Showing papers in "Operations Research in 1971"
TL;DR: In this paper, the location of emergency facilities is viewed as a set covering problem with equal costs in the objective, where sets are composed of the potential facility points within a specified time or
Abstract: This paper views the location of emergency facilities as a set covering problem with equal costs in the objective The sets are composed of the potential facility points within a specified time or
1,561 citations
TL;DR: The paper gives a simple formula for finding the equation of the hyperplane, discusses some ways of strengthening the cut, proposes an algorithm, and gives a finiteness proof.
Abstract: This paper proposes a new class of cutting planes for integer programming. A typical member of the class is generated as follows. Let X be the feasible set, and x the optimal (noninteger) solution...
314 citations
TL;DR: A number of resource-allocation problems, including that of multi-item scheduling, may be solved approximately as large linear programs, as in Manne, using the Dantzig-Wolfe decomposition principle.
Abstract: A number of resource-allocation problems, including that of multi-item scheduling, may be solved approximately as large linear programs, as in Manne [Management Sci. 4, 115-135 1958]. Dzielinski and Gomory [Management Sci. 11, 874-890 1965] applied the Dantzig-Wolfe decomposition principle to this problem. Here, the problem is attacked directly, using a column generation technique and Dantzig and Van Slyke's generalized upper-bounding method [J. Comp. and Syst. Sci. 1, 213-226 1967]. For problems involving I items and T time periods, one need deal with a basis matrix of dimension only T by T. A lower bound on the optimal cost may be developed, and intermediate solutions all have Manne's integer property loc. cit.. Computational experiments, including an option for pricing out subproblem solutions until none is useful, show a number of iterations to optimality of from one-half to one-ninth the number required by the decomposition principle with work per iteration remaining approximately the same. Extensions of the basic model are also described. These form the core of an automated production-scheduling and inventory-control system, currently being used by a major U. S. manufacturer. Computational experience with this extended model is presented.
257 citations
TL;DR: This paper considers a GI/M/1 queuing process with an associated linear cost-reward structure and stationary balking process, and, based on a probabilistic analysis of the system, derives optimal joining rules for an individual arrival, as well as for the entire community of customers.
Abstract: This paper considers a GI/M/1 queuing process with an associated linear cost-reward structure and stationary balking process, and, based on a probabilistic analysis of the system, it derives optimal joining rules for an individual arrival, as well as for the entire community of customers. For the infinite-horizon, average-reward criterion, it shows that, among all stationary policies, the optimal strategies are control-limit rules of the form: join if and only if the queue size is not greater than some specific number. However, it finds that, in general, exercising self-optimization does not optimize public good. Accordingly, the paper explores the idea of controlling the queue size by levying tolls-thus achieving the system's over-all-optimal economic performance. Finally, it analyzes a "competition" model in which customers face a service agency that is a profit-making organization, and shows it to be similar to the monopoly model of price theory.
178 citations
TL;DR: The paper characterizes an optimal policy for the infinite-horizon discounted problem, offers an optimality proof, and presents a computational algorithm.
Abstract: This paper studies the optimal operation of an M/G/1 queuing system with removable server and the following cost structure: a holding cost per customer in the system per unit time, a cost per unit time of keeping the server running, and fixed charges for turning the server on or off. The server can be turned on at arrival epochs or off at service-completion epochs. The paper characterizes an optimal policy for the infinite-horizon discounted problem, offers an optimality proof, and presents a computational algorithm.
169 citations
TL;DR: In this paper, a two-level modification of the M/M/1 queuing model where the rate of arrival and the service capacity are subject to Poisson alternations is studied.
Abstract: This paper studies a two-level modification of the M/M/1 queuing model where the rate of arrival and the service capacity are subject to Poisson alternations. The ensuing "two-dimensional" problem is analyzed by using partial-generating-function techniques, which appear to be essential in the present context. The steady-state probabilities and the expected queue are evaluated, and numerous special and extreme cases are analyzed in detail.
