Showing papers in "Operations Research in 1979"
TL;DR: Conditions for additive, multiplicative, and more complex forms of the measurable multiattribute value function are presented, providing a link between the additive value function and multiattribute utility theory.
Abstract: This paper presents a theory of measurable multiattribute value functions. Measurable value functions are based on the concept of a “preference difference” between alternatives and provide an interval scale of measurement for preferences under certainty. We present conditions for additive, multiplicative, and more complex forms of the measurable multiattribute value function. This development provides a link between the additive value function and multiattribute utility theory.
606 citations
TL;DR: A review of aggregate models developed on a priori grounds brings out similarities and differences among those of Vidale and Wolfe, Nerlove and Arrow, Little, and others and identifies ways in which the models agree or disagree with observed phenomena.
Abstract: Aggregate advertising models relate product sales to advertising spending for a market as a whole. Although many models have been built, they frequently contradict each other and considerable doubt exists as to which models best represent advertising processes. An increasingly rich literature of empirical studies helps resolve these issues by revealing major advertising phenomena that models should encompass. These include sales responding upward and downward at different rates, steady state response that can be concave or S-shaped and can have positive sales at zero advertising, sales affected by competitive advertising; and advertising dollar effectiveness that can change over time. A review of aggregate models developed on a priori grounds brings out similarities and differences among those of Vidale and Wolfe, Nerlove and Arrow, Little, and others and identifies ways in which the models agree or disagree with observed phenomena. A Lanchester-motivated structure generalizes many features of these model...
391 citations
TL;DR: The branch-and-bound algorithm for the multiple-choice knapsack problem resides with the quick solution of the linear programming relaxation and its efficient, subsequent reoptimization as a result of branching.
Abstract: The multiple-choice knapsack problem is defined as a binary knapsack problem with the addition of disjoint multiple-choice constraints The strength of the branch-and-bound algorithm we present for
344 citations
TL;DR: This paper presents a new sequential procedure based on the method of batch means for constructing a confidence interval with coverage close to the desired level that does not explicitly require a stochastic process to have regeneration points.
Abstract: A common problem faced by simulators is that of constructing a confidence interval for the steady-state mean of a stochastic process. We have reviewed the existing procedures for this problem and found that all but one either produce confidence intervals with coverages which may be considerably lower than desired or have not been adequately tested. Thus, in many cases simulators will have more confidence in their results than is justified. In this paper we present a new sequential procedure based on the method of batch means for constructing a confidence interval with coverage close to the desired level. The procedure has the advantage that it does not explicitly require a stochastic process to have regeneration points. Empirical results for a large number of stochastic systems indicate that the new procedure performs quite well.
223 citations
TL;DR: A new family of shortest-route methods are presented, which reduce an upper bound on running time, and make empirical comparisons for a certain class of networks, and allow for exploitation of structure by pruning arcs and/or nodes.
Abstract: We present a new family of shortest-route methods, which reduce an upper bound on running time, and make empirical comparisons for a certain class of networks. These methods also allow for exploitation of structure by pruning arcs and/or nodes.
209 citations
TL;DR: The marketing problem of determining the optimal timing of advertising expenditures over a finite planning horizon in a duopoly conflict situation is portrayed as a non-zero-sum differential game.
Abstract: The marketing problem of determining the optimal timing of advertising expenditures over a finite planning horizon in a duopoly conflict situation is portrayed as a non-zero-sum differential game. Advertising expenditures are determined which optimize multiobjective performance indices in a Nash equilibrium sense. The dynamics of the market are described by utilizing an extension of the Vidale-Wolfe model of the sales response to advertising. A numerical algorithm is used to solve the model.
194 citations
TL;DR: A continuous time Markov decision process with uniformly bounded transition rates is shown to be equivalent to a simpler discrete time MarkOV decision process for both the discounted and average reward criteria on an infinite horizon.
Abstract: A continuous time Markov decision process with uniformly bounded transition rates is shown to be equivalent to a simpler discrete time Markov decision process for both the discounted and average re...
179 citations
TL;DR: Age replacement policies are investigated and a preventive replacement is made when a unit reaches age T and if the random repair cost is less than a fixed constant, a minimal repair is made.
Abstract: Age replacement policies are investigated. When a unit reaches age T, a preventive replacement is made. If a failure occurs prior to age T and if the random repair cost is less than a fixed constant, a minimal repair is made. Otherwise the unit is replaced at failure.
170 citations
TL;DR: An algorithm to compute reliability measures on a stochastic network in which both nodes and links can fail, and also computes the latter two measures when all communication must proceed through a root node.
