A note on the “value” of bounds on EVPI in stochastic programming

The existing literature concentrates on determining sharp upper bounds for EVPI in stochastic programming problems. This seems to be a problem without an application. Lower bounds, which we view as having an important application, are only the incidental subject of study and in the few instances that are available are obtained at an extremely high cost. In order to suggest a rethinking of the course of this research, we analyze the need for bounds on EVPI in the context of its significance in decision problems.     

An easy solution for a special class of fixed charge problems

The fixed charge problem is a mixed integer mathematical programming problem which has proved difficult to solve in the past. In this paper we look at a special case of that problem and show that this case can be solved by formulating it as a set-covering problem. We then use a branch-and-bound integer programming code to solve test fixed charge problems using the setcovering formulation. Even without a special purpose set-covering algorithm, the results from this solution procedure are dramatically better than those obtained using other solution procedures.     

The bounded interval generalized assignment model

The bounded interval generalized assignment model is a “many-for-one” assignment model. Each task must be assigned to exactly one agent; however, each agent can be assigned multiple tasks as long as the agent resource consumed by performing the assigned tasks falls within a specified interval. The bounded interval generalized assignment model is formulated, and an algorithm for its solution is developed. Algorithms for the bounded interval versions of the semiassignment model and sources-to-uses transportation model are also discussed.     

Spares stocking policies for repairable items with dependent repair times

This paper analyzes the problem of determining desirable spares inventory levels for repairable items with dependent repair times. The problem is important for repairable products such as aircraft engines which can have very large investment in spares inventory levels. While existing models can be used to determine optimal inventory spares levels when repair times are independent, the practical considerations of limited repair shop capacity and prioritized shop dispatching rules combine to make repair times not independent of one another. In this research a simulation model of a limited capacity repair facility with prioritized scheduling is used to explore a variety of heuristic approaches to the spares stocking decision. The heuristics are also compared with use of a model requiring independent repair times (even though that assumption is not valid here). The results show that even when repair time dependencies are present, the performance of a model which assumes independent repair times is quite good.     

On a single-server queue with state-dependent service

This paper discusses a class of queueing models in which the service time of a customer al a single server facility is dependent on the queue size at the onset of its service. The Laplace transform for the wait in queue distribution is derived and the utilization of the server is given when the arrival is a homogeneous Poisson process.     

Adaptive disposal models

This paper reconsiders the classical model for selling an asset in which offers come in daily and a decision must then be made as to whether or not to sell. For each day the item remains unsold a continuation (or maintenance cost) c is incurred. The successive offers are assumed to be independent and identically distributed random variables having an unknown distribution F. The model is considered both in the case where once an offer is rejected it may not be recalled at a later time and in the case where such recall of previous offers is allowed.     

Redundant spares allocation to reduce reliability costs

The problem considered here is the optimal selection of the inventory of spares for a system built from two kinds of modules, the larger of which can be connected so it performs the role of the smaller one. The optimal inventory is the least costly one which achieves a specified probability that the spares will not be exhausted over the design lifetime. For some costs and failure rates it is most economical to use the larger module for both roles, due to the resulting increase in flexibility in the deployment of a single type of spare module. Both analytical and simulation methods have been used to study this problem.     

Engineering costs and customer costs in designing product support

Product support encompasses activities undertaken by durable goods producers to ensure their customers the continued use of the product. Examples of product support elements include after the sale activities such as providing repair services and warranty programs, as well as all the activities undertaken at the design and production stage to improve the reliability of products before they reach the market. The implications of incorporating customer costs while designing product support packages are the concern of this study. We study how the parameters of support package impact the costs incurred by customers and provide insights about selecting appropriate levels of product support. We show that the engineering orientation of maximizing the product's availability ignores market characteristics, and results in a mismatch between the corporation's support package and the customer's needs. The research is intended to be a step in understanding the interaction between design engineering parameters and customer's costs. © 1993 John Wiley & Sons, Inc.     

A new polynomial algorithm for maximum value flow with an efficient parallel implementation

A new algorithm is presented for finding maximal and maximum value flows in directed single-commodity networks. Commonly algorithms developed for this problem find a maximal flow by gradually augmenting (increasing) a feasible flow to a maximal flow. In the presented algorithm, at the beginning of each step or iteration, the flow on arcs is assigned to flow capacity. This may lead to an infeasible flow violating flow conservation at some nodes. During two passes of a MAIN step, consisting of a forward pass and a backward pass, the flow is reduced on some arcs to regain feasibility. The network is then pruned by omitting saturated arcs, and the process is repeated. The parallel implementation of the algorithm applies the two main steps at the same time to the same network. The outputs of the two steps are compared and the processing continues with the higher feasible flow. The algorithm is simple, intuitive, and efficient. © 1993 John Wiley & Sons, Inc.     

Minimal forecast horizons in equipment replacement models with multiple technologies and general switching costs

This article considers the problem of equipment replacement in which the replacement decision at a particular time must take into account (i) the state of the existing machine in use, (ii) the available replacement alternatives at the time, (iii) the future advances in the relevant technologies with regard to the equipment under consideration, and (iv) costs of switching between different technologies. A methodology that attains minimal forecast horizons for the problem is developed. A numerical example illustrates the methodology.