156 citations
TL;DR: This review summarizes in condensed form results known to date, providing some refinements to gain further generality, and clarified the structure underlying quasi-convex functions by presenting analogues to properties of convex functions and by illustrating where analogues do not exist.
Abstract: Many theorems involving convex functions have appeared in the literature since the pioneering work of Jensen. Recently some results have been obtained for a larger class of functions: quasi-convex....
144 citations
TL;DR: This paper lists, alphabetically by first author, over 100 papers and books dealing with competitive bidding.
Abstract: This paper lists, alphabetically by first author, over 100 papers and books dealing with competitive bidding.
143 citations
TL;DR: An underlying theory for the traveling-salesman problem is developed, pathological performance of some existing techniques are predicted, and two algorithms are presented, based upon the theory, with predictable polynomial growth in expected computation time and resistence to pathological problems.
Abstract: The traveling-salesman problem has been the target of a substantial number of computational algorithms over the last two decades. Reported computational experience with these algorithms varies widely; authors, however, have generally failed to explain this variation adequately, or to offer predictive theories for their approaches. This paper a develops an underlying theory for the problem, b predicts pathological performance of some existing techniques, and c presents two algorithms, based upon the theory, with predictable polynomial growth in expected computation time and resistence to pathological problems.
136 citations
TL;DR: Upper and lower bounding distributions for the activity starting- and finishing-time probability distributions are obtained, as well as upper and lower bounds for the expected starting and finishing time of each network activity, and for expected network resource flows.
Abstract: Where the durations of the activities in an acyclic scheduling network are random variables, this paper obtains upper and lower bounding distributions for the activity starting- and finishing-time probability distributions, as well as upper and lower bounds for the expected starting and finishing time of each network activity, and for expected network resource flows. The tightness of the bounds for various networks is examined, and a computational experience with the methods is reported.
132 citations
TL;DR: This paper presents a modification to the Ford-Fulkerson algorithm for maximal dynamic flow in a time-weighted, capacitated network, and produces a shipping schedule representing what has been termed the universal maximalynamic flow.
Abstract: This paper presents a modification to the Ford-Fulkerson algorithm for maximal dynamic flow in a time-weighted, capacitated network. The modification is mild, as conjectured by Gale, and produces a shipping schedule representing what has been termed the universal maximal dynamic flow. The universal feature is that, in constructing a schedule for P periods, this same schedule is maximal when truncated to p less than P periods. A numerical example compares the temporally repeated and universal-type solutions.
TL;DR: This paper shows that an optimal whereabouts search never searches the box to be guessed, and gives an algorithm for finding an optimal locations-search strategy, and is compared to a similar problem proposed by Bellman.
Abstract: An optimal whereabouts search maximizes the probability of correctly stating, at the end of a search costing no more than some budget C, which box contains the object. This can be accomplished either by finding the object in the search or by guessing, at the end of an unsuccessful search, which box contains the object. Generalizing work of Tognetti, this paper shows that an optimal whereabouts search never searches the box to be guessed, and gives an algorithm for finding an optimal whereabouts-search strategy. Finally, whereabouts search is compared to a similar problem proposed by Bellman.
TL;DR: This paper derives exact expressions for the stationary distributions of stock on hand, stock in repair, and backlogged demand at each facility, and indicates how these expressions may be utilized for optimization purposes.
Abstract: This paper considers a two-echelon inventory model for consumable or repairable parts in which the first-echelon facilities use one-for-one replenishment policies and the second-echelon facility uses a continuous-review s, S policy Repair may be accomplished at all facilities Repair and transportation times are assumed to be deterministic, and the failure processes that generate demands are assumed to be Poisson The paper derives exact expressions for the stationary distributions of stock on hand, stock in repair, and backlogged demand at each facility, and indicates how these expressions may be utilized for optimization purposes
TL;DR: The algorithm has been found to be highly effective for a good number of relatively large problems and stems from an efficient suboptimization procedure, which constructs excellent integer solutions from the solutions to linear-programming subproblems.
