Avraham Mehrez

Optimal routing of a single vehicle with loading and unloading constraints

A real-life situation in which a trucker has to collect a cargo of similar size from n different customers spread out in a given region and to deliver them to n locations spread out in another far-away region has been formulated as a route-design problem for a single vehicle. The minimal total time of loading, shipping and unloading is considered for different reshuffling methods, and the optimal method is determined. A solution procedure by enumeration is suggested to solve an actual small size problem, and an illustration is provided. (Author/TRRL)

Setting expediting repair policy in a multi-echelon repairable-item inventory system with limited repair capacity

Inventory systems with limited repair capacity are affected by congestion externalities, caused by use of a shared service. There is incompatibility between individual and system optimisation in considering congestion externalities. Three models are described that investigate the congestion effect in a multi-echelon inventory system which has two modes of repair, each with a limited repair capacity. An expanding repair policy employed by the bases in order to choose which repair mode to use is described and compared with different expediting policies related to congestion externalities. The expanding repair policy that considers congestion externalities was found to lead to better system performance measurement than an expanding policy with no congestion. The results of the numerical experiment indicate that the model that ignores congestion externalities—that is, the model that measures each base as an individual—leads to poorer performance measurement for every expediting repair policy, and particularly for the optimal expediting repair policy.

Bounds and properties of the expected value of sample information for a project‐selection problem

In this article we extend the work of Mehrez and Stulman [5] on the expected value of perfect information (EVPI) to the expected value of sample information (EVSI) for a class of economic problems dealing with the decision to reject or accept an investment project. It is shown that shifting the mean of the underlying a priori distribution of X, the projects monetary value from zero in either direction will decrease the associated EVSI of Y, the random sampled information. A theorem is then presented which gives an upper bound on the EVSI over all distributions of Y, as well as the structure of the posterior mean E[X|Y] for which this upper bound is achieved. Finally, the case where E[X|Y] is linear in Y is discussed and its performance compared with that of the optimal case.

An Inventory Model with Exogenous Failures

This note introduces a model where inventory is repeatedly wiped out due to exogenous failure processes. The difference between this model and perishable inventory models is pinpointed by two sample examples. Relevant applications are also mentioned.

A dynamic-programming approach to continuous-review obsolescent inventory problems

Inventory models of modern production and service operations should take into consideration possible exogenous failures or the abrupt decline of demand resulting from obsolescence. This article analyzes continuous-review versions of the classical obsolescence problem in inventory theory. We assume a deterministic demand model and general continuous random times to obsolescence (“failure”). Using continuous dynamic programming, we investigate structural properties of the problem and propose explicit and workable solution techniques. These techniques apply to two fairly wide (and sometimes overlapping) classes of failure distributions: those which are increasing in failure rate and those which have finite support. Consequently, several specific failure processes in continuous time are given exact solutions.

A three-dimensional statistical framework for performance measurement of robotic systems

Abstract A three-dimensional statistical evaluation framework for performance measurement of robotic systems has been developed. A specific experimental setup has been designed, implemented, and evaluated for different robot characteristics (velocities and target location) and for a specific task. A statistical analysis method to evaluate performance is demonstrated. Results indicate the significance of this methodology since the capabilities and performance of a particular robot depend on actual operating conditions.

The facility location problem when the underlying distribution is either dominated or dominating

The theory of choices involving Risk is used to solve some classes of the “Today” maximin and minimax one facility location problems. Solutions are shown when the underlying demand distribution is symmetric and unimodal.

Optimal capacity and operation of deterioratingchemical production service facilities

In this paper, we propose a model for the allocation of identical service facilities for restoring deteriorating production (e.g., batch chemical) processes. The problem is motivated by and solved for the new Dead Sea Works Ltd. magnesium plant. The production system consists of a number of identical production cells, each requiring a set of service tasks. The model determines both the optimal number of servers and the service rate allocated to each service task. The model takes into account the breakdown and repair processes for the service facilities. Thus, the optimal service rate is calculated and assigned according to the random number of available service facilities. Insightful results are provided by both analytical and numerical sensitivity analysis.

Principal-agent maintenance problem

This article studies a maintenance problem that is applicable for multidivision organizations on lessee-lessor relationships. It is assumed that the parties sign a contract for a fixed time period. Within the period, the lessor is allowed to use the equipment supplied by the lessee. The availability of the equipment that may suffer from breakdown depends on the preventive maintenance policy adopted by the lessor. The properties of this policy as well as other features of the problem are analyzed using a one-period model that takes into account the economic value of the contract as perceived by the lessor and the lessee. The optimal contracting arrangements are analyzed from the perspective of efficient risk sharing and incentive provisions.

Sample Size Limit When Sampling From a Nonhomogeneous Mixture

The variance associated with a random sample taken from a nonhomogeneous mixture is highly dependent on the degree of nonhomogeneity. In this paper we explore the upper limit on the variance with the aid of optimal control techniques. A specific numeric..