Showing papers in "Naval Research Logistics Quarterly in 1972"

An informal survey of multi‐echelon inventory theory

Abstract: : An informal nonmathematical survey of research in multi-echelon inventory theory is given, covering published results through 1971. An introductory section defines the term, 'multi-echelon', and establishes the kinds of problems involving multi-echelon considerations. Subsequent sections provide surveys of research on deterministic and stochastic multi-echelon inventory control problems, allocation models, and multi-echelon planning and evaluation models. A final section discusses the present state of the art and suggests directions for future research. A bibliography of papers concerning multi-echelon inventory theory and applications is included.

The payment scheduling problem

Abstract: Large complicated projects with interdependent activities can be described by project networks. Arcs represent activities, nodes represent events, and the network's structure defines the relation between activities and events. A schedule associates an occurrence time with each event: the project can be scheduled in several different ways. We assume that a known amount of cash changes hands at each event. Given any schedule the present value of all cash transactions can be calculated. The payment scheduling problem looks for a schedule that maximizes the present value of all transactions. This problem was first introduced by Russell [2]; it is a nonlinear program with linear constraints and a nonconcave objective. This paper demonstrates that the payment scheduling problem can be transformed into an equivalent linear program. The linear program has the structure of a weighted distribution problem and an efficient procedure is presented for its solution. The algorithm requires the solution of triangular systems of equations with all matrix coefficients equal to ± or 0.

An operator theory of parametric programming for the transportation problem‐II

Abstract: This paper investigates the effect on the optimum solution of a (capacitated) transportation problem when the data of the problem (the rim conditions-i. e., the warehouse supplies and market demands-the per unit transportation costs and the upper bounds) are continuously varied as a (linear) function of a single parameter. An operator theory is developed and algorithms provided for applying rim and cost operators that effect the transformation of optimum solution associated with changes in rim conditions and unit costs. Bound operators that effect changes in upper bounds are shown to be equivalent to rim operators. The discussion in this paper is limited to basis preserving operators for which the changes in the data are such that the optimum basis structures are preserved.

A note on the extension of a result on scheduling with secondary criteria

Abstract: A result of Smith previously published in this journal [3], on the use of secondary criterion in scheduling problems is extended, and an example presented.

Postoptimality analysis in zero‐one programming by implicit enumeration

Abstract: The procedures for postoptimality analysis that are so much a part of linear programming studies have no simple counterparts in an integer programming context In the case of Balas' Additive Algorithm, however, it would appear that the capacity of the technique to facilitate certain types of postoptimality analysis has not been fully exploited This paper proposes an extension of the additive algorithm that utilizes insights generated while solving the original problem to do subsequent analysis upon it In particular, procedures are developed for doing limited parameter ranging and for seeking new optima in light of parameter changes

Properties of a multifacility location problem involving euclidian distances

Abstract: This paper considers a problem of locating new facilities in the plane with respect to existing facilities, the locations of which are known The problem consists of finding locations of new facilities which will minimize a total cost function which consists of a sum of costs directly proportional to the Euclidian distances among the new facilities, and costs directly proportional to the Euclidian distances between new and existing facilities It is established that the total cost function has a minimum; necessary conditions for a mimumum are obtained; necessary and sufficient conditions are obtained for the function to be strictly convex (it is always convex); when the problem is “well structured,” it is established that for a minimum cost solution the locations of the new facilities will lie in the convex hull of the locations of the existing facilities Also, a dual to the problem is obtained and interpreted; necessary and sufficient conditions for optimum solutions to the problem, and to its dual, are developed, as well as complementary slackness conditions Many of the properties to be presented are motivated by, based on, and extend the results of Kuhn's study of the location problem known as the General Fermat Problem

On Optimal Assembly of Systems

Abstract: : The paper discusses the following reliability problem: A system has k different types of components. Associated with each component is a numerical value. Let the set(a sup j) (j = 1,...,k) denote the set of numerical values of the k components. Let R(a(sup 1),...,a(sup k) denote the probability that the system will perform satisfactorily (i.e. R(a(sup 1),...,a(sup k) is the reliability of the system) and assume R(a(sup 1),...,a(sup k) has the properties of a joint cumulative distribution function.

