Studies of inventory control and capacity planning with multiple sources - Zahrn, Frederick Craig (ProQuest Dissertations & Theses, 2009)
This dissertation consists of two self-contained studies. The first study, in the domain of stochastic inventory theory, addresses the structure of optimal ordering policies in a periodic review setting. We take multiple sources of a single product to imply an ordering cost function that is nondecreasing, piecewise linear, and convex. Our main contribution is a proof of the optimality of a finite generalized base stock policy under an average cost criterion. Our inventory model is formulated as a Markov decision process with complete observations. Orders are delivered immediately. Excess demand is fully backlogged, and the function describing holding and backlogging costs is convex. All parameters are stationary, and the random demands are independent and identically distributed across periods. The (known) distribution function is subject to mild assumptions along with the holding and backlogging cost function. Our proof uses a vanishing discount approach. We extend our results from a continuous environment to the case where demands and order quantities are integral. The second study is in the area of capacity planning. Our overarching contribution is a relatively simple and fast solution approach for the fleet composition problem faced by a retail distribution firm, focusing on the context of a major beverage distributor. Vehicles to be included in the fleet may be of multiple sizes; we assume that spot transportation capacity will be available to supplement the fleet as needed. We aim to balance the fixed costs of the fleet against exposure to high variable costs due to reliance on spot capacity. We propose a two-stage stochastic linear programming model with fixed recourse. The demand on a particular day in the planning horizon is described by the total quantity to be delivered and the total number of customers to visit. Thus, daily demand throughout the entire planning period is captured by a bivariate probability distribution. We present an algorithm that efficiently generates a “definitive” collection of bases of the recourse program, facilitating rapid computation of the expected cost of a prospective fleet and its gradient. The equivalent convex program may then be solved by a standard gradient projection algorithm. The two investigations making up this dissertation are united by a concern with multiple sources within their respective contexts. The first study posits multiple sources of a single product (for example, multiple suppliers or production technologies) within an inventory control context. The second study considers multiple sources of transportation capacity, in the form of vehicles of differing sizes and the alternative of fleet versus spot capacity. For each of the two investigations, our focus on multiple sources entails a richer analysis than that arising from a single-source setting.