Showing papers in "Naval Research Logistics Quarterly in 1969"
TL;DR: In this article, a mixed integer programming method for solving the facility location problem with capacities on the facilities is presented, which uses a Decomposition technique to solve the dual of the associated continuous problem in each branch-bound iteration.
Abstract: This paper discusses a mixed integer programming method for solving the Facilities Location Problem with capacities on the facilities. The algorithm uses a Decomposition technique to solve the dual of the associated continuous problem in each branch-bound iteration. The method was designed to produce the global optimum solution for problems with up to 100 facilities and 1,000 customers. Computational experience and a complete example are also presented in the appendix.
182 citations
TL;DR: A method is given for finding those solutions of a transportation problem which minimize the total time necessary for transporting goods from the suppliers to the consumers.
Abstract: A method is given for finding those solutions of a transportation problem which minimize the total time necessary for transporting goods from the suppliers to the consumers. Several extensions of the model are presented.
148 citations
TL;DR: In this paper, the exact bounds on dimensions of cycling examples are established, and it is shown that Beale's example is the smallest one which cycles at a non-optimal solution, that a smaller one can cycle at the optimum, and that, in general, a cycling example must have at least two equations, at least six variables, and at least three nonbasic variables.
Abstract: Although cycling in the simplex method has long been known, a number of theoretical questions concerning cycling have not been fully answered. One of these, stated in [3], is to find the smallest example of cycling, and Beale's example with three equations and seven variables is conjectured to be the smallest one. The exact bounds on dimensions of cycling examples are established in this paper. We show that Beale's example is the smallest one which cycles at a non-optimal solution, that a smaller one can cycle at the optimum, and that, in general (including the completely degenerate case), a cycling example must have at least two equations, at least six variables, and at least three non-basic variables. Examples and geometries are given for the extreme cases, showing that the bounds are sharp.
52 citations
TL;DR: In this article, the authors present a survey on the theory of semi-infinite programming as a generalization of linear programming and convex duality theory, and present a new generalisation of the Kuhn-Tucker saddle-point equivalence theorem for arbitrary convex functions in n-space where differentiability is no longer assumed.
Abstract: We first present a survey on the theory of semi-infinite programming as a generalization of linear programming and convex duality theory. By the pairing of a finite dimensional vector space over an arbitrarily ordered field with a generalized finite sequence space, the major theorems of linear programming are generalized. When applied to Euclidean spaces, semi-infinite programming theory yields a dual theorem associating as dual problems minimization of an arbitrary convex function over an arbitrary convex set in n-space with maximization of a linear function in non-negative variables of a generalized finite sequence space subject to a finite system of linear equations.
We then present a new generalization of the Kuhn-Tucker saddle-point equivalence theorem for arbitrary convex functions in n-space where differentiability is no longer assumed.
51 citations
TL;DR: In this paper, the authors consider the problem of simultaneously locating any number of facilities in three-dimensional Euclidean space, and the criterion to be satisfied is that of minimizing the total cost of some activity between the facilities to be located and any many of fixed locations.
Abstract: We consider the problem of simultaneously locating any number of facilities in three-dimensional Euclidean space. The criterion to be satisfied is that of minimizing the total cost of some activity between the facilities to be located and any number of fixed locations. Any amount of activity may be present between any pair of the facilities themselves. The total cost is assumed to be a linear function of the inter-facility and facility-to-fixed locations distances. Since the total cost function for this problem is convex, a unique optimal solution exists. Certain discontinuities are shown to exist in the derivatives of the total cost function which previously has prevented the successful use of gradient computing methods for locating optimal solutions. This article demonstrates the use of a created function which possesses all the necessary properties for ensuring the convergence of first order gradient techniques and is itself uniformly convergent to the actual objective function. Use of the fitted function and the dual problem in the case of constrained problems enables solutions to be determined within any predetermined degree of accuracy.
Some computation results are given for both constrained and unconstrained problems.
49 citations
TL;DR: In this article, an approximate solution method for solving the fixed charge problem is described, which is applied to a set of test problems to explore the margin of error, and the results indicate that the proposed fixed charge simplex algorithm is capable of finding optimal or near optimal solutions to moderate sized fixed charge problems.