A mixed optimization technique for the generalized machine replacement problem

Abstract: : A mixed optimization technique for optimal machine replacement is presented which allows much more flexibility than previous models. Optimal purchase, maintenance, and sale of a given machine between any two given points in time is treated as a sub-problem, which one may choose to solve via control theory, dynamic programming, or practical engineering considerations. (A control theory formulation is used in the paper as an illustration.) These sub-problem solutions are then incorporated into a Wagner-Whitin formulation for solution of the full problem. The technique is particularly useful for problems with such asymmetries as an existing initial machine or uneven technological change. (Author)

Tolerance intervals for univariate distributions

Abstract: A review of univariate tolerance intervals is presented from an application-oriented point of view. Both β-content and β-expectation intervals are defined and considered. Standard problems are discussed for the distribution-free case and with various distributional assumptions (normal, gamma, Poisson) which occur most frequently in practice. The determination of sample size is emphasized. A number of examples are used to illustrate the types of problems which permit solutions with the excellent tables now available.

Quadratic programming with quadratic constraints

Abstract: A program with a quadratic objective function and quadratic constraints is considered. Two duals to such programs are provided, and an algorithm is presented based upon approximations to the duals. The algorithm consists of a sequence of linear programs and programs involving the optimization of a quadratic function either unconstrained or constrained to the nonnegative orthant. An example involving production planning is presented.

Equivalent knapsack‐type formulations of bounded integer linear programs: An alternative approach

Abstract: In this paper we show that every bounded integer linear program can be transformed into an integer program involving one single linear constraint and upper and lower bounds on the variables, such that the solution space of the original problem coincides with that one of the equivalent knapsack-type problem.

A class of inventory models with customer impatience

Abstract: Classical inventory models generally assume either no backlogging of demands or unlimited backlogging. This paper treats the case wherein backlogged customers are willing to wait for a random period of time for service. A broad class of such models is discussed, with a more complete analysis performed on a simple subclass. Steady state equations are derived and solved assuming exponentially distributed interarrival times of customers, order delivery lead times, and customer patience.

Inventory allocation among an assembly and its repairable subassemblies

Abstract: In this paper we consider a major assembly composed of two or more subassemblies. The failure of any subassembly causes the major assembly to not function. Every failed subassembly is repaired or replaced. A total investment in stocks of spare components is to be distributed among the various subassemblies and the major assembly so as to provide the best possible customer service. This is a complicated problem: relevant factors are the failure rates, unit costs, and repair times of the various components. For the case of Poisson failures, a heuristic solution is developed which is a compromise between theoretical optimality and practical usefulness.

The multicommodity network flow model revised to include vehicle per time period and node constraints

Abstract: THE MINIMUM-COST FORMULATION OF THE PROBLEM OF DETERMINING MULTICOMMODITY FLOWS OVER A CAPACITATED NETWORK SUBJECT TO RESOURCE CONSTRAINTS HAS BEEN TREATED IN PREVIOUS PAPERS. IN THOSE TREATMENTS ONLY CAPACITATED ARCS WERE ASSUMED, AND A UNIFORM UNIT OF MEASURE LIKE SHORT TONS WAS USED FOR ALL COMMODITIES. THIS PAPER TREATS THE EFFECT OF CONSTRAINTS ON THE NODES OF THE NETWORK, ALLOWS THE COMMODITIES TO BE MEASUREED IN THEIR "NATURAL" UNITS, AND ALLOWS THE NETWORK CAPACITIES TO BE EXPRESSED IN VEHICLES PER TIME PERIOD - IN SOME CASES GIVING A MORE ACCURATE REPRESENTATION OF THE CAPACITIES OF THE NETWORK. THIS PAPER DESCRIBES THE SOLUTION PROCEDURE WHICH USES THE COLUMN GENERATION TECHNIQUE; IT ALSO DISCUSSES COMPUTATIONAL EXPERIENCE. /AUTHOR/

