Edward P. C. Kao

A Multi-Product Dynamic Lot-Size Model with Individual and Joint Set-up Costs

This paper considers a multi-product dynamic lot-size problem. In addition to a separate set-up cost for each product ordered, a joint set-up cost is incurred when one or more products are ordered. We present a dynamic programming formulation for finding the optimal ordering policy that calls for a smaller state space than that proposed by Zangwill. As a convenient substitute, we also introduce a very simple heuristic procedure and two of its variants. For the two-product problem we report computational experience for evaluating the performance of these procedures.

On Dynamic Programming Methods for Assembly Line Balancing

Two dynamic programming approaches for treating sequencing problems—one proposed by Schrage and Baker and the other by Lawler—are discussed in the context of an assembly line balancing problem. A variant of the Schrage-Baker method is proposed to extend its range of applicability. The three approaches are compared using randomly generated test problems. We find that Lawlers “reaching”-based approach is superior to the other two “pulling”-based alternatives in both time and storage requirements. Based on the empirical results, we present time and space estimates for solving problems of different sizes and order strengths, and discuss the relative merits of the three procedures.

Optimal Replacement Rules when Changes of State are Semi-Markovian

This paper investigates the use of a discrete-time semi-Markov process to model a system that deteriorates in usage. Replacement rules that are 1 state-dependent, 2 state-age-dependent, and 3 age-dependent are proposed. The system operating costs and replacement costs are functions of the underlying states. The optimization criterion is the expected average cost per unit time. Under the first two replacement rules, the paper generates semi-Markov decision processes so that optimal policies can be obtained by the policy-iteration method. Sufficient conditions for the existence of an optimal control-limit state-dependent replacement rule are derived. For the age-dependent policy, the objective function is obtained so that the minimization can be carried out over the integers. An illustrative example is given at the end.

A Preference Order Dynamic Program for a Stochastic Traveling Salesman Problem

Consider a traveling salesman problem with stochastic travel times. Our objective is to find a tour with maximum probability of completion by a specified time. This paper presents a preference order dynamic program for solving the problem. To facilitate computation, we introduce a branch-and-bound strategy in the solution procedure. Finally, we propose an implicit enumeration algorithm as an alternative approach.

Modeling the Movement of Coronary Patients within a Hospital by Semi-Markov Processes

This paper studies the use of a collection of semi-Markov processes (referred to as paths) to describe the movement of coronary patients within a hospital. Two earlier papers by the same author [Health Serv. Res. 7, 191–208 (1972) and IEEE Trans, on Systems, Man, and Cybernetics SMC-3, 327–336 (1973)] define the state of a patient by a specific set of care requirements dictated by his “state of health;” this paper considers a state definition based solely on the care unit in which the patient resides. This new state definition is simpler to administer, especially when patients of different diagnoses are included in the model. The paper uses field data to estimate the parameters of the underlying processes and evaluate the adequacy of using such a model. Procedures involving simple matrix operations are introduced to obtain length-of-stay and patient-day statistics in each care unit as well as in the hospital. An approach for reconstructing the original arrival distribution based on admission data is also ...

Analysis of nonpreemptive priority queues with multiple servers and two priority classes

In this paper, we model a priority multiserver queueing system with two priority classes. A high priority customer has nonpreemptive priority over low priority customers. The approaches for solving the problem are the state-reduction based variant of Kao, the modified boundary algorithm of Latouche, the logarithmic reduction algorithm of Latouche and Ramaswami, and the power-series method of Blanc. The objectives of this paper are to present a power-series implementation for the priority queue and to evaluate the relative efficiencies of alternative procedures to compute various performance characteristics. In the paper, we find that at times the logarithmic reduction algorithm may not perform as well as expected and the power-series approach can occasionally pose numerical difficulties.

Computing Steady-State Probabilities of a Nonpreemptive Priority Multiserver Queue

We consider a nonpreemptive priority exponential queue with multiple servers and two classes of customers—each with its own arrival and service rates. Our focus is on the computation of steady-state probabilities for problems in which the marginal distribution for the number of high priority customers in the system has a short tail. The model is formulated as a quasi-birth-and-death process and is solved by applying several variants of state reduction. The variants are designed to reduce the computation and storage requirements for handling problems of moderate size. A few numerical-examples are given at the end. INFORMS Journal on Computing , ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

Computing the phase-type renewal and related functions

This article presents a procedure for computing the renewal function, the renewal density, the integral of the renewal function, and the variance function of phase-type renewal processes. The procedure hinges on the computation of the state probability vector of a continuous-time Markov chain. This is accomplished by using a randomization approach that is simple, efficient, and numerically stable and does not require numerical integration. I discuss approximating arbitrary interrenewal distributions by phase-type distributions so that the procedure can be used to approximate renewal and related functions.

Forecasting demands for inpatient services in a large public health care delivery system

Abstract This paper studies the use of autoregressive integrated moving average (ARIMA) time-series models for forecasting demands for inpatient services in a large public health care delivery system. Here, demands are measured in terms of monthly admissions and patient days by services and forecasts are made yearly. This paper emphasizes the implementation aspect of ARIMA models when they are used on a large scale basis in an institutional setting, and compares forecasts with actuals. For forecasting patient days, the adequacy of an indirect approach using the formula L = λ W is also evaluated. Finally, we briefly describe how the forecasts are used in the context of resource allocation.

Computational experience with a stochastic assembly line balancing algorithm

Abstract This paper discusses approaches for coding a preference order dynamic programming algorithm for solving an assembly line balancing problem with stochastic task times. Our objective is to mitigate the “curse of dimensionality” so that problems of moderate sizes (say, those containing less than fifty tasks) can easily be solved on a computer. We start with a review of the solution algorithm given in [6] and the node processing procedure developed by Schrage and Baker [11]. We then propose the adaptations and enhancements needed for accomplishing our objective. Finally we present some computational experience, and suggest conditions (i.e. problem sizes and strengths of precedence relations) under which the solution procedure will be useful for practical applications.