Models for multi-item continuous review inventory policies subject to constraints

Models are formulated for determining continuous review (Q, r) policies for a multiitem inventory subject to constraints. The objective function is the minimization of total time-weighted shortages. The constraints apply to inventory investment and reorder workload. The formulations are thus independent of the normal ordering, holding, and shortage costs. Two models are presented, each representing a convex programming problem. Lagrangian techniques are employed with the first, simplified model in which only the reorder points are optimized. In the second model both the reorder points and the reorder quantities are optimized utilizing penalty function methods. An example problem is solved for each model. The final section deals with the implementation of these models in very large inventory systems.     

Location of facilities with rectangular distances among point and area destinations

This article is concerned with the optimal location of any number (n) of facilities in relation to any number (m) of destinations on the Euclidean plane. The criterion to be satisfied is the minimization of total weighted distances where the distances are rectangular. The destinations may be either single points, lines or rectangular areas. A gradient reduction solution procedure is described which has the property that the direction of descent is determined by the geometrical properties of the problem.     

Optimal location of a single service center of certain types

Hakimi has considered the problem of finding an optimal location for a single service center, such as a hospital or a police station. He used a graph theoretic model to represent the region being serviced. The communities are represented by the nodes while the road network is represented by the ares of the graph. In his work, the objective is one of minimizing the maximum of the shortest distances between the vertices and the service center. In the present work, the region being serviced is represented by a convex polygon and communities are spread over the entire region. The objective is to minimize the maximum of Euclidian distances between the service center and any point in the polygon. Two methods of solution presented are (i) a geometric method, and (ii) a quadratic programming formulation. Of these, the geometric method is simpler and more efficient. It is seen that for a class of problems, the geometric method is well suited and very efficient while the graph theoretic method, in general, will give only approximate solutions in spite of the increased efforts involved. But, for a different class of problems, the graph theoretic approach will be more appropriate while the geometric method will provide only approximate solutions though with ease. Finally, some feasible applications of importance are outlined and a few meaningful extensions are indicated.     

带混合误差的Ishikawa迭代格式

将Ishikawa型迭代格式的收敛性问题推广到带混合误差的Ishikawa型迭代格式的情形 ,同时所用的证明方法和技巧有所改进     

Many‐player rendezvous search: Stick together or split and meet?

Rendezvous search finds the strategies that players should use in order to find one another when they are separated in a region. Previous papers have concentrated on the case where there are two players searching for one another. This paper looks at the problem when there are more than two players and concentrates on what they should do if some but not all of them meet together. It looks at two strategies—the stick together one and the split up and meet again one. This paper shows that the former is optimal among the class of strategies which require no memory and are stationary, and it gives a method of calculating the expected rendezvous time under it. However, simulation results comparing both strategies suggest that in most situations the split up and meet again strategy which requires some memory leads to faster expected rendezvous times. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48:710–721, 2001     

A branch and bound algorithm for the minimum storage‐time sequencing problem

The minimum storage‐time sequencing problem generalizes many well‐known problems in combinatorial optimization, such as the directed linear arrangement and the problem of minimizing the weighted sum of completion times, subject to precedence constraints on a single processor. In this paper we propose a new lower bound, based on a Lagrangian relaxation, which can be computed very efficiently. To improve upon this lower bound, we employ a bundle optimization algorithm. We also show that the best bound obtainable by this approach equals the one obtainable from the linear relaxation computed on a formulation whose first Chvàtal closure equals the convex hull of all the integer solutions of the problem. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 313–331, 2001