Showing papers in "Operations Research in 1976"
TL;DR: A nurse scheduling system that poses the scheduling decision as a large multiple-choice programming problem whose objective function quantifies preferences of individual nursing personnel concerning length of work stretch, rotation patterns, and requests for days off is described.
Abstract: This paper describes a nurse scheduling system, the heart of which poses the scheduling decision as a large multiple-choice programming problem whose objective function quantifies preferences of individual nursing personnel concerning length of work stretch, rotation patterns, and requests for days off. The constraints provide for minimum numbers of nursing personnel of each skill class to be assigned to each day and shift of a four-or six-week scheduling period. The problem is solved by a modification of Balintfy and Blackburn's algorithm for multiple-choice programming problems. We include a description of the implementation of the scheduling system on nursing units of several hospitals.
285 citations
TL;DR: This paper formulates the nurse-scheduling problem as one of selecting a configuration of nurse schedules that minimize an objective function that balances the trade-off between staffing coverage and schedule preferences of individual nurses, subject to certain feasibility constraints on the nurse schedules.
Abstract: This paper formulates the nurse-scheduling problem as one of selecting a configuration of nurse schedules that minimize an objective function that balances the trade-off between staffing coverage and schedule preferences of individual nurses, subject to certain feasibility constraints on the nurse schedules. The problem is solved by a cyclic coordinate descent algorithm. We present results pertaining to a six-month application to a particular hospital unit and draw comparisons between the algorithm and hospital-generated schedules.
239 citations
TL;DR: A practical application of the proposed approach reveals that the consumer preference model has substantial reliability and predictive validity.
Abstract: A problem in planning the expansion of a rural primary health-care delivery system is to determine the set of facilities to be added to an existing system so as to maximize the incremental benefit to the community subject to a cost constraint. The proposed approach involves the following five steps: 1 identification of facility attributes relevant to patients in their choice of health-care facilities, 2 modeling of an individual's overall preference for alternate facilities as a weighted linear function of these facility attributes, 3 transformation of each consumer's preference model into a benefit function expressing the individual's benefit in dollars/year for an existing or potential facility, 4 provision of a method for determining the total incremental benefit to the community from a set of proposed health-care facilities, and 5 use of a heuristic procedure to determine a set of facilities that yields near-optimum total incremental benefit subject to the cost constraint. A practical application of the proposed approach reveals that the consumer preference model has substantial reliability and predictive validity.
184 citations
TL;DR: The problem is treated by a quadratic assignment algorithm with a linear programming adjustment, and a successful practical application for chemical reactor scheduling is described.
Abstract: Production orders for a number of products must be scheduled on a number of similar production lines so as to minimize the sum of product-dependent changeover costs, production costs, and time-constraint penalties. We treat the problem by a quadratic assignment algorithm with a linear programming adjustment, and describe a successful practical application for chemical reactor scheduling.
179 citations
TL;DR: The existence of an invariant measure for an inventory related process, which provides information sufficient for cost minimization is demonstrated, for the two-and three-period-lifetime cases.
Abstract: We consider the problem of finding the optimal solution from the class of single critical number order policies for an m-period lifetime perishable product. The objective function is expected cost per period, Accordingly, the steady-state characteristics of the inventory process induced by the order restriction are analyzed. We demonstrate the existence of an invariant measure for an inventory related process, which provides information sufficient for cost minimization. Particular results for the two-and three-period-lifetime cases are given.
132 citations
TL;DR: In this article, a nonlinear differential equation is used to represent the relation between throughput and the system load, which can give a good approximation of the dynamics of oversaturated or undersaturated system operation.
Abstract: This paper constructs a dynamic model of a general congestion-prone system using a nonlinear differential equation to represent the relation between throughput and the system load. Although the model is not stochastic, it can give a good approximation of the dynamics of oversaturated or undersaturated system operation. The model is used to study the stability and transient behavior of a congestion-prone system and to analyze policies for the control of congestion in a simple optimal control model.
128 citations
TL;DR: It is proved that for a givers number of replenishments m, there exists a unique vector of m time intervals that minimizes the total cost function and it is shown that the total carrying cost obtained after substituting the optimal value of that vector is a convex function of m.
Abstract: We reconsider the classical lot-size model with the assumption that demand rate is deterministic, starts at the origin, and linearly increases with time. Two relevant costs are involved: carrying cost and replenishment cost. The planning horizon is finite and known. The problem is to find the optimal schedule of replenishments, i.e., their number and the schedule of time intervals between consecutive orders. Mathematically, we have to find an integer m and the values of m continuous variables so as to minimize the total carrying and replenishments costs. We prove that for a givers number of replenishments m, there exists a unique vector of m time intervals that minimizes the total cost function. It is further shown that the total carrying cost obtained after substituting the optimal value of that vector is a convex function of m. The algorithm that determines the unique optimal value of m and the unique optimal scheduling of replenishments for m employs these mathematical results. Finally, we investigate the asymptotic properties of the model when the planning horizon is infinite.