Abstract: This paper describes an approximate solution method for solving the fixed charge problem. This heuristic approach is applied to a set of test problems to explore the margin of error. The results indicate that the proposed fixed charge simplex algorithm is capable of finding optimal or near optimal solutions to moderate sized fixed charge problems. In the absence of an exact method, this heuristic should prove useful in solving this fundamental nonlinear programming problem.
49 citations
TL;DR: The computational results show that if obsolescence is a distinct possibility in the near future, it is quite important that the probabilities of Obsolescence be incorporated into the model before computing the optimal policies.
Abstract: A stochastic single product convex cost inventory problem is considered in which there is a probability, πj, that the product will become obsolete in the future period j. In an interesting paper, Barankin and Denny essentially formulate the model, but do not describe some of its interesting and relevant ramifications. This paper is written not only to bring out some of these ramifications, but also to describe some computational results using this model. The computational results show that if obsolescence is a distinct possibility in the near future, it is quite important that the probabilities of obsolescence be incorporated into the model before computing the optimal policies.
47 citations
TL;DR: In this article, it is shown that this distribution is a special case of a compound generalized extreme value distribution which is derived by compounding a generalized extreme distribution with a gamma distribution.
Abstract: Logistic distribution is widely used in describing biological, engineering, industrial, and various other types of data In this paper it is shown that this distribution is a special case of a compound generalized extreme value distribution which is derived by compounding a generalized extreme value distribution with a gamma distribution The paper contains several useful results relevant to these distribution functions
44 citations
TL;DR: In this paper, the authors formulate the multi-commodity maximal flow problem into a node-arc form and show that when decomposition is applied to this form, the resulting master and subproblems become precisely those described by Ford & Fulkerson [3] using the arc-chain formulation.
Abstract: The purpose of this article is to formulate the multi-commodity maximal flow problem into a node-arc form and to show that when decomposition is applied to this form the resulting master and subproblems become precisely those described by Ford & Fulkerson [3] using the arc-chain formulation. A generalization to the problem is then considered which can potentially speed its convergence.
29 citations
TL;DR: In this article, the authors considered the problem of determining a few observations from a sufficiently large complete or censored sample from the extreme value distribution with location and scale parameters, respectively, such that the asymptotically best linear unbiased estimators (ABLUE) of the parameters in Ref.
Abstract: The present study is concerned with the determination of a few observations from a sufficiently large complete or censored sample from the extreme value distribution with location and scale parameters μ and σ, respectively, such that the asymptotically best linear unbiased estimators (ABLUE) of the parameters in Ref. [24] yield high efficiencies among other choices of the same number of observations. (All efficiencies considered are relative to the Cramer-Rao lower bounds for regular unbiased estimators.) The study is on the asymptotic theory and under Type II censoring scheme.
For the estimation of μ when σ is known, it has been proved that there exists a unique optimum spacing whether the sample is complete, right censored, left censored, or doubly censored. Several tables are prepared to aid in the numerical computation of the estimates as well as to furnish their efficiencies.
For the estimation of σ when μ is known, it has been observed that there does not exist a unique optimum spacing. Accordingly we have obtained a spacing based on a complete sample which yields high efficiency. A similar table as above is prepared.
When both μ and σ are unknown, we have considered four different spacings based on a complete sample and chosen the one yielding highest efficiency. A table of the efficiencies is also prepared.
Finally we apply the above results for the estimation of the scale and/or shape parameters of the Weibull distribution.
27 citations
TL;DR: It is proved that the properties of the shortest processing time rule and the due-date rule which are known for the deterministic situation also hold in the probabilistic environment when they are suitably, and reasonably, refined for this context.
Abstract: A single machine scheduling problem in which both the processing times and due-dates of the jobs awaiting servicing are random variables is analyzed It is proved that the properties of the shortest processing time rule and the due-date rule which are known for the deterministic situation also hold in the probabilistic environment when they are suitably, and reasonably, refined for this context
TL;DR: In this paper, the authors extend the generalized von Neumann model to an open model by assuming that there are exogeneously determined export and import prices and that any amount can be exported or imported at these prices.
