Academic journal article Journal of Management Information and Decision Sciences

Coordinating Pricing and Inventory Purchasing Decisions of a Supply Chain for an E-Tailer in Face of Quantity Discounts

Academic journal article Journal of Management Information and Decision Sciences

Coordinating Pricing and Inventory Purchasing Decisions of a Supply Chain for an E-Tailer in Face of Quantity Discounts

Article excerpt

(ProQuest: ... denotes formulae omitted.)

INTRODUCTION

Ford Harris's (1913) study on batch sizing started the studies on inventory policy a century ago. The Harris Model has then been forgotten until the idea was later published by Wilson (1934) in Harvard Business Review. Following the Review, the Harris's batching rule is now known as the Wilson Economic Order Quantity (EOQ) as it applies to inventory control.

This classic model assumes that a retailer buys a product at a constant unit cost, incurs a fixed cost per order, stores the product at a constant inventory carrying cost per unit per year, and faces a deterministic and constant demand rate over an infinite horizon, the retailer's optimal strategy is to buy a fixed quantity every time he or she replenishes the inventory. Ignoring inventory related costs, classical price theory tells us that when a product's demand is price sensitive but the demand curve is known and stationary, the retailer's optimal strategy is to charge a single price throughout the year. Although Whitin (1955) was the first one to integrate the concepts of inventory theory with the concepts of price theory, however, he did not formally investigate the simultaneous determination of price and order quantity decisions of a retailer.

Kunreuther and Richard (1971), perhaps the predecessors of supply chain management, then showed that when demand is price elastic, centralized/coordinated decision-making (using simultaneous determination of optimal price and order quantity) was superior to the common practice of decentralized decision-making whereby the pricing decisions were made by the marketing department while the order quantity decisions were made by the purchasing department independently. Although Kunreuther and Richard (1971) were perhaps unaware of Whitin's (1955) paper, their model was very similar to Whitin's (1955) model. Assuming a known and stationary demand curve along with the conditions of the EOQ model, Arcelus and Srinivasan (1987, page 173) asserted: "given constant marginal costs of holding and purchasing the goods, the firm will want to maintain the same price throughout the year". Again, they assumed a fixed single selling price throughout each inventory cycle. What they did not realize is that, even though marginal holding costs are constant per unit, a firm's holding costs at any particular time within an inventory cycle are a function of inventory on hand, which itself is a function of the time from the beginning of the inventory cycle.

Since Whitin's (1955) work, numerous authors (Tersine and Price, 1981; Arcelus and Srinivasan, 1987; Ardalan, 1997; Hall, 1992; Martin, 1994; Arcelus and Srinivasan, 1998; Abad, 2003) have used Whitin's (1955) and Kunreuther and Richard's (1971) models as foundations to their own models. But none of these authors have ever questioned Whitin's (1955) and Kunreuther and Richard's (1971) assumption that the retailer's optimal strategy would be to sell the product at a fixed price throughout the inventory cycle. The fact that Whitin's (1955) and Kunreuther and Richard's (1971) assumption of a single price throughout an inventory cycle leads to suboptimal profits for the retailer is due to declining carrying costs as a function of time. It seems that any optimization model allowing a retailer with a price-insensitive demand to set the selling price arbitrarily would push the price to infinity. In other words, in that situation, price is not seen as a decision variable for any mathematical model. Given an arbitrary price (and corresponding demand), the retailer's only strategy is to minimize his inventory ordering and holding costs by using the EOQ model.

Considering a situation of price sensitive demand, Abad (1997; 2003) found that, in the case of a temporary sale with a forward buying opportunity, a retailer's optimal strategy is to charge two different prices during the last inventory cycle of the quantity bought on sale-a low price at the beginning of the inventory cycle and a higher price starting somewhere in the middle of the cycle. …

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