Abstract: This paper presents an algorithm for the set-covering problem that is, min c'y: Ey ⧠e, y ⧠0, yi integer, where E is an m by n matrix of l's and 0's, and e is an m-vector of l's. The special problem structure permits a rather efficient, yet simple, solution procedure that is basically a 0, 1 search of the single-branch type coupled with linear programming and a suboptimization technique. The algorithm has been found to be highly effective for a good number of relatively large problems. Problems from 30 to 905 variables with as many as 200 rows have been solved in less than 16 minutes on an IBM 360 Model 50 computer. The algorithm's effectiveness stems from an efficient suboptimization procedure, which constructs excellent integer solutions from the solutions to linear-programming subproblems.
TL;DR: In this paper, a single-item multi-period inventory model is proposed in which future prices of the purchased item are assumed to be determined by a Markovian stochastic process instead of being known with certainty.
Abstract: This paper studies a single-item multi-period inventory model in which future prices of the purchased item are assumed to be determined by a Markovian stochastic process instead of being known with certainty. Convex holding and shortage costs and a set-up charge for ordering are assumed. Such a model applies to purchasing a commodity whose price fluctuates widely because of speculative activity and large variations in supply or demand. For both a finite and infinite planning horizon, the paper determines the form and bounds of optimal policies and discusses computational approaches exploiting structure.
TL;DR: A test of an algorithm proposed for the bottleneck assignment problem against a “threshold” algorithm, and it is found that the latter is superior computationally.
Abstract: Gross has proposed an algorithm for the bottleneck assignment problem. This note reports a test of it against a “threshold” algorithm, and finds that the latter is superior computationally.
TL;DR: In this paper, the authors present an exact solution of the fixed-charge transportation problem by decomposing it into a master integer program and a series of transportation subprograms, and a composite algorithm based on Murty's and the author's results is proposed.
Abstract: In the fixed-charge transportation problem, a fixed charge is associated with each route that can be opened, in addition to the variable transportation cost proportional to the amount of goods shipped- This note presents an exact solution of this mixed integer programming problem by decomposing it into a master integer program and a series of transportation subprograms. To reduce the number of vertices that need to be examined, bounds are established on the maximum and minimum values of the total fixed cost, and feasibility conditions for the transportation problem are used extensively. Computational results show the method to be particularly suitable when fixed costs are large compared to variable costs. A composite algorithm based on Murty's and the author's results is proposed.
TL;DR: The concept of utility independence is introduced, and general expressions for simplifying the assessment of multiattribute utility functions are derived, given that certain utility independence assumptions hold.
Abstract: This paper introduces and defines the concept of utility independence, and derives general expressions for simplifying the assessment of multiattribute utility functions, given that certain utility independence assumptions hold. These results are more general than the commonly used additive utility function, which is shown to be a special case. Finally, the paper discusses the relevance of this work as an approximation technique when requisite assumptions are not satisfied.
TL;DR: In this paper, the first two moments of the input were used to obtain bounds on the expected wait in an A/G/k queue with stationary input, in terms of the expected delay in the queue length.
Abstract: This paper obtains bounds, in terms of the first two moments of the input, on the expected wait in an A/G/k queue with stationary input. To this end, two single-server systems are constructed. The wait in queue for the first single-server system is stochastically larger than the wait in the given multiserver system, and the expected wait in the second single-server system is used to obtain a lower bound on the expected wait in the A/G/k system. The paper also develops, as a consequence of the lower bounds, some results concerning the optimum number of servers, given a fixed work capacity.
TL;DR: A search method, roughly resembling Balas's filter method, is proposed for the solution of the problem, and an application of the model to a real industrial problem is described.
Abstract: This paper considers a special class of transportation problems. There is a set of sources producing the same material with a fixed maximum capacity, and a set of users whose demands for the material are known. A cost is associated with the transportation of the material from each source to each user. Each user is to be supplied by one source only. The problem consists of finding the flow of the material from the sources to the users that satisfies their demands and minimizes the total transportation cost. The formulation of the problem is the same as the well-known Hitchcock problem with the further constraint that all the variables are binary. The paper proposes a search method, roughly resembling Balas's filter method, for the solution of the problem, and discusses it from a computational point of view. Finally, it describes an application of the model to a real industrial problem.
