System Balance for Extended Logistic Systems

An extended logistic system is a well-defined configuration of complex equipment, supporting inventory levels of components and modules, supporting maintenance facilities, supporting transportation system between local and remote inventory and maintenance sites, and procedures governing the allocation and shipment of components from remote and local sites. Examples of extended logistic systems are aircraft programs, radar systems, or networks of communication satellites. For each of these systems, the basic unit of interest (an aircraft, a radar unit, or a satellite) is a complex combination of components which are subject to failure. For each component there are supporting inventory and/or repair facilities, and specific replacement procedures for such failures. The evaluation of system performance includes system availability and the logistic costs required to obtain that level of availability. This paper reports extensions to our earlier work [2] in which we develop methods for studying the dynamic behavior of extended logistic systems. In particular, an optimization model is proposed here for examining system design and tradeoff decisions. We consider a single-echelon model for a multiple-component system where components are subject to failure. For the system to be operable, a prespecified number of each component must be available. .The optimization model maximizes system availability subject to a budget constraint on system cost and a dynamic time constraint on system failure time. The latter constraint is an effort to incorporate our understanding of system dynamics into the optimization by restricting the mean time between failures for the entire system. The use of the optimization model for system design and tradeoff decisions is illustrated by three examples using representative data from an Air Force program. Within the optimization context, the notion of system balance is defined. In essence, I I 11_ 111___ III a balanced system is a system for which any change in investment between any two system levels satisfying system constraints, raises total system cost. The paper is organized into four sections. In the first section we introduce the problem setting and define the problem of interest. In Section 2, we propose an optimization model for the stated problem which gives rise to an integer programming problem, and in turn to a linear programming approximation. Section 3 presents three numerical examples illustrating the potential utility of the model. Finally Section 4 compares the proposed approach to alternative approaches and suggests possible extensions.