121 citations
TL;DR: An important class of mathematical programs, in which the vector variable can be partitioned into two subvectors corresponding to independent constraint sets, is considered, and necessary and sufficient conditions for optimal solutions are developed and two approaches for obtaining solutions are reviewed.
Abstract: We consider an important class of mathematical programs, in which the vector variable can be partitioned into two subvectors corresponding to independent constraint sets. Necessary and sufficient conditions for optimal solutions are developed, and two approaches for obtaining solutions are reviewed. We present an enumeration approach, reducing the problem to a finite number of subproblems, and show that duality makes the solution of many of the subproblems unnecessary. Next, we develop an alternating approach, wherein the problem is solved for one of the subvectors while the other is held constant, and then the subvector roles are reversed. This procedure is observed to converge to partial optimum solutions. A widely applicable subclass of problems includes a linear program in one of the subvectors. For this subclass a sufficient condition for local optimality is determined. The condition is easily testable and fails to hold, in many cases, only if a better solution is obtained. Also, this condition shows that partial optimum solutions are almost always local optima.
110 citations
TL;DR: Under the assumptions that the transition matrix representing the process is upper-triangular and totally positive of order two, it is shown that the state-space can be broken up into at most four regions of action and that the optimal region of repair is of a special intuitive type.
Abstract: This paper presents a model of a deteriorating process with imperfect information. This model, unlike many previous efforts, stipulates that the operator most pay an inspection cost to determine the state of the system. This situation presents him with three choices at every time period: repair, inspection, or inaction. Under the assumptions that the transition matrix representing the process is upper-triangular and totally positive of order two, it is shown that the state-space can be broken up into at most four regions of action and that the optimal region of repair is of a special intuitive type.
102 citations
TL;DR: It is established that a large class of problems of finding optimal facility locations on an imbedding of a finite, undirected network having positive arc lengths is convex, in a well defined sense, for all choices of the data if and only if the network is a tree.
Abstract: This paper studies problems of finding optimal facility locations on an imbedding of a finite, undirected network having positive arc lengths. We establish that a large class of such problems is convex, in a well defined sense, for all choices of the data if and only if the network is a tree. A number of useful properties of related convex functions end convex sets are identified.
96 citations
TL;DR: A unified method for obtaining duality results for concave-convex fractional programs is presented and additional duality theorems, in particular, converse dualityTheorems for nondifferentiable as well as quadratic fractionsal programs are proved.
Abstract: This paper presents a unified method for obtaining duality results for concave-convex fractional programs. We obtain these results by transforming the original nonconvex programming problem into an equivalent convex program. Known results by several authors are related to each other. Moreover, we prove additional duality theorems, in particular, converse duality theorems for nondifferentiable as well as quadratic fractional programs.
TL;DR: This paper evaluates one way to cope with the problem of large or growing leadtimes, and suggests two approaches that may be suitable for small or growing businesses.
Abstract: The advent of relatively sophisticated information systems has made it possible for many businesses that keep inventories to know their needs very rapidly. However, the producers of these inventories have not all made comparable advances in scheduling production to meet the rapidly changing orders placed by their increasingly sophisticated customers. As a result, leadtimes have been growing rather than decreasing. Since in most cases the company needing the inventory cannot control the leadtime, it must either accept it or look for ways to mitigate its effect. This paper evaluates one way to cope with the problem of large or growing leadtimes.
TL;DR: Some computational evidence is presented to suggest that a version of Bellman's shortest-path algorithm outperforms Treesort-Dijkstra's for a certain class of networks.
Abstract: In this note we present some computational evidence to suggest that a version of Bellman's shortest-path algorithm outperforms Treesort-Dijkstra's for a certain class of networks.
TL;DR: A Markovian model in which the holding times in the various states are exponentially distributed is developed, which shows that the total expected cost per time unit is minimized.
Abstract: In this paper we examine maintenance policies for systems in which the degree of deterioration can be observed through inspections. We develop a Markovian model in which the holding times in the various states are exponentially distributed. The costs incurred include costs of inspections, state occupancy costs, costs of preventive repairs, and the costs for repairing a failed system either at an inspection event or immediately after the occurrence of a malfunction. The policies examined include the scheduling of inspections and preventive repairs so that the total expected cost per time unit is minimized.
TL;DR: This bibliography contains references to publications, reports, and articles dealing with stochastic programming in terms of their contents: formulation, applications, theory and computation, books and surveys.
Abstract: About 800 publications, reports, and articles dealing with stochastic programming are included in this bibliography. The references are classified in terms of their contents: formulation, applications, theory and computation, books and surveys.
