Date: 25 Feb 2011

Optimal policy with a total order quantity commitment contract in the presence of a spot market

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In this paper, the optimal policy is considered when the buyer faces two supply sources: one is the contract supplier from which the buyer orders over a specific contract period (say, a year) at a pre-agreed price, and the other is the spot market. However, when ordering from the contract supplier, the buyer must fulfill a pre-determined total order quantity, or the so-called definite total order quantity commitment, over the whole contract period. In other words, the commitment secures the buyer a fixed price but obliges him/her a total order quantity over the contract period. Although the spot market gives the buyer more flexibility in terms of order quantities, its prices are volatile. Such a combination of contract and spot procurements is often observed in practice. Within the contract period, there are multiple sub-periods, during each of which the buyer reviews the inventory, issues an individual order, and uses the on-hand inventory to meet the random demand. Thus, in each (ordering) period, the buyer will weigh between the current known spot price (by procuring from the spot market) and a lower future price (by waiting while consuming the remaining commitment). An optimal dual ordering policy is characterized for each period, depending on the on-hand inventory level, the spot price, and the remaining commitment quantity. The optimal policy in each period is also shown to be independent of the contract price. Through a numerical study, the inventory cost is demonstrated to be (1) insensitive to the contract price when the total commitment quantity is lower than the total expected demand over the contract period and (2) non-increasing in the variability of spot prices.

This work was partially supported by Hong Kong RGC Grant No. 410907, NSFC Grant Nos. 70725001, 70821001 and 71090401/71090400.
Wei Zhang is a Ph.D. candidate of School of Management at University of Science and Technology of China, Hefei, China. His research interests include production and operations management, and inventory management.
Youhua (Frank) Chen is an associate professor at the Department of Systems Engineering and Engineering Management, the Chinese University of Hong Kong. He obtained his Ph.D. degree from the University of Toronto. His current research is focused on interfaces between operations and marketing, and inventory models with risk considerations.
Zhongsheng Hua received his Ph.D. degree in computer science from the University of Science and Technology of China, Hefei, China, in 2000. He is currently a Professor and the Vice Dean of the School of Management, USTC. His research interests include decision analysis, production and operations management, and supply chain management.
Weili Xue graduated from the Chinese University of Hong Kong with a Ph.D. degree in Systems Engineering and Engineering Management in 2009. He obtained his BS and Master degrees from Nanjing University. Dr. Xue is current a consultant at Yurun Group, Nanjing, China.