The role of internal storage capacity in fixed cycle production systems

The reliability of a serial production line is optimized with respect to the location of a single buffer. The problem was earlier defined and solved by Soyster and Toof for the special case of an even number of machines all having equal probability of failure. In this paper we generalize the results for any number of machines and remove the restriction of identical machine reliabilities. In addition, an analysis of multibuffer systems is presented with a closed form solution for the reliability when both the number of buffers and their capacity is limited. For the general multibuffer system we present an approach for determining system reliability.     

Computational results with a branch-and-bound algorithm for the general knapsack problem

In this paper, a branch-and-bound procedure is presented for treating the general knapsack problem. The fundamental notion of the procedure involves a variation of traditional branching strategies as well as the incorporation of penalties in order to improve bounds. Substantial computational experience has been obtained, the results of which would indicate the feasibility of the procedure for problems of large size.     

Due-date assignment and early/tardy scheduling on identical parallel machines

This article examines the problem of simultaneously assigning a common due date to a set of independent jobs and scheduling them on identical parallel machines in such a way that the costs associated with the due date and with the earliness or tardiness of the jobs are minimized. We establish that, for certain values of the due-date cost, an optimal schedule for this problem is also optimal for an early/tardy scheduling problem studied by Emmons. We discuss the solution properties for the two problems, and show that both problems are NP-hard even for two machines. We further show that these problems become strongly NP-hard if the number of machines is allowed to be arbitrary. We provide a dynamic programming solution for the problems, the complexity of which indicates that the problems can be solved in pseudopolynomial time as long as the number of machines remains fixed. Finally, we present the results of a limited computational study. © 1994 John Wiley & Sons, Inc.     

Server scheduling on parallel dedicated machines with fixed job sequences

We consider server scheduling on parallel dedicated machines to minimize the makespan. Each job has a loading operation and a processing operation. The loading operation requires a server that serves all the jobs. Each machine has a given set of jobs to process, and the processing sequence is known and fixed. We design a polynomial‐time algorithm to solve the two‐machine case of the problem. When the number of machines is arbitrary, the problem becomes strongly NP‐hard even if all the jobs have the same processing length or all the loading operations require a unit time. We design two heuristic algorithms to treat the case where all the loading times are unit and analyze their performance.     

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     

Estimating the probability that a simulated system will be the best

Consider a stochastic simulation experiment consisting of v independent vector replications consisting of an observation from each of k independent systems. Typical system comparisons are based on mean (long‐run) performance. However, the probability that a system will actually be the best is sometimes more relevant, and can provide a very different perspective than the systems' means. Empirically, we select one system as the best performer (i.e., it wins) on each replication. Each system has an unknown constant probability of winning on any replication and the numbers of wins for the individual systems follow a multinomial distribution. Procedures exist for selecting the system with the largest probability of being the best. This paper addresses the companion problem of estimating the probability that each system will be the best. The maximum likelihood estimators (MLEs) of the multinomial cell probabilities for a set of v vector replications across k systems are well known. We use these same v vector replications to form v^k unique vectors (termed pseudo‐replications) that contain one observation from each system and develop estimators based on AVC (All Vector Comparisons). In other words, we compare every observation from each system with every combination of observations from the remaining systems and note the best performer in each pseudo‐replication. AVC provides lower variance estimators of the probability that each system will be the best than the MLEs. We also derive confidence intervals for the AVC point estimators, present a portion of an extensive empirical evaluation and provide a realistic example. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 341–358, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10019     

Bicriteria product design optimization: An efficient solution procedure using AND/OR trees

Competitive imperatives are causing manufacturing firms to consider multiple criteria when designing products. However, current methods to deal with multiple criteria in product design are ad hoc in nature. In this paper we present a systematic procedure to efficiently solve bicriteria product design optimization problems. We first present a modeling framework, the AND/OR tree, which permits a simplified representation of product design optimization problems. We then show how product design optimization problems on AND/OR trees can be framed as network design problems on a special graph—a directed series‐parallel graph. We develop an enumerative solution algorithm for the bicriteria problem that requires as a subroutine the solution of the parametric shortest path problem. Although this parametric problem is hard on general graphs, we show that it is polynomially solvable on the series‐parallel graph. As a result we develop an efficient solution algorithm for the product design optimization problem that does not require the use of complex and expensive linear/integer programming solvers. As a byproduct of the solution algorithm, sensitivity analysis for product design optimization is also efficiently performed under this framework. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 574–592, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10031     

Dominating sets for rectilinear center location problems with polyhedral barriers

In planar location problems with barriers one considers regions which are forbidden for the siting of new facilities as well as for trespassing. These problems are important since they model various actual applications. The resulting mathematical models have a nonconvex objective function and are therefore difficult to tackle using standard methods of location theory even in the case of simple barrier shapes and distance functions. For the case of center objectives with barrier distances obtained from the rectilinear or Manhattan metric, it is shown that the problem can be solved in polynomial time by identifying a dominating set. The resulting genuinely polynomial algorithm can be combined with bound computations which are derived from solving closely connected restricted location and network location problems. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 647–665, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10038