Application of perturbation analysis to a class of periodic review (s,S) inventory systems

In this article we apply perturbation analysis (PA), combined with conditional Monte Carlo, to obtain derivative estimators of the expected cost per period with respect to s and S, for a class of periodic review (s, S) inventory systems with full backlogging, linear holding and shortage costs, and where the arrivals of demands follow a renewal process. We first develop the general form of four different estimators of the gradient for the finite-horizon case, and prove that they are unbiased. We next consider the problem of implementing our estimators, and develop efficient methodologies for the infinite-horizon case. For the case of exponentially distributed demand interarrival times, we implement our estimators using a single sample path. Generally distributed interarrival times are modeled as phase-type distributions, and the implementation of this more general case requires a number of additional off-line simulations. The resulting estimators are still efficient and practical, provided that the number of phases is not too large. We conclude by reporting the results of simulation experiments. The results provide further validity of our methodology and also indicate that our estimators have very low variance. © 1994 John Wiley & Sons, Inc.     

Diagnostic analysis of inventory systems: An optimization approach

The objective of a diagnostic analysis is to provide a measure of performance of an existing system and estimate the benefits of implementing a new one, if necessary. Firms expect diagnostic studies to be done promptly and inexpensively. Consequently, collection and manipulation of large quantities of data are prohibitive. In this paper we explore aggregate optimization models as tools for diagnostic analysis of inventory systems. We concentrate on the dynamic lot size problem with a family of items sharing the same setup, and on the management of perishable items. We provide upper and lower bounds on the total cost to be expected from the implementation of appropriate systems. However, the major thrust of the paper is to illustrate an approach to analyze inventory systems that could be expanded to cover a wide variety of applications. A fundamental by-product of the proposed diagnostic methodology is to identify the characteristics that items should share to be aggregated into a single family.     

Time minimizing flows in directed networks

An important class of network flow problems is that class for which the objective is to minimize the cost of the most expensive unit of flow while obtaining a desired total flow through the network. Two special cases of this problem have been solved, namely, the bottleneck assignment problem and time-minimizing transportation problem. This paper addresses the more general case which we shall refer to as the time-minimizing network flow problem. Associated with each arc is an arc capacity (static) and a transferral time. The objective is to find a maximal flow for which the length (in time) of the longest path carrying flow is minimized. The character of the problem is discussed and a solution algorithm is presented.     

Multiple resource leveling in construction systems through variation of activity intensities

The resource leveling problem for a construction system producing a stream of output units is considered. The system is modeled using a critical-path-analysis activity network, from which an extended network is developed for an integrated planning effort of all output units. Activity intensity variables are defined which measure activity demand rates for resources and consequent activity durations for the production of each output unit. A heuristic approach consisting of an iterative nonlinear programming procedure is presented which computes activity durations (intensities) for the minimization of resource capacity costs subject to meeting construction due dates. The application to a major ship overhaul project is described, in which the procedure was used to level workloads of the various labor–trade shops.     

A general axiomatization of additive measurement with applications

Necessary and sufficient conditions are specified for a general theory of additive measurement that presumes very little set-theoretic structure. The theory is illustrated for numerical representations in extensive, conjoint, difference, threshold, expected utility, probability, ambiguity, and subset measurement. © 1992 John Wiley & Sons, Inc.     

Economic design of X¯ control charts for two manufacturing process models

Control charts are widely used for process surveillance. The design of a control chart refers to the choice of sample size, the width of the control limits, and the interval between samples. Economic designs have been widely investigated and shown to be an effective method of determining control chart parameters. This article describes two different manufacturing process models to which the X¯ control chart is applied: The first model assumes that the process continues in operation while searches for the assignable cause are made, and the second assumes that the process must be shut down during the search. Economic models of the control chart for these two manufacturing process models are developed, and the sensitivity of the control chart parameters to the choice of model is explored. It is shown that the choice of the proper manufacturing process model is critical because selection of an inappropriate process model may result in significant economic penalties.