rate

Solving the optimal order quantity for products with stock-dependent demand is a challenging task as both exact values of multiple parameters and complicated procedures are required. Motivated by this practical dilemma, this paper develops a new method to overcome the above-mentioned two challenges simultaneously. This new method, referred as two-stage AEOQ (adaptive economic order quantity) policy, includes the following two merits when managing products with stock-dependent demand and variable holding cost rate. First, it is feasible even when the values of underlying parameters are unknown. Second, it is easy-to-implement as decisions are made via adaptively recalibrating the inputs of classical EOQ formula by observable variables in the previous period. Theoretical analysis and numerical example show that this two-stage AEOQ policy could obtain the optimal order quantity. Moreover, this two-stage AEOQ policy is robust to parameter misestimation, and performs better than the traditional solution method when the underlying parameters are volatile. Finally, it is shown that this two-stage AEOQ policy could be further simplified when the fixed ordering cost is negligible. Therefore, this study provides a feasible order policy when the exact values of underlying parameters are unable to gain or when the economic environment is volatile.