Allocation rules for hypergraph communication situations

This paper considers hypergraph communication situations, where for a group of agents the economic possibilities are described by a coalitional game and the communication possibilities are described by a hypergraph in which the nodes are the agents and the edges are the subgroups of agents who can effect communication. Axiomatic characterizations are provided for two allocation rules, the Myerson value and the position value.     

Multi-stage sequencing situations

This paper introduces the idea of dynamics in cooperative games. The concrete case of multi-stage sequencing situations and the difficulties involved in defining stable cost savings allocations for the games arising from these situations is studied. The MEGS-rule is defined and proven to yield stable allocations. A characterization for the MEGS-rule is given.     

Analysis and design of sequencing rules for car sequencing

This paper presents novel approaches for generating sequencing rules for the car sequencing (CS) problem in cases of two and multiple processing times per station. The CS problem decides on the succession of different car models launched down a mixed-model assembly line. It aims to avoid work overloads at the stations of the line by applying so-called sequencing rules, which restrict the maximum occurrence of labor-intensive options in a subsequence of a certain length. Thus to successfully avoid work overloads, suitable sequencing rules are essential. The paper shows that the only existing rule generation approach leads to sequencing rules which misclassify feasible sequences. We present a novel procedure which overcomes this drawback by generating multiple sequencing rules. Then, it is shown how to apply both procedures in case of multiple processing times per station. For both cases analytical and empirical results are derived to compare classification quality.     

Partitioning sequencing situations and games

The interaction between sequencing situations and cooperative games starting from the paper of Curiel et al. [Curiel, I., Pederzoli, G., Tijs S., 1989. Sequencing games. European Journal of Operational Research 40, 344–351], has become an established line of research within the theory of operation research games.     

On interactive sequencing situations with exponential cost functions

This paper addresses interactive one-machine sequencing situations in which the costs of processing a job are given by an exponential function of its completion time. The main difference with the standard linear case is that the gain of switching two neighbors in a queue is time-dependent and depends on their exact position. We illustrate that finding an optimal order is complicated in general and we identify specific subclasses, which are tractable from an optimization perspective. More specifically, we show that in these subclasses, all neighbor switches in any path from the initial order to an optimal order lead to a non-negative gain. Moreover, we derive conditions on the time-dependent neighbor switching gains in a general interactive sequencing situation to guarantee convexity of the corresponding cooperative game. These conditions are satisfied within our specific subclasses of exponential interactive sequencing situations.     

The two-stage constrained equal awards and losses rules for multi-issue allocation situations

This paper considers two-stage solutions for multi-issue allocation situations, which are extensions of bankruptcy problems. Characterizations are provided for the two-stage constrained equal awards and constrained equal losses rules, based on the properties of composition up and composition down.     

Obligation rules for minimum cost spanning tree situations and their monotonicity properties

We consider the class of Obligation rules for minimum cost spanning tree situations. The main result of this paper is that such rules are cost monotonic and induce also population monotonic allocation schemes. Another characteristic of Obligation rules is that they assign to a minimum cost spanning tree situation a vector of cost contributions which can be obtained as product of a double stochastic matrix with the cost vector of edges in the optimal tree provided by the Kruskal algorithm. It turns out that the Potters value (P-value) is an element of this class.     

On games corresponding to sequencing situations with ready times

This paper considers the special class of cooperative sequencing games that arise from one-machine sequencing situations in which all jobs have equal processing times and the ready time of each job is a multiple of the processing time.By establishing relations between optimal orders of subcoalitions, it is shown that each sequencing game within this class is convex.This author is financially supported by the Dutch Organization for Scientific Research (NWO).     

Job sequencing rules for minimizing the expected makespan in flexible machines

We consider scheduling of a deteriorating flexible machine that is capable of processing a number of diverse jobs with negligible setup times between jobs. Specifically, we develop rules for sequencing N jobs on such a machine such that its expected makespan (sum of all job processing times and machine down-time) is minimized. Using the Weibull distribution to characterize machine failures in our model, we permit different jobs to contribute to machine deterioration (and hence its failure) at different failure rates, and do not require these rates to remain constant with machine-use time. We validate the effectiveness of these job sequencing rules for different cases, using extensive simulation tests.     

