A Lindley-type equation arising from a carousel problem

In this paper we consider a system with two carousels operated by one picker. The items to be picked are randomly located on the carousels and the pick times follow a phase-type distribution. The picker alternates between the two carousels, picking one item at a time. Important performance characteristics are the waiting time of the picker and the throughput of the two carousels. The waiting time of the picker satisfies an equation very similar to Lindley's equation for the waiting time in the PH/U/1 queue. Although the latter equation has no simple solution, we show that the one for the waiting time of the picker can be solved explicitly. Furthermore, it is well known that the mean waiting time in the PH/U/1 queue depends on to the complete interarrival time distribution, but numerical results show that, for the carousel system, the mean waiting time and throughput are rather insensitive to the pick-time distribution.Comment: 10 pages, 1 figure, 19 reference

Periodic multiprocessor scheduling

A number of scheduling and assignment problems are presented involving the execution of periodic operations in a multiprocessor environment. We consider the computational complexity of these problems and propose approximation algorithms for operations with identical periods as well as for operations with arbitrary integer periods

Periodic multiprocessor scheduling

A number of scheduling and assignment problems are presented involving the execution of periodic operations in a multiprocessor environment. We consider the computational complexity of these problems and propose approximation algorithms for operations with identical periods as well as for operations with arbitrary integer periods

Periodic assignment and graph colouring

We analyse the problem of executing periodic operations on a minimum number of identical processors under different constraints. The analysis is based on a reformulation of the problem in terms of graph colouring. It is shown that different constraints result in colouring problems that are defined on different classes of graphs, viz. interval graphs, circular-arc graphs and periodic-interval graphs. We discuss the colouring of such graphs in detail

Affiliation, equilibrium existence and the revenue ranking of auctions

We consider private value auctions where bidders’ types are dependent, a case usually treated by assuming affiliation. We show that affiliation is a restrictive assumption in three senses: topological, measure-theoretic and statistical (affiliation is a very restrictive characterization of positive dependence). We also show that affiliation’s main implications do not generalize for alternative definitions of positive dependence. From this, we propose new approaches to the problems of pure strategy equilibrium existence in first-price auctions (PSEE) and the characterization of the revenue ranking of auctions. For equilibrium existence, we slightly restrict the set of distributions considered, without loss of economic generality, and offer a complete characterization of PSEE. For revenue ranking, we obtain a characterization of the expected revenue differences between second and first price auctions with general dependence of types

Tools for the Interfacing between Dynamical Problems within Decision Support Systems. COSOR-memorandum 91-29

Abstract This paper particularly addresses the difficulties arising from formulating models for dynamical problems in such a way that they can be treated by appropriate solvers. One of these difficulties is that different types of solvers are recommendable for different questions within the same situation. Therefore it is recommended to use solver-independent specification methods. Since specification and respecification can be time-consuming and boring, it is also recommended to develop rule-based specification tools. The paper is illustrated with a sketch of possible specification methods for manpower policy making and for goods flow control

Markov programming by successive approximations with respect to weighted supremum norms

Markovian decision processes are considered in the situation of discrete time, countable state space, and general decision space. By introducing a Banach space with a weighted supremum norm, conditions are derived, which guarantee convergence of successive approximations to the value function. These conditions are weaker then those required by the usual supnorm approach. Several properties of the successive approximations are derived