Abstract: This paper presents an algorithm to compute reliability measures on a stochastic network in which both nodes and links can fail. The measures considered are the probability that nodes s and t can communicate for all node pairs s and t, the probability that all operative node pairs can communicate, and the expected number of node pairs communicating. It also computes the latter two measures when all communication must proceed through a root node. A specialized version of the algorithm is given for networks in which only nodes can fail.
162 citations
TL;DR: A simulator that determines the best S or (s, S) policies by a Fibonacci search of the appropriate response surface is developed and the performance of the approximations derived with the optimal policies for leadtimes of one and two periods is compared.
Abstract: This paper treats three realistic versions of the classical leadtime lost-sales inventory problem: inclusion of a set-up for ordering, partial backordering, and the random leadtime lost-sales inventory problem, as well as all possible combinations of these three models. The goal of the study is to construct simple myopic approximations for these various models. We report extensive computations that compare the approximations derived with the optimal policies for leadtimes of one and two periods. In addition, we develop a simulator that determines the best S or (s, S) policies by a Fibonacci search of the appropriate response surface and compares the performance of the approximations to these policies for maximum leadtimes of five, ten, and twenty periods for a variety of configurations of the cost structure, demand distribution, and leadtime distribution.
151 citations
TL;DR: This paper proposes a dynamic programming algorithm for decision CPM (DCPM) networks that simultaneously determines the optimal solution for any desired number of project due dates with only a slight increase in computer time.
Abstract: This paper proposes a dynamic programming algorithm for decision CPM (DCPM) networks. DCPM is a natural, powerful, and general way of handling the discrete-time/cost-tradeoff problem. Solution approaches developed to date have not been efficient enough to handle realistically sized problems. The main approaches have been general integer programming algorithms and the specialized branch-and-bound methods for DCPM of Crowston and Wagner. Both of these approaches have many inherent shortcomings solution times grow exponentially with the number of decision nodes, storage requirements quickly become excessive, pre-processing or decomposition of the problem must be undertaken before the algorithms themselves can be called upon to solve the problem, and large variations in solution times have been found based on differences in the structure of the problem. The algorithm presented here overcomes all of these shortcomings. Most significantly, it exhibits only a linear growth in the solution times based on the numb...
TL;DR: In order to obtain mean waiting time approximations it appears to be useful to introduce a quantity (the “normed cooperation coefficient”) which is inversely proportional to WGs andWhich is in some sense a measure for the “cooperation” between the servers of the service facility.
Abstract: This paper considers the problem of obtaining approximate expressions for the first moment WGs of the stationary waiting time distribution in an M/G/s queueing system. Special attention is paid to the case G ≡ D, i.e., constant service times. Most known approximations are in fact heavy traffic approximations which have rather large relative errors in the light traffic case. In the present study both the light traffic and heavy traffic behavior of WGs (WDs) are taken into account. In order to obtain mean waiting time approximations it appears to be useful to introduce a quantity (the “normed cooperation coefficient”) which is inversely proportional to WGs and which is in some sense a measure for the “cooperation” between the servers of the service facility. A part of the paper is devoted to the analysis of this normed cooperation coefficient.
TL;DR: Four heuristic methods are developed to obtain approximate solutions to the multidimensional 0-1 knapsack problem and are compared to the rigorous optimum as well as to a heuristic method of Toyoda.
Abstract: In this paper, we develop four heuristic methods to obtain approximate solutions to the multidimensional 0-1 knapsack problem. The four methods are tested on a number of problems of various sizes. The solutions are compared to the rigorous optimum as well as to a heuristic method of Toyoda. They are statistically better than the latter, with average relative errors of the order of less than 1%.
TL;DR: A dynamic programming formulation for finding the optimal ordering policy that calls for a smaller state space than that proposed by Zangwill is presented and a very simple heuristic procedure and its variants are introduced.
Abstract: 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.
TL;DR: These algorithms for the knapsack sharing problem extend the sharing problem algorithm in a companion paper to any piecewise linear, nonlinear, or piecewise nonlinear tradeoff functions.
Abstract: The knapsack sharing problem has a utility or tradeoff function for each variable and seeks to maximize the value of the smallest tradeoff function (a maximin objective function). A single constraint places an upper bound on the sum of the non-negative variables. We develop efficient algorithms for piecewise linear, nonlinear, and piecewise nonlinear tradeoff functions and for any knapsack sharing problem with integer variables. These algorithms for the knapsack sharing problem extend the sharing problem algorithm in a companion paper to any piecewise linear, nonlinear, or piecewise nonlinear tradeoff functions.