TL;DR: It is shown that an optimal solution to this problem is a basic feasible solution to a slightly modified generalized transportation problem, and a branch-and-bound solution procedure prevents possible splitting of a job among computers.
Abstract: This paper investigates the assignment of tasks in a network of functionally similar computers. We formulate the problem by a periodic review model with Boolean variables. A computationally efficient, integer-generalized transportation model is applicable because of the existence of relative efficiencies of computers for jobs. Since a job is to be processed exclusively by one computer, we show that an optimal solution to this problem is a basic feasible solution to a slightly modified generalized transportation problem. A branch-and-bound solution procedure prevents possible splitting of a job among computers. We provide an algorithm and computational results.
TL;DR: In this paper, a class of simple plant-location problems under uncertainty are decomposed into two simpler problems that can be solved sequentially with surprising ease, where the risk-averse nature of the firm is incorporated into this model with a mean variance formulation of the objective function.
Abstract: There is a class of simple plant-location problems under uncertainty that can be decomposed into two simpler problems that can be solved sequentially with surprising ease. The salient characteristic of this class of problems is that for any demand generating region, one plant dominates all others as a supply source. We develop and discuss the conditions required for this dominance. The risk-averse nature of the firm is incorporated into this model with a mean-variance formulation of the objective function. The general formulation is particularized to four paradigms of firms characterized by a range of behavioral and market assumptions.
TL;DR: This paper presents a bibliography of the articles that were published before March 1976 and that describe applications of operations research techniques to health-care delivery systems.
Abstract: This paper presents a bibliography of the articles that were published before March 1976 and that describe applications of operations research techniques to health-care delivery systems.
TL;DR: The basic principles enabling one to define essential characteristics of the feasible solutions for a job-shop scheduling problem in which the jobs are constrained by fixed starting times and due dates are presented.
Abstract: This note is concerned with some essential characteristics of the feasible solutions for a job-shop scheduling problem in which the jobs are constrained by fixed starting times and due dates. These characteristics are related to the scheduling order of operations on each machine and to the fixed starting and completion times for each operation. We present the basic principles enabling one to define these characteristics and propose a procedure for finding them.
TL;DR: This paper describes the use of decision analysis to facilitate a group decision-making problem in the selection of trajectories for the two spacecraft of the Mariner Jupiter/Saturn 1977 Project.
Abstract: This paper describes the use of decision analysis to facilitate a group decision-making problem in the selection of trajectories for the two spacecraft of the Mariner Jupiter/Saturn 1977 Project. This NASA project includes the participation of some eighty scientists, divided by specialization among eleven science teams. A set of thirty-two candidate trajectory pairs was developed by the Project, in collaboration with the science teams. Each science team then ordinally ranked and assigned cardinal utility function values to the trajectory pairs. The scientists used these data and statistics derived from collective choice rules in selecting the preferred trajectory pair.
TL;DR: This work addresses the problem of solving a linear program whose objective function coefficients are known only to lie in a given convex set and presents optimality criteria that characterize the desired solution and strengthen earlier results due to Soyster.
Abstract: We address the problem of solving a linear program whose objective function coefficients are known only to lie in a given convex set. We seek a solution that is optimal against the worst possible realization of the objective function, i.e., a max-min solution. We present optimality criteria that characterize the desired solution and strengthen earlier results due to Soyster. The conditions are computationally implementable.
TL;DR: In this paper, the authors give a general result showing when a valid inequality or facet of an integer polytope can be obtained from a valid equality or facet in a subset of the variables.
Abstract: We give a general result showing when a valid inequality or facet of an integer polytope can be obtained from a valid inequality or facet in a subset of the variables.
TL;DR: A method for determining an optimum distribution of beds in a ward by assuming that ward patients can be classified into two categories, that admissions follow Poisson distribution, and that length of stay in the ward follows the negative exponential distribution is developed.
Abstract: Ward beds are a primary resource under the control of hospital management. We develop a method for determining an optimum distribution of beds in a ward by assuming that ward patients can be classified into two categories, that admissions follow Poisson distribution, and that length of stay in the ward follows the negative exponential distribution. After defining a cut-off level as "the number of beds beyond which type 2 non-serious patients are not admitted," we develop a system of differential and difference birth and death process equations for the process. An objective function made up of shortage and holding costs is then developed and optimized for various values of cut-off priority level. An application of this model to a university teaching hospital in Cleveland is illustrated. The model is then extended to a situation where overflows are temporarily housed in a buffer accommodation or inappropriate ward.
TL;DR: The potential applicability of a new choice model and scaling procedure to the marketing decisions of health-care organizations and some suggestions for future use of conjoint measurement and related techniques in marketing studies of health care organizations are discussed.
