Capacity planning is an area in which engineers can affect business performance. The size of the expansions and the timing in which they take place are the most important variables in capacity planning. The Economic Investment Time (EIT) Model is a tool that enables planners to accurately determine the investment time in which profits resulting from the proposed expansion can be maximized. This thesis presents the results yielded by the EIT. Validation is performed using the utilization results yielded by the Newsboy Model. This paper explains the methodology used and the conclusions that can be drawn. / Master of Science

We consider the problem of capacity expansion in telecommunication networks under uncertain economic conditions with various market structures. We assume that the demands for network capacity have constant price-elasticity, and demand functions are parameterized by an economic condition that is modeled by a discrete time Markov process. We apply dynamic programming to obtain a state-dependent capacity expansion strategy that maximizes expected total discounted cash flow. We incorporate partial reversibility of investment by differentiating the purchasing cost and the salvage value of the capacity. This partial reversibility makes the value function non-differentiable and divides the solution space into BUY, KEEP, and SELL regions. By identifying certain structural properties of the optimal solution, we perform sensitivity analyses on the optimal investment decisions with respect to market parameters. Under the condition that the level of cost depreciation is larger than that of the downside movement of the economic condition in each time period, we are able to obtain an analytical expression for the optimal capacity level and reduce the multi-period investment decision problem into a single-period myopic problem. As a result, optimal capacity increment depends only on the current economic condition. We study this problem under both monopolistic and oligopolistic market structures. In particular, we investigate investment decisions by two firms in a duopoly setting with Cournot competition. We prove the existence and the uniqueness of the Cournot equilibrium strategies in the duopolistic capacity investment problem. In addition, we show how competition between firms affects total available capacity in the market, capacity price, consumer surplus, expected time to a certain level of price reduction, and expected time to the first investment. We perform an empirical analysis to test a theoretical prediction obtained from our model through linear regression utilizing historical market data. By examining several alternative indices as a proxy to the economic condition considered in our model, we show that the Civilian Employment is the best proxy to use in validating the linear relationship between telecommunications capacity expansion and the economic indicator.

Thesis (M.S. in Management)--Naval Postgraduate School, December 1990. / Thesis Advisor(s): Gates, William. Second Reader: Doyle, Richard. "December 1990." Description based on title screen as viewed on April 2, 2010. DTIC Identifier(s): NATO, Defense Planning, Industrial Production, Economics, Burden Sharing, Defense Industries, Sharing, Costs, Military Forces (Foreign), Military Forces (United States), Military Equipment, Mathematical Models, Military Reserves, Industrial Capacity. Author(s) subject terms: Burden-sharing, NATO. Includes bibliographical references (p. 75-80). Also available in print.

The petroleum industry has one of the most complex supply chains in the world. A unique characteristic of Petroleum Supply Chain (PSC) is the high degree of uncertainty which propagates through the network. Therefore, it is necessary to develop quantitative models aiming at optimizing the network and managing logistics operations. This work proposes a deterministic Mixed Integer Linear Program (MILP) model for downstream PSC to determine the optimal distribution center (DC) locations, capacities, transportation modes, and transfer volumes. Three products are considered in this study: gasoline, diesel, and jet fuel. The model minimizes multi-echelon multi-product cost along the refineries, distribution centers, transportation modes and demand nodes. The relationship between strategic planning and multimodal transportation is further elucidated. Furthermore, this work proposes a two stage Stochastic Mixed Integer Linear Program (SMILP) models with recourse for PSC under the risk of random disruptions, and a two stage Stochastic Linear Program (SLP) model with recourse under the risk of anticipated disruptions, namely hurricanes. Two separate types of mitigation strategies – proactive and reactive – are proposed in each model based on the type of disruption. The SMILP model determines optimal DC locations and capacities in the first stage and utilizes multimode transportation as the reactive mitigation strategy in the second stage to allocate transfer volumes. The SLP model uses proactive mitigation strategies in the first stage and employs multimode transportation as the reactive mitigation strategy. The goal of both stochastic models is to minimize the expected total supply chain costs under uncertainty. The proposed models are tested with real data from two sections of the U.S. petroleum industry, PADD 3 and PADD 1, and transportation networks within Geographic Information System (GIS). It involves supply at the existing refineries, proposed DCs and demand nodes. GIS is used to analyze spatial data and to map refineries, DCs and demand nodes to visualize the process. Sensitivity analysis is conducted to asses supply chain performance in response to changes in key parameters of proposed models to provide insights on PSC decisions, and to demonstrate the impact of key parameters on PSC decisions and total cost. / Upper Great Plains Transportation Institute (UGPTI) / Mountain Plains Consortium (MPC)

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.

Dans cette thèse, nous abordons le problème de la planification de la production dans un système de type flow-shop, en tenant compte de l’aspect énergétique. Le système de production est composé de différentes machines fiables, séparées par des zones de stockage à capacité infinie. L’horizon de planification est composé de différentes périodes, chacune étant caractérisée par une durée, un coût d’électricité, une puissance maximale et des demandes de chaque produit. L’objectif consiste en la minimisation du coût total de production en terme d’électricité, stockage, mise marche (ou changement de série) et puissance demandée par période. Dans un premier temps, nous proposons une modélisation pour le problème de lot-sizing dans un système de type flow-shop, à capacité finie, dans le cas mono-produit. Étant donné que ce type de problème est NP-difficile, des méthodes approchées ont été développées afin de fournir des solutions de bonne qualité dans un temps réduit (heuristiques dédiées, heuristique de type Fix and Relax, algorithme génétique). Dans un deuxième temps, une généralisation du modèle pour le cas multi-produits a été considérée. De même, des méthodes approchées ont été proposées pour la résolution de ce type de problème / In this thesis, we deal with the production planning problem in a flow-shop system with energy consideration. The manufacturing system is composed of reliable machines separated by buffers with infinite capacities. The planning horizon is defined by a set of periods where each one is characterized by a length, an electricity price, a maximal allowed power and an external demand of each product. The purpose is to minimize the total production cost composed of electricity, inventory, set-up (or product series change) costs and a required power per period.In the first step, we propose mathematical models for a single item capacitated lot-sizing problem in a flow-shop system. Since this problem is known to be NP-hard, approximating methods are developed in order to provide solutions with good quality in a reasonable time (dedicated heuristics, Fix and Relax heuristic, genetic algorithm).In the second step, a generalization of the model for multi-items is considered. Similarly to the first case, approximating methods are proposed to solve this problem