TL;DR: By further restricting holding and penalty costs to be proportional, the author has extended preliminary work by Karlin and Scarf to obtain good bounds for both the optimal order policy and the associated minimum-expected-discounted-cost function for the stationary problem.
Abstract: A considerable literature has been devoted to periodic-review inventory problems with proportional ordering costs and known independent demand distributions, because of the optimality under broad conditions of “base-stock” policies. An important exception is the case when order delivery is lagged and excess demand is simply lost, which is more complicated. By further restricting holding and penalty costs to be proportional, the author has extended preliminary work by Karlin and Scarf to obtain good bounds for both the optimal order policy and the associated minimum-expected-discounted-cost function for the stationary problem. These bounds possess a “newsboy” interpretation primarily in terms of costs to be incurred specifically for the review period (the period marked by the arrival of this order). In fact, the upper ordering bound is precisely the “myopic” policy in Veinott's sense. (However, the myopic policy is not base stock.) Experimental results for the one- and two-period lag problems strongly supp...
TL;DR: This paper analyzes the M/G/1 queue under the well known round-robin RR discipline and proposes an effective calculating method for obtaining the expected response time under an arbitrary processing-time distribution with overhead.
Abstract: In order to discuss scheduling algorithms for time-sharing computer systems, this paper analyzes the M/G/1 queue under the well known round-robin RR discipline. Three models are considered: the constant-quantum RR model, the processor-shared or zero-quantum RR model, and the variable-quantum RR model. The paper proposes an effective calculating method for obtaining the expected response time under an arbitrary processing-time distribution with overhead. By the theoretical analysis, one can show how the response time is affected by the scheduling and processing-time distributions, as is demonstrated by some typical examples.
TL;DR: Two extensions of the successful Beale and Small branch-and-bound mixed-integer algorithm are proposed, utilizing the integer requirements on nonbasic variables to calculate stronger "penalties" when searching down the solution tree and to give a stronger criterion for abandoning unprofitable branches of the tree when backtracking.
Abstract: This note proposes two extensions of the successful Beale and Small branch-and-bound mixed-integer algorithm. The integer requirements on nonbasic variables are utilized to calculate stronger "penalties" when searching down the solution tree and to give a stronger criterion for abandoning unprofitable branches of the tree when backtracking. This stronger criterion is obtained by making use of Gomory cutting-plane constraints. These modifications have produced considerable reductions of the searching effort required for pure integer and predominantly integer problems, and have the further advantage of being very easy to incorporate.
TL;DR: This note describes a method for locatingAny number of facilities optimally in relation to any number of existing facilities to minimize the total of load-times-distance costs in the system.
Abstract: This note describes a method for locating any number of facilities optimally in relation to any number of existing facilities. The objective is to minimize the total of load-times-distance costs in the system. Any amount of loading may be present between the new facilities and the existing facilities and between the new facilities themselves. Distances are assumed to be rectangular.
TL;DR: It is shown that, under certain assumptions, problems of maximizing a sum of linear or concave-convex fractional functions on closed and bounded polyhedral sets can be transformed into equivalent ones of maximizing multiparameter linear or Concave functions subject to additional feasibility constraints.
Abstract: The paper deals with problems of maximizing a sum of linear or concave-convex fractional functions on closed and bounded polyhedral sets. It shows that, under certain assumptions, problems of this type can be transformed into equivalent ones of maximizing multiparameter linear or concave functions subject to additional feasibility constraints. The problems are transformed into those finding roots of monotone-decreasing convex functions. Where the objective function is separable, such a root is unique, and any local optimum is a global one, i.e., the objective function is quasi-concave. In problems involving separable linear fractional functions, under some additional assumptions, the parametric presentation results in a combinational property. Where the number of terms in the objective function is equal or less than three, this property leads to an efficient algorithm.
