Showing papers in "Naval Research Logistics in 1991"

Future supply uncertainty in EOQ models

Abstract: This article deals with an inventory problem where the supply is available only during an interval of (random) length X. The unavailability of supply lasts for a random duration Y. Using concepts from renewal theory, we construct an objective function (average cost/time) in terms of the order-quantity decision variable Q. We develop the individual cost components as order, holding, and shortage costs after introducing two important random variables. Due to the complexity of the objective function when X and Y are general random variables, we discuss two special cases and provide numerical examples with sensitivity analysis on the cost and noncost parameters. The article concludes with a discussion of the comparison of the current model with random yield and random lead-time models. Suggestions for further research are also provided.

Optimal inventory policies for substitutable commodities with stochastic demand

Abstract: In this article we consider a stochastic model for two products which have a single-period inventory structure and which can be used as substitutes for each other should the need arise. Substitution will occur with probability one, but at perhaps a different revenue level. We prove that the expected profit function is concave, allowing us to find optimal stocking levels for the two products. We compare optimum inventory levels for the case of single substitution with that where there is no substitution. It is demonstrated for the case of single substitution that total optimum order quantities can actually increase or decrease with the substitution revenue.

A new heuristic solution method in resource‐constrained project scheduling

Abstract: A new heuristic method is presented for the resolution of multiresource constrained conflicts in project scheduling. In attempting to find a minimal makespan solution, the algorithm employs a simple procedure to generate a feasible solution with no backtracking. A postanalysis phase then applies a hill-climbing search. The solution method is different from existing heuristic methods in that it repairs resource conflicts rather than constructs detailed schedules by dispatching activities. Resource-violating sets of activities are identified which must be prevented from concurrent execution because this would violate resource constraints. Repairs are made by imposing an arc to sequence two activities in such a resource violating set. Computational results are compared with those of existing heuristics for the minimal makespan problem.

Parallel machine replacement

Abstract: We consider the parallel replacement problem in which there are both fixed and variable costs associated with replacing machines. Increasing maintenance costs motivate replacements, and the fixed replacement cost provides incentive for replacing machines of different ages together in “clusters.” We prove two intuitive results for this problem. First, it is never optimal to split a cluster of like-aged machines, and second, it is never optimal to replace newer clusters before older clusters. By incorporating these two results into an algorithmic approach, we vastly reduce the amount of computation required to identify an optimal replacement policy.

Minimizing flow time on a single machine with job classes and setup times

Abstract: We examine the static sequencing problem of ordering the processing of jobs on a single machine so as to minimize the average weighted flow time. It is assumed that all jobs have zero ready times, and that the jobs are grouped into classes with the property that setup tasks are only required when processing switches from jobs of one class to jobs of another class. The time required for each setup task is given by the sum of a setdown time from the previous class and a setup time for the new class. We show that an algorithm presented in the literature for solving a special case of this problem gives suboptimal solutions. A number of properties of the optimal solution are derived, and their use in algorithms is evaluated. Computational results are presented for both a branch-and-bound procedure and a simpler depth-first search.

Facility location when demand is time dependent

Abstract: In this article we investigate the problem of locating a facility among a given set of demand points when the weights associated with each demand point change in time in a known way. It is assumed that the location of the facility can be changed one or more times during the time horizon. We need to find the time “breaks” when the location of the facility is to be changed, and the location of the facility during each time segment between breaks. We investigate the minisum Weber problem and also minimax facility location. For the former we show how to calculate the objective function for given time breaks and optimally solve the rectilinear distance problem with one time break and linear change of weights over time. Location of multiple time breaks is also discussed. For minimax location problems we devise two algorithms that solve the problem optimally for any number of time breaks and any distance metric. These algorithms are also applicable to network location problems.

Heuristics for minimizing mean tardiness form parallel machines

Abstract: The concept of parallel operations has been widely used in manufacturing and data processing. However, not many efficient methods have been proposed to reduce job tardiness. This article proposes an efficient heuristic to minimize the mean tardiness of a set of tasks with known processing times and due dates for single and m parallel machines. For the single-machine case, the proposed heuristic is compared with the well-known Wilkerson and Irwin algorithm; for the m parallel machine case, it is compared with an extension of the Wilkerson-Irwin algorithm. We also introduce a simple dispatching rule, and it is compared with some existing dispatching rules. The comprehensive simulation results show that the proposed heuristic performs better than the Wilkerson-Irwin algorithm at a significantly reduced computational time.

