Efficiency of equilibria in restricted uniform machine scheduling with total weighted completion time as social cost

In the last decade, there has been much progress in understanding scheduling problems in which selfish jobs aim to minimize their individual completion time. Most of this work has focused on makespan minimization as social objective. In contrast, we consider as social cost the total weighted completion time, that is, the sum of the agent costs, a standard definition of welfare in economics. In our setting, jobs are processed on restricted uniform parallel machines, where each machine has a speed and is only capable of processing a subset of jobs; a job's cost is its weighted completion time; and each machine sequences its jobs in weighted shortest processing time (WSPT) order. Whereas for the makespan social cost the price of anarchy is not bounded by a constant in most environments, we show that for our minsum social objective the price of anarchy is bounded above by a small constant, independent of the instance. Specifically, we show that the price of anarchy is exactly 2 for the class of unit jobs, unit speed instances where the finite processing time values define the edge set of a forest with the machines as nodes. For the general case of mixed job strategies and restricted uniform machines, we prove that the price of anarchy equals 4. From a classical machine scheduling perspective, our results establish the same constant performance guarantees for WSPT list scheduling. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

Economic lot scheduling of fully loaded processes with external setups

Without restricting the class of permissible schedules, we derive optimal schedules for economic lot scheduling problems that are fully loaded, have external setups, and have only two products. The fully loaded condition accurately represents certain types of bottlenecks. We show that the optimal schedule must have the Wagner-Whitin property. We also develop a measure of aggregate inventory, derive an optimal steady-state aggregate inventory policy, and provide conditions under which the aggregate inventory level of an optimal schedule must approach a steady state. By restricting the class of permissible schedules to rotation cycle schedules, we extend these results to more than two products.     

Floor layouts using a multifacility location model

A procedure for obtaining a facilities scatter diagram within a rectangular boundary is developed using a multifacility location model. This method gives favorable computational results and has the advantage over other scatter diagram methods of being able to accommodate fixed facility locations. Examples illustrate how this method can be used by a designer/analyst either as a one-step algorithm or iteratively to build a layout.     

Estimating a survival curve when new is better than used in expectation

Let X be a positive random variable. The distribution F of X is said to be “new better than used in expectation,” or “NBUE,” if E(X) ⩾ E(X – t|X > t) for all t ⩾ 0. Suppose X₁, …, X_n, is a random sample from an NBUE distribution F. The problem of estimating F by a distribution which is itself NBUE is considered. The estimator G_n, defined as the NBUE distribution supported on the sample which minimizes the (sup norm) distance between the NBUE class and the empirical distribution function, is studied. The strong uniform consistency of G_n, is proven, and a numerical algorithm for obtaining G_n, is given. Our approach is applied to provide an estimate of the distribution of lifetime following the diagnosis of chronic granulocytic leukemia based on data from a National Cancer Institute study.     

Some two-on-two homogeneous stochastic combats

In this article we consider two versions of two-on-two homogeneous stochastic combat and develop expressions, in each case, for the state probabilities. The models are natural generalizations of the exponential Lanchester square law model. In the first version, a marksman whose target is killed resumes afresh the killing process on a surviving target; in the second version, the marksman whose target is killed merely uses up his remaining time to a kill on a surviving target. Using the state probabilities we then compute such important combat measures as (1) the mean and variance of the number of survivors as they vary with time for each of the sides, (2) the win probabilities for each of the sides, and (3) the mean and variance of the battle duration time. As an application, computations were made for the specific case of a gamma (2) interfiring time random variable for each side and the above combat measures were compared with the appropriate exponential and deterministic Lanchester square law approximations. The latter two are shown to be very poor approximations in this case.     

An operational analysis of system calibration

Mathematical models are proposed for studying the impact of miscalibration upon operational effectiveness. Methodology for assessing the system effectiveness and an approach for optimizing the effectiveness of a calibration program are examined. The theory application is discussed and the results of some specific and convenient models are presented.     

A model for geographically distributed combat interactions of swarming naval and air forces

This article describes the Distributed Interaction Campaign Model (DICM), an exploratory campaign analysis tool and asset allocation decision‐aid for managing geographically distributed and swarming naval and air forces. The model is capable of fast operation, while accounting for uncertainty in an opponent's plan. It is intended for use by commanders and analysts who have limited time for model runs, or a finite budget. The model is purpose‐built for the Pentagon's Office of Net Assessment, and supports analysis of the following questions: What happens when swarms of geographically distributed naval and air forces engage each other and what are the key elements of the opponents’ force to attack? Are there changes to force structure that make a force more effective, and what impacts will disruptions in enemy command and control and wide‐area surveillance have? Which insights are to be gained by fast exploratory mathematical/computational campaign analysis to augment and replace expensive and time‐consuming simulations? An illustrative example of model use is described in a simple test scenario. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 562–576, 2016     

Two heuristics for the economic lot scheduling problem: An experimental study

In this article we present and test two heuristics for the economic lot scheduling problem. The first heuristic was developed by one of us (P.C. Geng) during Ph.D. research, while the other is a convergent implementation of an algorithm due to Doll and Whybark. We study the performance of these heuristics on a large set of test problems constructed using a new form of problem generation that yields random problems within an experimental design.     

Multiperiod allocation of limited resources: A minimax approach

We consider a multiperiod model in which limited resources are allocated among competing activities in each period. The objective is to minimize the maximum weighted deviation of the cumulative activity levels from the cumulative demands among all activities at all periods. All resources are assumed to be storable; that is, surpluses at one period can be used later on. This model is useful, for example, in multiperiod production planning for high-technology industries that assemble a large variety of circuit boards using numerous electronic components. The model is formulated with a minimax objective. We develop an efficient algorithm that can solve large-scale problems very quickly. At each iteration, the algorithm makes use of the solution to a relaxed problem to identify activities that should be permanently set to zero, as well as groups of activities that should have the same value.