Generalized implicit enumeration using bounds on variables for solving linear programs with zero‐one variables

Abstract: In an earlier paper [1] we put forth a framework that helps to tie together a number of approaches for solving integer programming problems. We outlined there how Balas' Additive Algorithm can be explained and generalized in terms of the framework. In the present paper we review Balas' algorithm, and our earlier framework, and present an algorithm generalizing Balas' scheme. In addition, some examples are presented and future research to be done is discussed.

On the economic application of airlift to product distribution and its impact on inventory levels

Abstract: In many resupply situations, the decisionmaker has the option of “purchasing” faster replenishment leadtimes. For example, a premium may be paid for delivery by parcel post rather than slower but less expensive delivery by railway express. It may be economically advantageous to pay shipment premiums for faster leadtimes when considering the possible cost reductions in pipeline (on-order) inventory and safety stock levels. This paper develops a decision rule which, for any given item, will indicate whether it is economically advantageous to purchase a faster leadtime. The general methodology is then applied to a peacetime military resupply operation involving several million items, each requiring a decision as to whether the item should be shipped by air or sea.

Constructing bimatrix games with special properties

Abstract: This work is concerned primarily with presenting techniques for constructing bimatrix games with predetermined equilibrium points. Some partial results on Nash-solvability are also given.

The reliability of multicomponent systems subject to cannibalization

Abstract: A reliability model for multicomponent multistate systems is presented. This is a generalization of a model previously studied by Hirsch, Meisner, and Boll. In the earlier model, when a failure occurs for which no replacement spare is available, the locations using the same type of part as that having failed are “cannibalized” so as to allocate the shortages to locations where they are least detrimental to system performance. Here, we permit certain restrictions to be imposed upon the cannibalization procedure, and develop effective techniques for relating the probability laws governing the level of system performance to the system structure, cannibalization policy, kit of spare parts, and part reliabilities.

Optimal location of public facilities

Abstract: Location of both public and private facilities has become an important consideration in today's society. Progress in solution of location problems has been impeded by difficulty of the fixed charge problem and the lack of an efficient algorithm for large problems. In this paper a method is developed for solving large-scale public location problems. An implicit enumeration scheme with an imbedded transportation algorithm forms the basis of the solution technique.

Determining optimal growth paths in logistics operations

Abstract: This paper considers a logistics system modelled as a transportation problem with a linear cost structure and lower bounds on supply from each origin and to each destination. We provide an algorithm for obtaining the growth path of such a system, i. e., determining the optimum shipment patterns and supply levels from origins and to destinations, when the total volume handled in the system is increased. Extensions of the procedure for the case when the costs of supplying are convex and piecewise linear and for solving transportation problems that are not in “standard form” are discussed. A procedure is provided for determining optimal plant capacities when the market requirements have prespecified growth rates. A goal programming growth model where the minimum requirements are treated as goals rather than as absolute requirements is also formulated.

On the isbell and marlow fire programming problem

Abstract: A complete solution is derived to the Isbell and Marlow fire programming problem. The original work of Isbell and Marlow has been extended by determining the regions of the initial state space from which optimal paths lead to each of the terminal states of combat. The solution process has involved determining the domain of controllability for each of the terminal states of combat and the determination of dispersal surfaces. This solution process suggests a solution procedure applicable to a wider class of tactical allocation problems, terminal control attrition differential games. The structure of optimal target engagement policies in “fights to the finish” is discussed.

Readiness and the optimal redeployment of resources

Abstract: : The paper considers the problem of the optimal redeployment of a resource among different geographical locations.