TL;DR: A continuous deterministic-demand, stochastic lead-time inventory model such that the individual unit demands are non-interchangeable is considered and a lower bound, independent of the order size, is developed for the optimal ordering time.
Abstract: We consider a continuous deterministic-demand, stochastic lead-time inventory model such that the individual unit demands are non-interchangeable. We derive equations that define the optimal values of the two decision variables: order size and timing. This model is shown to be a stochastic lead-time generalization of the EOQ model with backlogging of demand. An illustrative example is presented. Finally, a lower bound, which is independent of the order size, is developed for the optimal ordering time.
TL;DR: This survey provides an exposition of seven technoeconomic models that are representative of recent work on energy policy, and offers suggestions on the future role of modeling in the public policy process.
Abstract: This survey provides an exposition of seven technoeconomic models that are representative of recent work on energy policy. The paper begins with several microeconomic concepts related to energy conservation and to energy-economy interactions. We then examine three representative medium-term models which deal with pricing, import policy and investment decisions in today's conventional supply technologies. Next, we analyze four studies dealing with longer-range issues-alternative research and development strategies for a transition away from depletable energy resources. The paper concludes with a summary of unresolved issues, and with suggestions on the future role of modeling in the public policy process.
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TL;DR: A new approach to resource distribution problems is presented as a network flow problem with a maximum objective function and the value of the smallest linear tradeoff function at the terminal points in a capacitated network is maximized.
Abstract: Many important problems are concerned with the equitable distribution of resources. A new approach to resource distribution problems is presented as a network flow problem with a maximum objective function. The value of the smallest linear tradeoff function at the terminal points in a capacitated network is maximized. We develop a polynomially bounded algorithm and give computational experience. We illustrate the importance and usefulness of the sharing-problem model by considering the equitable distribution of coal during a prolonged coal strike.
TL;DR: Monotonicity results for a fairly general class of partially observable Markov decision processes when there are only two actual states and when the actions taken are primarily intended to improve the system, rather than to inspect it are examined.
Abstract: This paper examines monotonicity results for a fairly general class of partially observable Markov decision processes. When there are only two actual states in the system and when the actions taken are primarily intended to improve the system, rather than to inspect it, we give reasonable conditions which ensure that the optimal reward function and the optimal action are both monotone in the current state of information. Examples of maintenance systems and advertising systems for which our results hold are given. Finally, we examine the case where there are three or more actual states and indicate the difficulties encountered when we attempt to extend the monotonicity results to this situation.
TL;DR: Bounds on heuristics and relaxations for the problem of determining a maximum weight hamiltonian circuit in a complete, undirected graph with non-negative edge weights are given and extended to arbitrary edge weights and minimization problems.
Abstract: We give bounds on heuristics and relaxations for the problem of determining a maximum weight hamiltonian circuit in a complete, undirected graph with non-negative edge weights. Three well-known heuristics are shown to produce a tour whose weight is at least half of the weight of an optimal tour. Another heuristic, based on perfect two-matchings, is shown to produce a tour whose weight is at least two-thirds of the weight of an optimal tour. Assignment and perfect two-matching relaxations are shown to produce upper bounds that are, respectively, at most 2 and 3/2 times the optimal value. By defining a more general measure of performance, we extend the results to arbitrary edge weights and minimization problems. We also present analogous results for directed graphs.
TL;DR: An 0(n log mn) algorithm is presented to preemptively schedule n tasks on m identical machines that meets all due dates (when possible) and generates schedules with at most n − 2 preemptions.
Abstract: An 0(n log mn) algorithm is presented to preemptively schedule n tasks on m identical machines. The tasks are assumed to have due dates. All tasks are initially available. The objective is to obtain a preemptive schedule that meets all due dates (when possible). Our algorithm generates schedules with at most n − 2 preemptions. The algorithm may also be used to schedule a set of n tasks all having the same due date but having different release dates.
TL;DR: Time-dependent and stationary distributions of inventory position and on-hand inventory under the (s, S) policy for a continuous review inventory system with general inter-arrival and demand distributions and a constant lead time are derived.
Abstract: We derive time-dependent and stationary distributions of inventory position and on-hand inventory under the (s, S) policy for a continuous review inventory system with general inter-arrival and demand distributions and a constant lead time. Some results are also obtained for the characterization of the optimal policies.
TL;DR: Desirable features of software for solving nonlinear optimization problems are discussed, and several available codes for solving NLPs are described in terms of these features.
