| In managing economic risks, it is necessary for a company in the process industries to allow for uncertainties in the amount of each product that can be sold, how much material is available for production, as well as prices and costs. The goal is to optimize a company's profit criterion without undue risk, and determine resource requirements such as materials and capacity to operate the supply chain. The planning model in this thesis accounts for the economic effect of overproduction with uncertain market demands and overestimation of material availability, with uncertain inventories. The expected profit and its variance are calculated by polytope volume integration without the need for simulation. This new method allows for several probability distributions, incorporating correlations as well as price-demand dependence. It implies short-term profit-maximizing behavior in each period, making it similar to a recourse method. It can yield exact results and provide derivative information for use in optimization. An approximate evaluation method is also developed to contend with the complexity of some instances. The parameters of the distributions of uncertainties may be estimated by a forecasting approach which selects the number of random variables, their coefficients in models of uncertainties, and the joint probability distribution.; The company should expect the manufacturing operation to provide an average return greater than an equally risky investment in the financial market, such as a portfolio of stocks and bonds as observed in the Capital Asset Pricing Model. The manufacturing investment is viewed as an alternative to a financial investment, where its average return and variance are found by this new uncertainty analysis. The planning problem is a nonlinear optimization formulation, with nonlinearities arising from the treatment of uncertainty in the objective and the financial equations. The key decisions about material requirements, production capacity, and capacity location are made based on the solution. Example problems illustrate several features which may be accommodated by the new methodology. A simplified model of a chemical manufacturing supply chain is posed, and the solutions are compared for different initial points in cases with and without price uncertainty. It is also demonstrated on a case study using information on economic uncertainties and plant processes from the Argentine fruit industry. |
