An EOQ model for MRO customers under stochastic price to quantify bullwhip effect for the manufacturer

Motivated by a particular multinational cutting-tools manufacturer, we extend the traditional economic order quantity (EOQ) model for maintenance-repair-and-overhaul (MRO) customers under stochastic purchase price and use it to show how price variance leads to bullwhip effect for the MRO manufacturer despite constant consumption by the customer. Our extension of the EOQ model is based on two assumptions that are reasonable for MRO customers: (a) customer consumption rate of the product is constant; and (b) the customer places each order when the inventory level drops to a pre-specified level (say, zero). We determine the customer's optimal ordering quantity in closed form expressions, which enables us to examine the impact of sales price variance on the variance in the orders the customer places on the manufacturer, thus creating a pricing-induced bullwhip effect. We then extend our analysis to multiple products and multiple customer segments and discuss ways for the manufacturer to mitigate the variance in the customer's orders.