Dror Zuckerman

Optimal Maintenance Strategies for Repairable Systems with General Degree of Repair

Abstract : Our project focuses on a single unit system which is subject to random failure. The age of the system in service is maintained as a control variable. Upon failure, an age-dependent maintenance action specifying the degree of repair is taken by a controller. By employing analytical tools and numerical procedures, we investigate and characterize the structures of the optimal repair policy under a discounted cost optimality criterion. Special analytical and numerical effort is directed throughout the study for the development of efficient computational procedures for the optimal strategy.

Optimal repair policies with general degree of repair in two maintenance models

Two maintenance models for repairable systems with exponential lifetimes are studied. A maintenance strategy in the proposed framework specifies the degree of repair to be taken as a function of the virtual age of the system upon failure. In Model I we restrict attention to maintenance strategies in which only minimal or perfect repair can be employed upon failure. In Model II the degree of repair may vary. For some age-dependent cost functions, optimal maintenance strategies (minimizing the expected discounted costs over an infinite horizon) are determined analytically.

Optimal stopping in a continuous search model

On considere un modele de recherche continu dans lequel les gains sont recus aleatoirement selon un processus de renouvellement determine par une fonction de repartition connue

Expenditure patterns and timing of patent protection in a competitive R&D environment

In this paper we consider a stochastic R&D decision model for a single firm operating in a competitive environment. The study focuses on the firms optimal policy which maximizes the expected discounted net return from the project. The firms policy is composed of two ingredients: a stopping time which determines when the developed technology should be introduced and protected by a patent, and an investment strategy which specifies the expenditure rate throughout the R&D program. The main findings of the study are:(a)Under a constant expenditure rate strategy, the optimal stopping time of the project is a control limit policy of the following form: stop whenever the projects state exceeds a fixed critical value, or when a similar technology is introduced and protected by one of the firms rivals, whichever occurs first. (b)For a R&D race model in which the winner-takes-all competition and the losers return is zero, we show that the firms optimal expenditure rate throughout the R&D program increases monotonically as a function of the projects state. In order to gain a better insight regarding optimal R&D programs in competitive markets we examine the effect of key economic parameters on the firms optimal policy.

Review of recent development: A replacement model for an additive damage model with restoration

A system existing in a random environment receives shocks at random points of time. Each shock causes a random amount of damage which accumulates over time. A breakdown can occur only upon the occurrence of a shock according to a known failure probability function. Upon failure the system is replaced by a new identical one with a given cost. When the system is replaced before failure, a smaller cost is incurred. Thus, there is an incentive to attempt to replace the system before failure. The damage process is controlled by means of a maintenance policy which causes the accumulated damage to decrease at a known restoration rate. We introduce sufficient conditions under which an optimal replacement policy which minimizes the total expected discounted cost is a control limit policy. The relationship between the undiscounted case and the discounted case is examined. Finally, an example is given illustrating computational procedures.

On preserving the reservation wage property in a continuous job search model

Abstract The purpose of this article is to examine a continuous model of job search. Job offers are received randomly over time according to a renewal process. The wage offers are assumed to be positive, independent, and identically distributed random variables. There is a search cost of c monetary units per unit time. The only decision the searcher must make is when to stop searching and accept an offer. It is shown that the optimal stopping strategy which maximizes the searchers expected net return over the class of all stopping times possesses the reservation wage property, provided that the interarrival time between two successive job offers in NBUE (new better than used in expectation).

Random vehicle dispatching with options and optimal fleet size

A dispatching problem with random availability of vehicles and options to send rented vehicles is considered. We assume passenger arrivals to be described by a pure-birth process. Such a problem is analytically attractive and is shown to have practical applications in vehicle dispatching models. An average cost criterion is used to determine firms fleet size and option (renting) strategy.

A note on the optimal control of a cash balance problem

Abstract This paper provides an analytical solution to a cash management problem when cash income and demand are described by Compound Poisson processes. The paper generalizes past results in the cash management literature to arbitrary income and demand distribution functions. Further, our results can be applied as well in the area of banking. Throughout the paper we restrict attention to the family of control barrier policies. These consist in hedging cash up to a critical level and investing all incoming cash exceeding this level. We employ a long-run average cost criterion to determine an optimal control barrier. A diffusion approximation of the cash level process (income less demand) is used to obtain a simpler expression for the average cost and to yield a closed form solution to the optimal control barrier. For demonstration purposes, an example is resolved.

Vehicle dispatching with competition

This paper considers a vehicle dispatching problem with competition. For Poisson arrival processes, three dispatching policies are considered, (i) a C-policy, consisting in sending a vehicle as soon as it is filled to capacity C, (ii) a T-policy, assuming an infinite capacity and consisting in sending a vehicle every T periods and (iii) a (T, C)-policy consisting in sending a vehicle every T periods or whenever it is filled to capacity C, whichever comes first. Two firm models with cooperating and non-cooperating solution modes are resolved and results summarized in a table. Applications and examples are resolved for demonstration purposes.

Optimal investment-dividend policy of an insurance firm under regulation

Abstract An insurance decision model including intervention by a regulating agency is defined. The insurance firms problem is to establish an investment policy as well as a dividend strategy. Regulation is exercised by a minimal barrier policy for cash holding and penalities for violating this barrier. The joint Insurance Firm-Regulating Agency problem is discussed by using concepts drawn from Stackleberg strategies in game theory. As in the classical model of collective risk theory it is assumed that premium payments are received deterministically from policyholders at a constant rate, while the claim process is determined by a Compound Poisson process. Finally a diffusion approximation is used in order to obtain tractable results for a general claim size distribution.