Evaluating supply chain flexibility with order quantity constraints and lost sales

In a flexible supply chain buyers and suppliers are willing to accommodate the uncertainties and variations in each other's businesses. In many instances the buyer may prefer to use supply flexibility, as opposed to an inventory holding strategy, to counter demand uncertainty. We consider the case where the buyer releases a fixed period replenishment order to the supplier under a supply contract defined by three parameters: (i) supply price per unit (ii) minimum order quantity and (iii) order quantity reduction penalty. Following a demand drop the buyer therefore has two flexibility options in the order cycle: (i) to place an order less than the supplier specified minimum order quantity and pay the associated penalty, or (ii) place no order and lose the sales for the current period. There is no penalty for not placing an order. A key buyer decision then is Q_lost, the order or replenishment quantity level below which no order is placed and the sales are lost. A model for deriving the expected supply and lost sales cost as a function of Q_lost is presented, and it is shown that the optimal value of Q_lost is the inflexion point of the lost sales cost and the quantity penalty. The model is then used to select the supplier that minimizes the procurement plus lost sales costs from a given set of supply bids and a known expected customer demand behavior. Finally, the buyer also has the option to make capital investments in the supplier so as to reduce the minimum order quantity and hence reduce the projected supply costs. We evaluate the economics of this tactic.