A cumulative damage shock model with imperfect preventive maintenance

Abstract: In this article we consider a cumulative damage shock model under a periodic preventive maintenance (PM) policy. The PM is imperfect in the sense that each PM reduces the damage level by 100(1 – b)%, 0 < b < 1. A system suffers damage due to shocks and fails when the damage level exceeds some threshold. We derive a sufficient condition for the time to failure to have an IFR distribution. We also discuss the associated problem of finding the number of PM's that minimizes the expected cost rate.

Optimal clustering: A model and method

Abstract: Classifying items into distinct groupings is fundamental in scientific inquiry. The objective of cluster analysis is to assign n objects to up to K mutually exclusive groups while minimizing some measure of dissimilarity among the items. Few mathematical programming approaches have been applied to these problems. Most clustering methods to date only consider lowering the amount of interaction between each observation and the group mean or median. Clustering used in information systems development to determine groupings of modules requires a model that will account for the total group interaction. We formulate a mixed-integer programming model for optimal clustering based upon scaled distance measures to account for this total group interaction. We discuss an efficient, implicit enumeration algorithm along with some implementation issues, a method for computing tight bounds for each node in the solution tree, and a small example. A computational example problem, taken from the computer-assisted process organization (CAPO) literature, is presented. Detailed computational results indicate that the method is effective for solving this type of cluster analysis problem.

Developing production schedules which balance part usage and smooth production loads for just‐in‐time production systems

Abstract: A mixed-model multilevel manufacturing facility running under a just-in-time (JIT) production system is controlled by setting the production schedule for the highest level in the facility, which is usually a mixed-model final assembly line. The schedule is set to achieve the goals of the organization, which under JIT are (1) to keep a constant rate of part usage, and (2) to maintain a smooth production load. In this article we extend earlier work in the literature, which focused on the first goal, by developing scheduling procedures which satisfy both goals. Properties of the resulting production schedules are analyzed and illustrative examples are presented.

Timing replacement decisions under discontinuous technological change

Abstract: We consider the problem of deciding whether to keep a piece of equipment or replace it with a more advanced technology in an environment of technological change. Our model assumes that the costs associated with the presently available technology and future technologies are known, but that the appearance times of future technologies are uncertain. We develop a procedure for computing the optimal keep-or-replace decision that iteratively incorporates a technological forecast. For a certain class of situations, we show that our approach requires the minimum possible amount of forecasted data.

On hazard rate processes

Abstract: Hazard rate processes are discussed in the context of doubly stochastic Poisson processes. We derive an explicit expression for the reliability function corresponding to an increasing hazard rate processes with independent increments. Also, bounds are obtained for the reliability function of a system with a general hazard rate process.

A proof for the longest‐job‐first policy in one‐machine scheduling

Abstract: We consider a one-machine scheduling problem with earliness and tardiness penalties. All jobs are assigned a common due date and the objective is to minimize the total penalty due to job earliness and tardiness. We are interested in finding the optimal combination of the common due-date value and the job sequence. Despite the fact that this problem in general is very hard to solve, we prove that there exists at least a common property for all optimal solutions: The first job in an optimal sequence is one of the longest jobs. We also prove that this property holds for a general class of unimodal penalty functions.

A generalized inspection game

Abstract: The paper addresses the problem of a patrol trying to stop smugglers who are attempting to ship a cargo of perishable contraband across a strait in one of M time units. The situation was modeled as a two-person zero-sum game of exhaustion by Thomas and Nisgav and this article extends their results. The game has many characteristics in common with the Inspection Game in Owen's book on Game Theory; this Inspection Game is generalized and the relations between the two games are discussed.

