Production/inventory policies for systems with uncertain capacities and demands.

Abstract

This thesis addresses two different production/inventory models, each facing uncertain demand. Managerial response to these problems is somewhat handicapped by capacity uncertainties that restrict the control action. These uncertainties can be a result of unavailable internal resources or they may arise due to unpredictable market forces. While responding to uncertain demand, a decision maker must take into account the possibility of restricted control action in future periods or stages. The impact of capacity and demand uncertainties on managerial decisions can be complex in a multi-stage or multi-period setting. This thesis provides structured policies which simplify the decision making considerably. An understanding of how capacity or demand uncertainties affect the policy parameters is also explored. The first problem considers a one-time production of an application-specific product which must follow a fixed routing through the manufacturing system. The flow of items is modeled as a multi-stage serial production line. The productive capacity is uncertain at each stage and the decision to produce at any stage incurs a significant setup cost. Inability to satisfy the demand incurs a penalty for each unit of unmet demand. The analysis indicates that the optimal production policy for this system can be characterized by two critical numbers, which can be computed a priori based on the cost parameters and distributional information for all downstream stages. The second problem addresses a multi-period cash balance model in order to manage cash level for firms facing stochastic cash-flows. Cash level is adjusted through the purchase or sale of earning assets. These adjustments are similar to the replenishment and disposal of stocks in production/inventory systems. The cash adjustment or cash transfer may not materialize due to negotiation delays, limited liquidity of assets or restricted mobility in financial structures. As a result, the transfer capacity is restricted and uncertain. Transfer costs are proportional to the amount of cash adjustment. A negative cash balance incurs a penalty, so does the excess cash on hand due to opportunity loss. We show that the optimal cash adjustment policy can be characterized by two return points.