TL;DR: An analytic model that evaluates the expected number of aircraft not operationally ready at a random point in time because of supply NORS is developed, and it is shown that the optimal allocation is virtually the same as the METRIC allocation.
Abstract: This paper develops an analytic model that evaluates the expected number of aircraft not operationally ready at a random point in time because of supply NORS. The model was developed for application to the F-111 aircraft for a multilevel problem, where demand on a first-level line replaceable unit LRU eventually causes second-level demands for one or more modules that are components of the LRU. The model is for a single base. Since it is evaluative in nature, the inputs include item stock levels as well as item demand rates, average repair times, and resupply times. An optimization model to determine stock levels that minimize the number of NORS aircraft subject to a budget constraint would be preferable to the evaluation model. The paper shows, however, that an optimization model is not mathematically tractable because the criterion function is not separable into independent item calculations. But an example using F-111 data indicates that if the METRIC model [see Opns. Res. 16, 122-141 1968] is used to optimize stock levels, the resulting number of aircraft NORS is within 1 percent of the minimum number of aircraft achievable with the same budget. Finally, the well-known formula of Erlang for the M/G/s service system with no queue allowed is generalized to the case where demand rates and repair rates may be a function of the number of units already in repair. This enables us to examine the sensitivity of the optimal allocation of budget across a group of items when expediting may take place. Though expediting improves system performance, the conclusion is that the optimal allocation is virtually the same as the METRIC allocation.
TL;DR: In this paper, a game between two players who choose from a collection of objects is considered, where players make their choices alternately and the value or amount that the ith player will gain if he selects the jth object.
Abstract: This paper considers a game between two players who choose from a collection of objects. The players make their choices alternately and Vi,j represents the value or amount that the ith player will gain if he selects the jth object. In relation to these values, the players may have various strategies or approaches to the game, and each of them constitutes a distinct theoretical problem. The paper formulates and solves three of these problems, each one having practical significance for example, for the draft of professional football players.
TL;DR: This paper investigates two queue disciplines: alternating priority and strict priority and obtains the Laplace-Stieltjes transforms of the waiting-time distributions for a stationary process, as well as the first moments of the wait time distributions.
Abstract: A single server attends to two separate queues. Each queue has Poisson arrivals and a general service time distribution. A changeover time, with a general distribution, is required whenever the server crosses from one queue to the other. This paper investigates two queue disciplines: alternating priority and strict priority. In each case, it obtains the Laplace-Stieltjes transforms of the waiting-time distributions for a stationary process, as well as the first moments of the waiting-time distributions.
TL;DR: Along with modularity and cannibalization, multistage commonality is an essential component of a theory of efficient engineering design.
Abstract: The problem of commonality is posed as a problem of economic balance. It involves the disutility of refusing to provide each segment of customers with an item fitting its exact requirements versus economies of scale achieved in producing and inventorying each item. The depth of the product line the optimal number of items to produce is determined by finding the minimum concave cost flow through a network. An efficient dynamic program developed in production smoothing is used to find this flow. Many products consist of interacting subassemblies; such multistage problems of finding the number of types of each subassembly can also be solved; a computational procedure is developed and an example presented. Along with modularity and cannibalization, multistage commonality is an essential component of a theory of efficient engineering design.
TL;DR: Examples of the application of extreme value distributions and the Weibull distribution as mechanisms for estimating optimum limits are provided and the development of decision rules applicable to the decision of continuing or halting the heuristic analysis is illustrated.
Abstract: Heuristic algorithms have frequently been developed in the attempt to solve combinatorial problems such as those that frequently exist in plant-layout planning, sequencing, scheduling, and routing situations. In these algorithms there has been no basis available to evaluate the progress of the heuristic results in relation to an optimum. This paper outlines and provides examples of the application of extreme value distributions and, more particularly, the Weibull distribution as mechanisms for estimating optimum limits. Given such estimates, the paper further illustrates the development of decision rules applicable to the decision of continuing or halting the heuristic analysis.