Systems approach to the multistage manufacturing connected-unit situation

Abstract: This paper investigates the relationships among incoming quality limit (AIQL), manufacturing quality level in each stage of production, and outgoing quality limit (AOQL), for a multistage manufacturing connected-unit situation from the systems cost-effectiveness point of view. An objective function is developed and the formulated problem is solved using discrete optimization technique. The study is restricted to the development of single sampling plans where inspection is by attribute. Lot size and sample size are fixed for incoming and outgoing inspection for each stage of manufacturing.

Duality in fractional programming

Abstract: : The paper develops theoretical and computational aspects of the dual problem in linear fractional programming. This is done on the basis of two alternative algorithms for the primal fractional programming problem, both of which were presented in earlier literature. Parametric programming is considered, and attention is given to infinitesimal as well as to discrete changes in the resource-vector. (Author)

Bayes adaptive control of two-echelon inventory systems i: development for a special case of one-station lower echelon and monte carlo evaluation

Abstract: Bayes adaptive control policies are developed in the present paper for the special case of a one-station lower echelon: a Poisson distribution of demand, whose mean is assumed to have a prior gamma distribution. The cost structure is of a common type. The ordering policy for the upper echelon, which minimizes expected cost, is replaced by a new type of policy, called Bayes prediction policy. This policy does not require tedious computations, of the sort required by dynamic programming solutions. The characteristics of the policies are studied by Monte Carlo simulation, and supplemented by further theoretical development.

Expectation of contract incentives

Abstract: The application of statistical expectation to risk density functions and fee/incentive-element relationships is shown to be useful in structuring contract incentives. A mathematical procedure for calculating the expected value of fee for a given risk/incentive arrangement is described along with cost examples and related sensitivity analyses. The structuring of equivalent incentives is demonstrated by the use of the contracting procedure used for procuring the C-5A aircraft.

Minimal disconnecting sets in directed multi‐commodity networks

Abstract: The problem of finding minimal disconnecting sets for multi-commodity directed networks may be solved using an arc-path formulation and Gomory's all-integer integer programming algorithm. However, the number of network constraints may be astronomical for even moderately sized networks. This paper develops a finite algorithm similar to Gomory's, but requiring no more than m rows in the tableau, where m is the number of arcs in the network.

Sequential bid selection by stochastic approximation

Abstract: Suppose that a contractor is faced with a sequence of “minimum bid wins contract” competitions. Assuming that a contractor knows his cost to fulfill the contract at each competition and that competitors are merely informed whether or not they have won, bids may be selected sequentially via a tailored stochastic approximation procedure. The efficacy of this approach in certain bidding environments is investigated.

Productivity estimates of the strategic airlift system by the use of simulation

Abstract: Although the strategic airlift system is under continuous analysis, C-5A problems provided impetus to analyze the airlift system productivity function by using a large-scale simulation model. Development of the simulation model (Simulation of Airlift Resources - SOAR) was initiated by the Office of Secretary of Defense (Systems Analysis) in 1966. SOAR had barely become operational in time for the study in November 1968. Since limited verification and validation tests had been performed on the simulation model, the design of experiments was of critical importance. The experimental design had to be flexible enough to salvage the maximum amount of information possible upon the discovery of either a verification or validation error. In addition, the experimental design was required to accommodate the estimation of a large number of possibly changing independent variables. The experimental design developed for the analysis was full factorial design sets for a finite number of factors. Initial analysis began with aggregated sets of factors at two levels, and information gained from experiment execution was used to parse the sets. The process was sequential and parsing continued until the major explanatory independent variables were identified or enough information was obtained to eliminate the factor from further direct analysis. This design permitted the overlapping of simulation runs to fill out the factorial design sets. In addition to estimating the airlift productivity function, several other findings are reported which tended to disprove previous assumptions about the nature of the strategic airlift system.