Optimal single ordering policy with multiple delivery modes and Bayesian information updates

We investigate in this paper a retailer's optimal single ordering policy with multiple delivery modes. Due to the existence of different delivery modes, the unit delivery cost (and hence the product cost) is formulated as a decreasing function of the lead-time. Market information can be collected in the earlier stages and used to update the demand forecast by using a Bayesian approach. The trade-off between ordering earlier or later is evident. The former enjoys a lower product cost but suffers a less accurate demand forecast. The latter pays a higher product cost, but benefits from a lower uncertainty in the demand forecast. In this paper, a multi-stage dynamic optimization problem is formulated and the optimal ordering policy is derived using dynamic programming. The characteristics of the ordering policy are investigated and the variance of profit associated with the ordering decision is discussed. Numerical analyses through simulation experiments are carried out to gain managerial insights. Implementation tips are also proposed.