Moshe Kaspi

Optimal flow path design of unidirectional AGV systems

SUMMARY This paper describes an alternative formulation of the AGV flow path layout (FPL) problem which was first formulated by Gaskins and Tanchoco (1987) as a zero-one integer programming problem. A computationally efficient procedure is proposed which is based on the branch-and-bound technique. An algorithm for satisfying the reachability condition for nodes in the AGV flow path network is also presented. A simple illustrative example is discussed to demonstrate the procedure, and a more complex problem is also given.

On the economic ordering quantity for jointly replenished items

A solution procedure is provided for solving the joint replenishment problem using a basic cycle approach. The solution procedure is very simple, and involves comparing possible values between the ‘minimum’ and ‘maximum’ cycle times. Extensive simulation demonstrates that this solution procedure is superior to previously known algorithms for solving this problem.

A survey on offline scheduling with rejection

In classical deterministic scheduling problems, it is assumed that all jobs have to be processed. However, in many practical cases, mostly in highly loaded make-to-order production systems, accepting all jobs may cause a delay in the completion of orders which in turn may lead to high inventory and tardiness costs. Thus, in such systems, the firm may wish to reject the processing of some jobs by either outsourcing them or rejecting them altogether. The field of scheduling with rejection provides schemes for coordinated sales and production decisions by grouping them into a single model. Since scheduling problems with rejection are very interesting both from a practical and a theoretical point of view, they have received a great deal of attention from researchers over the last decade. The purpose of this survey is to offer a unified framework for offline scheduling with rejection by presenting an up-to-date survey of the results in this field. Moreover, we highlight the close connection between scheduling with rejection and other fields of research such as scheduling with controllable processing times and scheduling with due date assignment, and include some new results which we obtained for open problems.

An Improvement of Silver's Algorithm for the Joint Replenishment Problem

Abstract Silvers algorithm for the joint replenishment problem is modified and improved. Computational requirements due to this modification are relatively very small. Extensive experimentation shows that the errors of Silvers algorithm can, on the average, be reduced by an order of magnitude.

Minimizing the total weighted flow time in a single machine with controllable processing times

The scheduling problem of a single machine with the minimum total weighted flow time criterion is extended to the case of allocating a continuously nonrenewable limited resource where the model of operations is assumed to be a specific convex function of the amount of resource consumed. The optimal resource allocation is obtained for any arbitrary job sequence. The computational complexity of the general problem remains an open question, but we present and analyze some special cases that are solvable by using polynomial time algorithms. An exact dynamic programming algorithm for small to medium size problems is suggested, while for large-scale problems we suggest some heuristic algorithms which appear to be very efficient.

A bicriterion approach to time/cost trade-offs in scheduling with convex resource-dependent job processing times and release dates

This paper presents a bicriterion analysis of time/cost trade-offs for the single-machine scheduling problem where both job processing times and release dates are controllable by the allocation of a continuously nonrenewable resource. Using the bicriterion approach, we distinguish between our sequencing criterion, namely the makespan, and the cost criterion, the total resource consumed, in order to construct an efficient time/cost frontier. Although the computational complexity of the problem of constructing this frontier remains an open question, we show that the optimal job sequence is independent of the total resource being used; thereby we were able to reduce the problem to a sequencing one. We suggest an exact dynamic programming algorithm for solving small to medium sizes of the problem, while for large-scale problems we present some heuristic algorithms that turned out to be very efficient. Five different special cases that are solvable by using polynomial time algorithms are also presented.

Convex resource allocation for minimizing the makespan in a single machine with job release dates

We consider the problem of scheduling jobs on a single machine where job-processing times are controllable through the allocation of a common limited resource. The release dates are known and the job-processing time is described by a convex decreasing resource consumption function. Our objective is to simultaneously determine the optimal job permutation and the resource allocation, such that the maximal completion time is minimized. We provide an O(n) time optimization algorithm for the case of identical job release dates, and an O(n2) time optimization algorithm for the case of non-identical job release dates.

Optimization of the machining economics problem for a multistage transfer machine under failure, opportunistic and integrated replacement strategies

In the extensive literature dealing with the machining economics problem, the optimization of the multistage production system is rarely discussed, and when so it is considered mostly in terms of the Failure Replacement Strategy. However, when analysing this problem, the possibility of using the Opportunistic or Integrated Replacement Strategies also arises. In this work, we minimize the expected cost per unit under three different tool replacement strategies: Failure Replacement, Opportunistic Replacement and Integrated Replacement. For the first strategy, we show that the optimal solution is obtained using a one-dimensional search algorithm. For each of the other two strategies, we develop approximate models that are studied using simulations. These models appear to be very efficient.

Location and sequencing of imperfect inspection operations in serial multi-stage production systems

Abstract An integrated approach to the problem of allocation of inspection effort in multistage production systems is presented. The problem addresses multiple inspection operations, different disposition policies and inspection, production and repair errors. Quality and cost transfer functions are developed to model production operations and different types of inspection operations in a unified manner and to facilitate the recursive computations required to evaluate alternative system configurations. We formulate the combined inspection location and sequencing problem as a nonlinear mathematical programming problem and solve it with a branch and bound technique, using a heuristic to generate a feasible solution and upper bound. These developments are illustrated with a numerical example.

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.