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UBC Theses and Dissertations

Production-inventory systems : optimal control and empirical analysis Wu, Owen Qun

Abstract

This thesis consists of three independent essays in the area of production and inventory management. The first essay is concerned with a competitive equilibrium production-inventory model with application to the petroleum refining industry. We first examine an individual firm controlling production and inventories and facing uncertain raw material price, finished goods price and operating costs. The firm maximizes the expected discounted profit over an infinite horizon. We show that, the optimal control is of a threshold type. Next, we consider an economy with many raw material suppliers, production firms and consumers. Both the supply and the demand are uncertain and price-sensitive. We establish and characterize the rational expectations equilibrium price process for this economy, and further derive the equilibrium in an explicit form for a special economy. Finally, we simulate the equilibrium model to reproduce some stylized facts of the petroleum refining industry and fit the model with actual data. The second essay studies an inventory system that supplies price-sensitive demand modeled by Brownian motion. The optimal pricing and inventory replenishment, decisions under both long-run average and discounted objectives are derived, and related to or contrasted with previously known results. In addition, we emphasize the interplay between pricing and replenishment decisions, and the ways in which they react to the demand uncertainty. We show that the joint optimization of both decisions may result in significant profit improvement compared to the traditional method of making decisions separately or sequentially. We also show that multiple price changes result in only a limited profit improvement over the optimal single price. In the third essay, we examine the inventories of publicly traded American manufacturing companies between 1981 and 2000. The median of inventory holding periods were reduced from 96 days to 81 days. The average rate of inventory reduction is about 2% per year. The greatest reduction was found for work-in-process inventory, which declined by about 6% per year. Finished-goods inventories did not decline. Inventory holdings significantly affect firms’ long-term stock returns. Firms with abnormally high inventories have abnormally poor long-term stock returns. Firms with slightly lower than average inventories have good stock returns, but firms with the lowest inventories have only ordinary returns.

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