The mixed ordering policy in periodic review stochastic multi-commodity inventory systems

In multi-commodity inventory systems with variable setup costs, the mixed ordering policy assumes that commodities may be ordered either individually, or may be arbitrarily grouped for joint ordering. Thus, for a two-commodity system, commodity one or commodity two or commodities one and two may be ordered incurring respectively fixed order costs of K, K₁, or K₂, where max (K₁, K₂) ≤ K ≤ K₁ + K₂, This paper considers a two-commodity periodic review system. The stationary characteristics of the system are analyzed, and, for a special case, explicit solutions are obtained for the distribution of the stock levels at the beginning of the periods. In a numerical example, optimal policy variables are computed, and the mixed ordering policy is compared with individual and joint ordering policies.     

A note on duality in homogeneous fractional programming

For a linear fractional programming problem, Sharma and Swarup have constructed a dual problem, also a linear fractional program, in which the objective functions of both primal and dual problems are the same. Craven and Mond have extended this result to a nonlinear fractional programming problem with linear constraints, and a dual problem for which the objective function is the same as that of the primal. This theorem is now further extended from linear to differentiable convex constraints.     

A complete importance ranking for components of binary coherent systems,with extensions to multi-state systems

Means of measuring and ranking a system's components relative to their importance to the system reliability have been developed by a number of authors. This paper investigates a new ranking that is based upon minimal cuts and compares it with existing definitions. The new ranking is shown to be easily calculated from readily obtainable information and to be most useful for systems composed of highly reliable components. The paper also discusses extensions of importance measures and rankings to systems in which both the system and its components may be in any of a finite number of states. Many of the results about importance measures and rankings for binary systems are shown to extend to the more sophisticated multi-state systems. Also, the multi-state importance measures and rankings are shown to be decomposable into a number of sub-measures and rankings.     

Multi-item service constrained (s,S) policies for spare parts logistics systems

Many organizations providing service support for products or families of products must allocate inventory investment among the parts (or, identically, items) that make up those products or families. The allocation decision is crucial in today's competitive environment in which rapid response and low levels of inventory are both required for providing competitive levels of customer service in marketing a firm's products. This is particularly important in high-tech industries, such as computers, military equipment, and consumer appliances. Such rapid response typically implies regional and local distribution points for final products and for spare parts for repairs. In this article we fix attention on a given product or product family at a single location. This single-location problem is the basic building block of multi-echelon inventory systems based on level-by-level decomposition, and our modeling approach is developed with this application in mind. The product consists of field-replaceable units (i.e., parts), which are to be stocked as spares for field service repair. We assume that each part will be stocked at each location according to an (s, S) stocking policy. Moreover, we distinguish two classes of demand at each location: customer (or emergency) demand and normal replenishment demand from lower levels in the multiechelon system. The basic problem of interest is to determine the appropriate policies (s_i S_i) for each part i in the product under consideration. We formulate an approximate cost function and service level constraint, and we present a greedy heuristic algorithm for solving the resulting approximate constrained optimization problem. We present experimental results showing that the heuristics developed have good cost performance relative to optimal. We also discuss extensions to the multiproduct component commonality problem.     

Lagrangian solution of maximum dispersion problems

We address the so‐called maximum dispersion problems where the objective is to maximize the sum or the minimum of interelement distances amongst a subset chosen from a given set. The problems arise in a variety of contexts including the location of obnoxious facilities, the selection of diverse groups, and the identification of dense subgraphs. They are known to be computationally difficult. In this paper, we propose a Lagrangian approach toward their solution and report the results of an extensive computational experimentation. Our results show that our Lagrangian approach is reasonably fast, that it yields heuristic solutions which provide good lower bounds on the optimum solution values for both the sum and the minimum problems, and further that it produces decent upper bounds in the case of the sum problem. For the sum problem, the results also show that the Lagrangian heuristic compares favorably against several existing heuristics. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 97–114, 2000     

Continuous sampling plans for markov-dependent production processes

This article discusses the behavior of three continuous sampling plans: continuous sampling plan 1 (CSP 1) and continuous sampling plan 2 (CSP 2) developed by Dodge [5] and Dodge and Torrey [7], and multilevel continuous sampling plan 2 (MLP 2) developed by Lieberman and Solomon [11], when the quality of successive units in a continuous production process follows a two-state time-homogeneous Markov chain. We first derive the average outgoing quality (AOQ) expressions of these plans. Exact procedures for determining the average outgoing quality limit (AOQL) can be obtained only for CSP 1. For CSP 2 and MLP 2 plans, iterative procedures have been used to obtain the AOQL contours. For these plans, it is assumed that the serial correlation coefficient between the two consecutive random variables of the Markov chain is known. In addition, estimation procedures for the coefficient are given. We show that if the serial correlation coefficient of the Markov chain is positive (negative), the AOQL is increased (decreased) as compared to the case when the successive units in the production process follows a Bernoulli pattern. Let r denote the number of production units examined in succession which are found to be of good quality and k denote the inverse of the sampling fraction employed when quality is good. Then if r and k are sufficiently small, it is observed from the graph that, for small departures of the serial correlation coefficient from zero, the AOQL values do not differ significantly for each of the three plans; whereas for sufficiently large values of r and k, the AOQL values differ significantly. Various aspects of these plans, such as their operating characteristics 2 (OC 2) and the serial correlation coefficient, are discussed.