Abstract: Desirable features of software for solving nonlinear optimization problems are discussed, and several available codes for solving NLPs are described in terms of these features. Codes are classified by algorithm type. Addresses where codes may be obtained are given. The paper concludes with a brief survey of available computational experience with several classes of algorithms and with some of the specific codes considered.
TL;DR: This paper presents a methodology for the allocation of natural gas that consists of several objective functions, a set of linear constraints, and aSet of nonlinear constraints that represent the momentum balance necessary for each pipe segment, compressor, or valve.
Abstract: This paper presents a methodology for the allocation of natural gas. The model consists of several objective functions, a set of linear constraints, and a set of nonlinear constraints. The objective functions represent allocation in various categories and can be optimized sequentially. The linear constraints represent the conservation of flow equations for the pipeline network and various accounting relationships. The nonlinear constraints represent the momentum balance necessary for each pipe segment, compressor, or valve. The nonlinear constraints are linearized in a method similar to the method of approximate programming (MAP). A matrix generator is used to create the necessary files for the program execution. We have solved example problems with over 250 linear constraints, 240 nonlinear constraints, and 800 structural columns.
TL;DR: A novel analysis of the steady-state probabilities of a class of infinite Markov chains of this type, which appear in the study of bulk queues and a variety of other stochastic models, is given.
Abstract: We give a novel analysis of the steady-state probabilities of a class of infinite Markov chains. Markov chains of this type appear in the study of bulk queues and a variety of other stochastic models. We present algorithms that involve only real arithmetic and avoid the traditional analysis based on Rouche's theorem.
TL;DR: This work examines the problem of scheduling parallel production lines in the glass-container industry with a resource constraint imposed by the furnace melting rate and concludes that a shortest processing time based dispatching rule probably provides the most efficient operating policy.
Abstract: By means of a computer simulation we examine the problem of scheduling parallel production lines in the glass-container industry with a resource constraint imposed by the furnace melting rate. The results of the simulation model are combined with relevant aspects of scheduling theory to arrive at the conclusion that a shortest processing time based dispatching rule probably provides the most efficient operating policy.
TL;DR: The n-job 2-machine flow shop problem with series-parallel precedence constraints is considered with the objective to minimize makespan with results utilized in the development of a polynomial bounded optimal algorithm.
Abstract: The n-job 2-machine flow shop problem with series-parallel precedence constraints is considered with the objective to minimize makespan. Recent results of Kurisu are utilized in the development of a polynomial bounded optimal algorithm.
TL;DR: The proposed method for the degree-two exponential polynomial model is more efficient than time-scale transformation of a homogeneous Poisson process, and should be applicable to other rate function models.
Abstract: A new method for simulating a nonhomogeneous Poisson process with rate function λ(t) = exp{α0 + α1t + a2t2} in a fixed time interval (0, t0] is given. The method is based on a decomposition of the process, it employs a rejection technique, in conjunction with a method for simulating the nonhomogeneous Poisson process with rate function exp {γ0 + γ1t} by generation of gap statistics from a random number of exponential random variables with suitably chosen parameters. The proposed method for the degree-two exponential polynomial model is more efficient than time-scale transformation of a homogeneous Poisson process, and should be applicable to other rate function models.
TL;DR: A method of decomposing integer programs with block angular structure based on the notion of searching for the optimal solution to an integer program among the near-optimal solutions to its Lagrangian relaxation and an optimality theorem is obtained.
Abstract: A method of decomposing integer programs with block angular structure is presented. It is based on the notion of searching for the optimal solution to an integer program among the near-optimal solutions to its Lagrangian relaxation. An optimality theorem is obtained and a generic decomposition algorithm is presented. An application of this approach is discussed and some computational results are reported.
TL;DR: This paper analyzes mathematically a queueing model where a single server dispenses service to several, m, non-preemptive priority classes and finds an implicit function as well as upper and lower bounds on the expected waiting time of k customer.
Abstract: This paper analyzes mathematically a queueing model where a single server dispenses service to several, m, non-preemptive priority classes. It is assumed that the arrival process of customers who belong to the k class (k customers) is Poisson, and their service times are independent, identical, arbitrarily distributed random variables. The priority degree of a customer at a certain moment is not only a function of his class, but is also a general concave function of the time he has already spent in the system. (The discipline is termed “dynamic-priority.”) Upon departure the server selects for service, from the customers present, the one with the highest instantaneous priority degree, breaking ties by the FIFO rule. An implicit function as well as upper and lower bounds on the expected waiting time of k customer are found. The effectiveness of the bounds is demonstrated by a numerical example.