Abstract: : The authors extend the generalized von Neumann model to an open model by assuming that there are exogeneously determined export and import prices and that any amount can be exported or imported at these prices. The open model is characterized by means of seven axioms. It is shown, by applying the theory of linear programming, that if four economically reasonable assumptions hold, the open model has at least one solution in which at least one good with positive export price is exported and at least one good with positive import price is imported. It is also shown that, in general, a continuum of expansion rates can be achieved by varying certain control variables. The choice of these expansion rates gives indirectly the choice of a suitable sub-economy and also determined the exports and imports of the economy. (Author)
TL;DR: This article describes an analytic approach to flight scheduling within an airlift system that consists of a monthly planning model that produces an initial schedule and a daily model for making periodic changes in the schedule, formulated as two-stage stochastic linear programs.
Abstract: This article describes an analytic approach to flight scheduling within an airlift system. The model takes explicit account of the uncertainty present in cargo requirements or demands. For computational feasibility, the approach consists of two related models: (1) a monthly planning model that produces an initial schedule, and (2) a daily model for making periodic changes in the schedule. Both are formulated as two-stage stochastic linear programs. A detailed mathematical description of each model and its physical interpretation is given.
The monthly model determines the number of flights each type of aircraft in the fleet. Excess demands on certain routes are assumed to be met, at least in part, by spot procurement of commerical lift from outside the system. The flight assignment is determined by minimizing the expected total system cost, which consists of operating costs, costs of reallocating aircraft to different routes, spot commercial procurement costs, and other penalty costs of excess demand. The model accounts for limitations on the number of flying hours and the carrying capacities of various aircraft in satisfying demands.
In the daily model the number of aircraft of each type to switch from one route to another and the number of commercial flights on spot contract to add on the current day are the principal decision variables. These are determined by balancing operating, procurement, and redistribution costs against the expected costs of additional cargo delay. The current state of the system — the amount of unmoved cargo on various routes andathe position of aircraft throughout the system — plays a role in determining these decisions.
A description of two variants of an algorithm recently developed for this class of problems is presented. Both versions, which use ideas from convex programming, make extensive use of linear programming codes for the brunt of the calculations. The models may thus be solved by augmenting existing linear programming routines.
TL;DR: In this paper, the authors convert a quadratic assignment problem with a nonconvex objective function into an integer linear program and then solve the equivalent integer program by a simple enumeration that produces global minima.
Abstract: We convert a quadratic assignment problem [1] with a nonconvex objective function into an integer linear program. We then solve the equivalent integer program by a simple enumeration that produces global minima.
TL;DR: An empiric Bayes estimation procedure of the optimal Bayesian stock level is presented, and a dynamic programming method for obtaining the general Bayes sequential procedure is outlined.
Abstract: Bayesian determination of optimal stock levels is studied for the case of Poisson distribution of the demand variable, and prior gamma distribution of the expected demand. Bayes sequential procedure is derived, assuming that stock level can be adjusted at the beginning of each period so that a shortage can be immediately replenished and an overstock can be corrected. The Bayes sequential procedure is more difficult to obtain if this assumption is removed. A dynamic programming method for obtaining the general Bayes sequential procedure is outlined. Finally, an empiric Bayes estimation procedure of the optimal Bayesian stock level is presented.
TL;DR: In this article, the authors examined the effectiveness of incentive contracts as a means for controlling defense procurement costs, and presented empirical evidence suggesting that these contracts may not have accomplished their intended goal of increased efficiency and lower procurement costs.
Abstract: Incentive contracts are intended to motivate defense contractors to perform more efficiently and control costs more closely. By increasing the total profit as actual costs are reduced below a predetermined cost target, they encourage contractors to achieve cost under runs. Consequently, the principal advantage claimed for these contracts is that they make the financial incentives to reduce costs more effective.
This study examines the effectiveness of incentive contracts as a means for controlling defense procurement costs. The study considers the various effects that incentive contracts may have on both contractors' performance and contract costs, and presents empirical evidence suggesting that these contracts may not have accomplished their intended goal of increased efficiency and lower procurement costs.
TL;DR: In this article, the emphasis is upon problems of parameter estimation, and the present paper is related to certain articles that have appeared in this journal, which can be found in Section 2.1.