Efficient power computation for r out of m runs rules schemes

In this article we develop a power computation code in the R language which provides an easy to use tool to researchers in designing Shewhart control charts. It enables researchers to use different existing and newly introduced sensitizing rules and runs rules schemes designed for Shewhart-type control charts for location and spread. The code provides researchers to compute the power for different options of r out of m rules/schemes. The code is flexible to apply for any sample size, false alarm rate, type of control limits (one- or two-sided), amount of shift in the process parameters and a variety of popular distributions for commonly used Shewhart-type control charts (i.e. ${\bar{{X}} ,R ,S}$ and S ² charts). These mentioned benefits of the developed functional code are only partially found in features of the existing software packages and these programs may be enhanced by adding the features of the developed code as a function in their libraries dealing with quality control charting.     

Convex games with an infinite number of players and sequencing situations

In this paper we study convex games with an infinite countable set of agents and provide characterizations of this class of games. To do so, and in order to overcome some shortcomings related to the difficulty of dealing with infinite orderings, we need to use a continuity property. Infinite sequencing situations where the number of jobs is infinite countable can be related to convex cooperative TU games. It is shown that some allocations turn out to be extreme points of the core of an infinite sequencing game.     

The MC-value for monotonic NTU-games

The MC-value is introduced as a new single-valued solution concept for monotonic NTU-games. The MC-value is based on marginal vectors, which are extensions of the well-known marginal vectors for TU-games and hyperplane games. As a result of the definition it follows that the MC-value coincides with the Shapley value for TU-games and with the consistent Shapley value for hyperplane games. It is shown that on the class of bargaining games the MC-value coincides with the Raiffa-Kalai-Smorodinsky solution. Furthermore, two characterizations of the MC-value are provided on subclasses of NTU-games which need not be convex valued. This allows for a comparison between the MC-value and the egalitarian solution introduced by Kalai and Samet (1985).     

On the convexity of games corresponding to sequencing situations with due dates

This paper considers sequencing situations with due date criteria. Three different types of criteria are considered: the weighted penalty criterion, the weighted tardiness criterion and the completion time criterion. The main focus is on convexity of the associated cooperative games.     

Queueing models of certain manufacturing cells under product-mix sequencing rules

This paper considers a manufacturing cell composed of a machining center and several parallel downstream production stations. In the machining center, there is an ample supply of raw material for a number of different part-types. For each type, parts are first processed in the machining center, and then in one of parallel production stations (one for each type). The decision to determine which type to produce (production sequence) occurs whenever the machining center completes the process of a part. The production sequencing rules under consideration are rotation rules and random rules, respectively. By using such rules, the resulting product-mix meets a preset level. Based on a decomposition technique, solution procedures are developed to compute the response time of parallel stations in the manufacturing cell using such product-mix sequencing rules. Numerical examples are given to demonstrate the solution procedures and to investigate the impact of the production sequence on the overall average response time.     

A simulation analysis of sequencing rules in a flexible flowline

The paper concerns a flexible flowline scheduling problem, which arises in the footwear industry. Flexibility of the line allows for manufacturing simultaneously more products in lower quantities, but it also increases the complexity of the task of balancing the line, specially because the mix of products changes everyday. A simulation model to deal with the flexible line is developed and several job sequencing rules and different part input criteria are implemented. The impact of each rule on the quality of the schedules is measured, namely, according to makespan, productivity and average machine utilisation. Computational results concerning a real application are also presented. SIMPLE++ is the simulation language used.     

Uniform estimates for monotonic polynomial approximation

The uniform estimate is established for a monotone polynomial approximation of functions whose smoothness decreases at the ends of a segment.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 1, pp. 38–43, January, 1993.     

Entropy estimate for high-dimensional monotonic functions

We establish upper and lower bounds for the metric entropy and bracketing entropy of the class of d-dimensional bounded monotonic functions under L^p norms. It is interesting to see that both the metric entropy and bracketing entropy have different behaviors for p<d/(d-1) and p>d/(d-1). We apply the new bounds for bracketing entropy to establish a global rate of convergence of the MLE of a d-dimensional monotone density.