Abstract: We discuss the potential applicability of a new choice model and scaling procedure to the marketing decisions of health-care organizations. After a brief exposition of this analytical procedure the paper focuses on an illustrative application to the hospital selection decision under two scenarios-surgery with a rapid recovery period and serious surgery that requires a long hospitalization period. The paper concludes with some suggestions for future use of conjoint measurement and related techniques in marketing studies of health care organizations.
TL;DR: This note introduces a general approach to obtain lower bounds for the expected completion time in PERT networks where activity durations are random (discrete or continuous) variables and some well-known bounds can be derived as particular cases of this general approach based on Jensen's inequality.
Abstract: This note introduces a general approach to obtain lower bounds for the expected completion time in PERT networks where activity durations are random (discrete or continuous) variables. We show that some well-known bounds can be derived as particular cases of this general approach based on Jensen's inequality. We assume that the durations of the activities terminating at a node are independent of the durations of the activities terminating at another node and that all the activity durations have a finite positive range.
TL;DR: A cyclic queue model that represents fleet operations of liquid natural gas vessels operating between one loading and one or two discharge ports is developed and analytic and simulation results are presented for the exponential service case under several sets of system parameters.
Abstract: Fleets of liquid natural gas vessels operating between one loading and one or two discharge ports are an example of vehicles that operate in closed cycles between a small number of terminals. We extend previous work to develop a cyclic queue model that represents such fleet operations. For any specific system we obtain the expected number of vessels in each stage, the expected number waiting in each stage, and, most important, the expected waiting time in port. Exponential service time distributions are assumed, but a series of parallel simulation computations examines the effects of other distributions. The results for exponential service are obtained in closed form, so that the simulation model can be tested and the confidence interval of the simulations estimated. Both analytic and simulation results are presented for the exponential service case under several sets of system parameters. Simulation results for the same sets are presented for normally distributed service and travel times. We restrict the...
TL;DR: This work presents a Bayesian procedure that does allow using both sets of test data gathered both at the component level of a multicomponent system and at the system level.
Abstract: On occasion, reliability analysts have test data gathered both at the component level of a multicomponent system and at the system level. When the system test data provide no information on component performance, classical statistical techniques in all but trivial cases do not allow using both sets of data. We present a Bayesian procedure that does allow using both sets. The procedure for attribute data makes use of a lemma that relates the moments of the prior and posterior distributions of reliability to the test data. The procedure for variables data assumes the time to failure distribution of each component is exponential.
TL;DR: This paper presents extensive computational experience with a special-purpose primal simplex code using the augmented threaded index method for solving capacitated and uncapacitated transshipment and transportation problems.
Abstract: This paper presents extensive computational experience with a special-purpose primal simplex code using the augmented threaded index method for solving capacitated and uncapacitated transshipment and transportation problems. This code is distinguished from other codes for solving such problems in that not all of the data resides in central memory simultaneously; thus, it is referred to as an in-core, out-of-core code. The major advantages of such a code over an in-core code are 1 it can solve problems that the latter can not solve because of central memory requirements; 2 even for problems that the latter can solve, it requires less central memory, which is critical for fast job processing on multiprogrammed computer systems; and 3 the code can also be used as an in-core code.
The design of such codes presents numerous computational difficulties in selecting the best starting and pivot procedures in order to minimize central as well as peripheral processing time. We present computational experience with various pivot, start and capacity buffer procedures, as well as different buffer sizes. Computational results are also provided for different types of network problems, including assignment, transportation, and minimum cost flow problems. These computational results are compared with in-core, out-of-kilter, negative cycle, and primal simplex network codes for problem sizes that these codes could solve.
TL;DR: This paper examines a longitudinal model of a manpower system and presents an operational method for calculating optimal accession policies, which can in turn be used to find the equilibrium operating rules for the system.
Abstract: This paper examines a longitudinal model of a manpower system. The demand for effective manpower is determined by the state of a finite Markov chain. There are delays in training effective manpower, and effective manpower is an input to the training process. Thus it is not always available to meet demand. We present an operational method for calculating optimal accession policies. This calculation can in turn be used to find the equilibrium operating rules for the system. The model is a useful device for measuring the impact of alternate assumptions about continuation rates, manpower utilization policies, demand levels, and transition probabilities in the demand process.
TL;DR: The research reported in this paper extends the analysis by considering concave production cost functions and substitution cost functions that add either a unit fixed cost or a unit-independent fixed charge to the previously considered "scrap" cost.
Abstract: The early work done on the assortment problem assumed a linear production cost and a substitution cost based only on the difference in value of the item used and the item required. The research reported in this paper extends the analysis by considering concave production cost functions and substitution cost functions that add either a unit fixed cost or a unit-independent fixed charge to the previously considered "scrap" cost. The form of an optimal stocking policy is developed for each case and horizon theorems are proved to aid in the computations. Algorithms for finding optimal policies are described.