Modeling Inventory Considerations in Supply Contracts

Tim Urban has published numerous articles in the field of inventory control and is the Editor of the International Journal of Inventory Research. While his research deals primarily with the mathematical modeling of inventory-control systems, it has focused on a variety of applications, such as evaluating the replenishment of radioactive source material in irradiation sterilizers, coordinating inventory decisions with pricing, production, quality, product assortment and shelf-space allocation considerations, as well as incorporating ordering decisions in the context of supply contracts.

For example, the article “Supply Contracts with Periodic, Stationary Commitment” published in Production and Operations Management focuses on the operational, as opposed to the legal, aspects of supply contracts, (full article). A commitment contract is analyzed, which imposes some restriction on the buyer to purchase certain quantities (either order quantity or dollar value) of the product; in particular, the periodical commitment contract is considered, in which the buyer commits to purchase a certain quantity every period of the contract. This type of contract would be particularly attractive for a supplier with a low degree of volume flexibility—where fluctuations in the production output result in higher costs or lower quality levels—with the contract written to allow changes in the order quantity at an additional cost to the buyer. A mathematical model and solution methodology are developed for various demand distributions, and an analysis of the effect of the service level, demand variability, and demand patterns on the optimal solution is conducted.