Showing papers in "Journal of The Operations Research Society of Japan in 1986"

Extension of newton and quasi-newton methods to systems of pc^1 equations

Abstract: This paper extends Newton and quasi-Newton methods to systems of PC 1 equations and establishes the quadratic convergence property of the extended Newton method and the Q-superlinear convergence property of the extended quasi-Newton method.

Flowshop schedules with sequence dependent setup times

Abstract: The flowshop scheduling problem with sequence dependent setup times is considered and shown to be NP-complete A traveling salesman problem formulation is proposed for the case where jobs are processed continuously through the shop These results are used to describe an approximate algorithm for the case where limited or infinite intermediate storage space is available to hold partially completed jobs The effectiveness of the proposed approximate approach is discussed and some empirical results are reported

Approximation of a tessellation of the plane by a voronoi diagram

Abstract: In this paper the problem of obtaining the Voronoi diagram which approximates a given tessellation of the plane is formulated as the optimization problem, where the objective function is the discrepancy of the Voronoi diagram and the given tessellation. The objective function is generally non-convex and nondifferentiable, so we adopt the primitive descent algorithm and its variants as a solution algorithm. Of course, we have to be content with the locally minimum solutions. However the results of the computational examples suggest that satisfactory good solutions can be obtained by our algorithm. This problem includes the problem to restore the generators from a given Voronoi diagram (Le., the inverse problem of constructing a Voronoi diagram from the given points) when the given diagram is itself a Voronoi diagram. We can get the approximate position of the generators from a given Voronoi diagram in practical timl:; it take~ db out 10 s to restore the generators from a Voronoi diagram generated from thirty-two points on a computer of speed about 17 MIPS. Two other practical examples are presented where our algorithm is efficient, one being a problem in ecology and the other being one in urban planning. We can get the Voronoi diagrams which approximate the given tessellations l which have 32 regions and are defmed by 172 points in the former example, 11 regions and 192 points in the latter example) within 10s in these two examples on the same computer.

On the representation of the rigid sub-systems of a plane link system

Abstract: A combinatorial characterization of the rigidity of plane link systems was fIrst established by Laman(9) (he used the term 'skeletal structure' instead of 'link syst,em' of this paper). This paper presents a combinatorial analysis method for the structures of plane link systems. More precisely, the proposed method affords a representa­ tion of the family of all the rigid sub-systems of a plane link system. A link system is a mechanical object composed of rods and joints(links). A rod is a rigid bar connected with some other rods by joints at its ends and it moves freely around a joint. A link system was first studied systematically by Laman(9) , who estab­ lished a graph-theoretic charact-erization of the rigidity of link systems on a 2-dimensional space. But the generalization of the results of Laman to the 3-dimensional case is not yet known. As for the further researches about this problem, we refer to (2)(4). Bolker-Crapo(3) presented a matroid-theoretic approach to the bracing problem on a one-story-building. Lovasz(12) reduced the pinning down problem of a plane link system to a matroid parity problem. This paper presents a method for the representation of the inner struc­ tures of a plane link system. The main tool used in this paper is based on matroid theory.

A polynomial algorithm for the maximum balanced flow problem with a constant balancing rate function

Abstract: M. Minoux considered the maximum balanced flow problem, which is a maximum flow problem with an additional constraint described in terms of a balancing rate function. In this paper, we propose an algorithm for the maximum balanced flow problem which is practically fast and simple. When the balancing rate function is constant, the proposed algorithm requires O(mT(n,m» time, where T(n,m) is the time for the maximum flow computation for a network with n vertices and m arcs.

Equipment replacement under technological advances

Abstract: Suppose a problem of determining whether the replacement of old equipment is economical or not when new equipment with technological advances is expected to appear at each period of the equipment planning interval. Since equipment always keeps in danger of obsolescence under technological advances, the decision maker needs grasp the state of obsolescence constantly to reflect it adaptively in the present and future decisions. Especially the decision to replace now or not becomes urgent in most cases and he is much concerned with the present decision. At this time he must also consider the fact that the present decision depends on the subsequent future decisions. This paper derives a simple criterion by which it becomes easily possible in some circumstances to decide whether immediate replacement is economical or not without determining the subsequent sequence of replacement times for the planning interval. Some informations on next replacement time are presented by para­ metric analysis of the criterion and the upper bound number of replacement times is given for the inteml!. These will become a guideline for the decision maker to plan future equipment replacement. The proposed method is applied to a practical case and some characteristics aw examined by sensitivity analysis. It is clarified that the method is relatively insensitive to changes of parameters at the present decision.

Replacement policy for components in a markovian deteriorating system with minimal repair

Abstract: This paper deals with a discrete time replacement model for a system with minimal repair. The system consists of n components under Markovian deterioration. The transition probability of its component is not inde­ pendent each other and the cost of replacing several components jointly is less than the sum of the costs of separate replacements. Then we investigate the structural properties of the optimal replacement policy which minimizes the expected total discounted cost, and propose the simple replacement policy which lets easily implementable policy. Also a numerical example is presented.

Worst-case analysis for planar matching and tour heuristics with bucketing techniques and spacefilling curves

Abstract: The worst-case performance of heuristics with bucketing techniques and/or spacefilling curves for the planar matching problem and the planar traveling salesman problem is analyzed. Two types of heuristics are investigated, one is to sequence given points in a spacefilling-curve order and the other is to sequence the points in the order of buckets which are arranged according to the spacefilling curve. The former heuristics take O(n log n) time, while the latter ones run in O(n) time when the number of buckets is O(n). It is shown that the worst-case performance of the former and that of the latter are the same if a sufficient number of O(n) buckets are provided, which is investigated in detail especially for the heuristics based on the Sierpifiski curve. The worst-case perfor­ mance of the heuristic employing the Hilbert curve is also analyzed.

A capacity-constrained single-facility multi- product production planning model

Abstract: A single-facility multi-product production planning model with time-variant capacity constraints is analyzed, in which known demands must be satisfied. In the model, in every production period the single facility produces a fixed number of distinct products each taking a prespecifIed part of the involved production activity (or input resource quantity). Concave production and inventory costs are assumed. Both the cases of nonbacklogging and backlogging are considered, and piecewise concave inventory costs are assumed for the case of backlogging. The structure of an optimal solution is characterized and this is used in developing a tree-search algorithm.

A fluid flow approximation analyser for buffer type queueing systems

Abstract: Queueing systems in which idle times of servers seldom occur are commonly seen in many practical areas such as manufacturing, transportation, etc. Here we call such a system buffer type queueing system. It is known that the fluid flow approximation technique is efficient in analysing such systems. This paper presents an algorithm based on this technique and a comprehensive computing tool (FFQA) which employs it. The applicability and the accuracy of FFQA are illustrated through some examples.

An approach for the optimal production rate of a single product system with dynamic demands

Abstract: The optimal production rate (production capadty) for a single product system with some deterministic dynamic demands is considered. Under a linear-additivity assumption on the associated cost information, the existence of the optimal solution for production capacity is verified. For the model, two solving techniques (point­ wise computation and L.P. approaches) are developed for both uniilled-demand handling cases of lost-sales and backlOgging, with which example problems are tested to show the superiority of the point-wise computation ap­ proach to L.P. approach.