Scheduling on a single machine with a single breakdown to minimize stochastically the number of tardy jobs

Abstract: Jobs with known processing times and due dates have to be processed on a machine which is subject to a single breakdown. The moment of breakdown and the repair time are independent random variables. Two cases are distinguished with reference to the processing time preempted by the breakdown (no other preemptions are allowed): (i) resumption without time losses and (ii) restart from the beginning. Under certain compatible conditions, we find the policies which minimize stochastically the number of tardy jobs. Copyright

Distance-Directed Augmenting Path Algorithms for Maximum Flow and Parametric Maximum Flow Problems

Abstract: Until recently, fast algorithms for the maximum flow problem have typically proceeded by constructing layered networks and establishing blocking flows in these networks However, in recent years, new distance-directed algorithms have been suggested that do not construct layered networks but instead maintain a distance label with each node The distance label of a node is a lower bound on the length of the shortest augmenting path from the node to the sink In this article we develop two distance-directed augmenting path algorithms for the maximum flow problem Both the algorithms run in O(n 2 m) time on networks with n nodes and m arcs We also point out the relationship between the distance labels and layered networks Using a scaling technique, we improve the complexity of our distance-directed algorithms to O(nm log U), where U denotes the largest arc capacity We also consider applications of these algorithms to unit capacity maximum flow problems and a class of parametric maximum flow problems

Multivariate age-dependent imperfect repair

Abstract: In this article we consider models of systems whose components have dependent life lengths with specific multivariate distributions. Upon failure, components are repaired. Two types of repair are distinguished. After perfect repair, a unit has the same life distribution as a new item. After imperfect repair, a unit has the life distribution of an item which is of the same age but has never failed. We study a model in which the mechanism for determining the nature of the repair is age dependent.

Evaluation of base‐stock policies in multiechelon inventory systems with compound‐poisson demands

Abstract: This article analyzes a model of a multiechelon inventory system: The exogenous demands form independent compound-Poisson processes. Each location follows a base-stock policy. The transit times between locations may be stochastic. Instead of assuming independent transit times, we follow an approach closer to the standard treatment of single-location models. We develop procedures to compute steady-state performance measures, including average backorders and average inventories. The model and the analysis generalize those of Svoronos and Zipkin, who treat the case of pure Poisson demands.

Accelerated life test plans under intermittent inspection and type-I censoring: The case of weibull failure distribution

Abstract: For the case where the lifetime at a stress level has a Weibull distribution, statistically optimal and practical accelerated life test plans are developed under the assumptions of intermittent inspection and Type-I censoring. For a statistically optimal plan the low stress level, the proportion of test units allocated, and the inspection times are determined such that the asymptotic variance of the maximum-likelihood estimator of a certain quantile at the use condition is minimized. Although the practical plan adopts the same design criterion, it involves three rather than two overstress levels and easily calculated inspection schemes. Despite some loss in efficiency the practical plan has several advantages over the statistically optimal one. For instance, the practical plan can provide means for checking the validity of the assumptions made, may reduce the danger of extrapolation, and is more convenient to determine and implement. Computational experiments are conducted to evaluate the relative efficiency of a practical plan to the corresponding statistically optimal plan. Guidelines for selecting an appropriate practical plan are also described with an example.

Multiobjective fractional programming duality theory

Abstract: Results of Geoffrion for efficient and properly efficient solutions of multiobjective programming problems are extended to multiobjective fractional programming problems. Duality relationships are given for these problems where the functions are generalized convex or invex.

Simulation of stochastic activity networks using path control variates

Abstract: This article details several procedures for using path control variates to improve the accuracy of simulation-based point and confidence-interval estimators of the mean completion time of a stochastic activity network (SAN). Because each path control variate is the duration of the corresponding directed path in the network from the source to the sink, the vector of selected path controls has both a known mean and a known covariance matrix. This information is incorporated into estimation procedures for both normal and nonnormal responses. To evaluate the performance of these procedures experimentally, we examine the bias, variance, and mean square error of the controlled point estimators as well as the average half-length and coverage probability of the corresponding confidence-interval estimators for a set of SANs in which the following characteristics are systematically varied: (a) the size of the network (number of nodes and arcs); (b) the topology of the network; (c) the percentage of activities with exponentially distributed durations; and (d) the relative dominance of the critical path. The experimental results show that although large improvements in accuracy can be achieved with some of these procedures, the confidence-interval estimators for normal responses may suffer serious loss of coverage probability in some applications.

An infiltration game onk arcs

Abstract: An infiltrator, starting at a safe base, tries to pass, undetected by a guard and within a time limit, along one of k nonintersecting arcs to a safe destination. Optimal strategies and the value are obtained for this discrete zero-sum search-evasion game.