Abstract: Work by the present authors on life distributions derived from stochastic hazard functions [4] is related to certain articles that have appeared in this journal. This relationship is illustrated. The emphasis of this article is upon problems of parameter estimation.
TL;DR: Bounds are determined for the optimal inventory which indicate that the inclusion of the replacement cost lowers the optimal Inventory, and procedures are given for calculating the optimal spares level.
Abstract: A mathematical model is formulated for determining the number of spare components to purchase when components stochastically fail according to a known life distribution function and there is a cost incurred when a component is replaced. Bounds are determined for the optimal inventory which indicate that the inclusion of the replacement cost lowers the optimal inventory.
Since these bounds are no easier to calculate than the optimal spares level, the theory is specialized to components with exponentially distributed time to failure. Procedures are given for calculating the optimal spares level, and numerical examples are provided.
TL;DR: The result of the study is not a conclusive selection among policies, but a schedule of present values on the basis of which, together with values of the external benefits, a decision can be reached on how to replace aircraft in the Naval Advanced Jet Pilot Training mission.
Abstract: This paper describes a method of solving aircraft service life problems. The particular application concerns aircraft in the Naval Advanced Jet Training Command. The method of solution is comparative present value analysis of alternative replacement policies. The likely risks of estimation errors are reflected in the comparisons of present values. Differences are noted in the benefits associated with each policy, but external to Naval Aviation. Since the values of these benefits can be determined only at a higher level of decision-making, the result of the study is not a conclusive selection among policies, but a schedule of present values on the basis of which, together with values of the external benefits, a decision can be reached.
This paper discusses replacement policies for aircraft used in the Naval Advanced Jet Pilot Training mission. Taking engineering technology and the training syllabus as given, four feasible plans for introducing replacement aircraft into service are evaluated in terms of the present values of differential costs associated with the plans and in terms of the likely errors in cost estimates used in calculation of the present values. The trade-off between present value of costs and planning flexibility is emphasized in choosing a recommended time pattern of aircraft replacement. The specific aircraft mixes considered are the TF–9J/TAF–9J and the TA–4F/A–4B. The first is the currently employed mix; the second is the proposed replacement.
The problem is to select an optimal time-pattern of replacement of F–9's by A–4's, given technological differences favoring the A–4 and increasing costs of maintaining squadrons of F–9's. Replacements by aircraft types other than the A–4 are considered impractical. Four feasible plans for introducing A–4's through a 5-year period are evaluated in terms of current best estimates of the related costs of the plans and in terms of the flexibility of modifying each plan given future better information concerning the relevant costs. The method of analysis is comparative present value of expected costs.
TL;DR: Applications of results obtained by these authors for a generalized version of a problem proposed by Smirnov, are considered and the relationship between the limiting and exact expressions relating to this table is explored.
Abstract: In this paper applications of results obtained by these authors for a generalized version of a problem proposed by Smirnov, are considered. The areas of application explored are system interface, queueing, transportation flow, and sequential analysis. The included table should be invaluable to the reader in applying these results. Finally the relationship between the limiting and exact expressions relating to this table is also explored.
TL;DR: For the case of no time lag in delivery, one stage deterioration, and either binomial or uniform deterioration, optimal ordering policies are obtained for the n‐period dynamic model with the standard cost structure.
Abstract: : This report considers the problem of maintaining an inventory of an item which can deteriorate and become useless. Several models are considered. New items are assumed to be delivered immediately or after a delay. Items are considered to deteriorate through one or two states before becoming useless. Optimal and suboptimal ordering policies are obtained for these models which minimize ordering, shortage, and holding costs when the deterioration is assumed to depend on the number of items in the inventory. The policies are the single critical number type. (Author)
TL;DR: In this paper, the authors generalized the notion of k-convexity to guarantee a relatively simple form for the optimal policy in an n decision problem and showed that when there is no setup cost, a convexity argument can be used to show that optimal policy has a simple form.
