UCLA

As a general trend, firms are moving towards mass customization by allowing customers to configure products by selecting among options (features), e.g. automotive industry, consumer electronics, computers, furniture, and aircraft. This dissertation is motivated by the problems faced by a global auto manufacturer that offers 100-500 options for a car. These options can be combined in different ways resulting in 10^25-10^40 different configurations (end-products). Since it is impossible to forecast the demand for configurations, firms forecast options' demand.

In this dissertation, we study three major problems. First, the current forecasting approach ignores the relationships between options and, as a result, the forecasts are frequently incorrect (inconsistent), which results in excess inventories, shortages, and customer dissatisfaction. We present an effective approach that verifies consistency of the forecast and finds the best consistent forecast in the case of inconsistency. The second problem is to determine how many units of each part is required over the planning horizon, known as parts' capacity planning problem. The firm signs contracts with parts' suppliers based on the predicted parts' capacities. We present a methodology for predicting parts' capacities. Last, we generalize and extend the methodology developed in the first problem and introduce a new variation of the Non-Negative Least-Squares (NNLS) problem that is defined as finding the Euclidean distance to a convex cone generated by a set of discrete points. Our new variation considers the cases where the discrete points are implicitly known and there are an exponentially large number of them. We present an effective approach for solving this new variation of NNLS, design a lower bound, and establish the convergence rate of the lower and upper bounds.