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Combined Sourcing with Capacity Reservation

Kelle_Peter_250x350Dr.  Peter Kelle
Louisiana State University
Friday, April 1, 2016
2:30-3:30 JDT 410

Purchasing based on capacity reservation contracts and buying on the spot market are two alternative purchasing practices. Spot market purchasing is a benefit in case of low spot market prices or insufficient reserved capacity, and the capacity reservation contract is an operational risk hedging for high spot market price incidents.
We analyze the combined sourcing decision for several periods under stochastic demand and random spot market price fluctuations. It has to be decided – period by period – which quantities to procure from the two sources. The combined procurement strategy has to protect against risks of insufficient demand fulfillment and exploit the benefits of forward buying in periods with low spot price levels. Additionally, a long-term decision has to be made regarding the reserved capacity level to be fixed with the long-term supplier to create sufficient protection for high spot market price incidents. The decision on capacity reservation has to take into account the short-term capacity utilization of each source which itself depends on the available long-term capacity. Thus, we face a highly complex interdependence of long-term and short-term decisions under uncertainties in demand and spot market price.
We model the above decision problem as a stochastic dynamic optimization problem and analyze the optimal procurement strategy by means of stochastic dynamic programming. Thereby, we are able to prove that the optimal procurement policy is a three-parameter policy with a fixed order-up-to level for ordering from the long-term supplier and price-dependent order-up-to levels for short-term spot market procurement. The third policy parameter is the capacity reservation level. It is very cumbersome to numerically calculate the optimal values of all policy parameters, especially the price-dependent order-up-to levels. Therefore, we develop a heuristic approach for determining all parameters and parameter functions which is based on the solution of appropriately adjusted news vendor problems and on the results from a related simplified base stock policy. Finally, we present the managerial analysis and a comprehensive numerical study showing that our heuristic policy performs very well and provides major cost savings compared to single sourcing.

Peter Kelle is the Ourso Family Distinguished Professor of Decision Sciences at the E.J. Ourso College of Business, Louisiana State University, Baton Rouge. He has been working at LSU since 1988. He obtained a Ph.D. in Operations Research from the L. Eotvos University of Budapest, Hungary in 1980. He had several visiting appointments including a British Academy fellowship and a two-year visiting research position at the University of Calgary, Canada.
His current research is mainly in supply chain management and optimization for private companies and government agencies. He has been working on several research grants, lately with the US Dept. of Homeland Security in disaster supply chain management area and with the US Dept. of Transportation on safety improvement and optimization.  Dr. Kelle is the co-author of three books and over fifty of his research publications have appeared in various prestigious professional journals.
Professor Kelle is very active in academic services.  He is the American Editor of the International Journal of Production Economics since 2000.

Phone: 1-225-578-2509; e-mail:

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