Abstract: The system to be controlled produces n products simultaneously in fixed proportions every time it is activated. Demands for the products in any period are components of an n dimensional vector random variable with known distribution function. Cases of excess demands backlogged and excess demands lost are considered. In the former the notion of k convexity can be generalized to guarantee relatively simple form for the optimal policy in an n decision problem. In the latter, this generalization was not successful although when there is no setup cost, a convexity argument can be used to show that the optimal policy has a simple form.
TL;DR: Inventory models with a new objective function and a model with incompletely known demands which depend on the state of the inventory are considered, and the optimal ordering policy is shown to be a myopic single critical level policy.
Abstract: : This report considers inventory models with a new objective function and a model with incompletely known demands which depend on the state of the inventory. The shortage probability criterion is defined, and the form of optimal policies under this new criterion is proved. Optimal policies are obtained for a particular model with unknown binomial demands when Bayesian estimation methods are used. The object of the shortage probability criterion is to minimize the order costs subject to the restriction that the probability that inventory falls below a given level not to exceed a given value. Inventory models with state dependent and independent demands and with various delivery lags are considered, and the optimal ordering policy in all cases is shown to be a myopic single critical level policy. A Bayesian estimation procedure is developed for a model with binomially distributed demands where the parameter p is unknown. The Bayesian estimate is incorporated into a myopic policy which is shown to be optimal. (Author)
TL;DR: Some optimal strategies of targeting and firing of missiles are derived and conditions under which such a war can be prevented are developed.
Abstract: The present article considers a problem of missile warfare. It is formulated as a problem of economics and treated as a differential game. Some optimal strategies of targeting and firing of missiles are derived. Conditions under which such a war can be prevented are also developed.
TL;DR: In this paper, the authors present a quantitative index of the level of risk assumed by a contractor in various contract type situations, which includes expression of real world uncertainty and contractor's utility for money.
Abstract: This paper presents a quantitative index of the level of risk assumed by a contractor in various contract type situations. The definition includes expression of real world uncertainty and contractor's utility for money. Examples are given for the major contract types and special applications are discussed.
TL;DR: In this paper, the uniformly minimum variance unbiased estimates of two indices of performance of a system which alternates between two states "up" or "down" in accordance with a Markov process were obtained.
Abstract: This paper obtains the uniformly minimum variance unbiased estimates of two indices of performance of a system which alternates between two states “up” or “down” in accordance with a Markov process. The two indices are (1) operational readiness, which measures the probability that the system will be up when needed; and (2) operational reliability, which measures the probability that the system will be up during the entire time of need. For the purpose of obtaining these estimates, two types of observations are considered: (a) those which reveal only the state of system at isolated time-points, and (b) those which continuously record the duration of the “up” and “down” times of the system.
TL;DR: A brief description of a new general approach to demand prediction problems based on the demand characteristics of parent components and the parts installed in these components is given.
Abstract: : A brief description of a new general approach to demand prediction problems is given. This is based on the demand characteristics of parent components and the parts installed in these components. A specific model is presented which employs this information. The paper concludes with empirical tests fof the model. (Author)
TL;DR: In this paper, a statistic is determined for testing the hypothesis of equality for scale parameters from two populations, each of which has the first asymptotic distribution of smallest (extreme) values.
Abstract: A statistic is determined for testing the hypothesis of equality for scale parameters from two populations, each of which has the first asymptotic distribution of smallest (extreme) values. The probability distribution is derived for this statistic, and critical values are determined and given in tabular form for a one-sided or two-sided alternative, for censored samples of size n1 and n2, n1 = 2, 3, …. 6, n2 = 2, 3, …. 6. The power function of the test for certain alternatives is also calculated and listed in each case considered.
TL;DR: In this paper, the authors consider production processes which undergo stochastic deterioration and demonstrate that under appropriate conditions a smallest optimum reject allowance exists and can be easily computed and investigate the optimality of periodic process inspections and show that in some cases one can do better by following an (r, R) inspection-processing policy.
Abstract: Since most manufacturing processes inevitably produce some defective items, it is common practice to produce a quantity larger than the actual order size. This excess is called a reject allowance. In this paper we consider production processes which undergo stochastic deterioration and demonstrate that under appropriate conditions a smallest optimum reject allowance exists and can be easily computed. We also investigate the optimality of periodic process inspections and show that in some cases one can do better by following an (r, R) inspection-processing policy.