An algorithm for solving 2-stage linear programs, especially useful for a Program arising from a nested multi-level approach to multi-period planning [3] is presented, The proposed algorithm is of a two-level scheme and similar to Beale's method [4] , but the procedure is more systematic and simpler, Computational experience is reported for a series of small test problems, The results show that our algorithm is more efficient than a Beale-like method, and moreover that the number of times for adjusting given initial values of linking variables is unexpectedly small for the test problems, which may also imply an aspect of usefulness of the algorithm for large real problems, especially when a good initial value can be obtained for the linking variable, The algorithm can be also extended to a weakly coupled three or more-stage case.

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Given a capacitated network with the entrance-vertex set V_1 and the exit-vertex set V_2 on which polymatroids are defined, an independent flow is a flow in the network such that a vector corresponding to the supplies in V_1 and a vector corresponding to the demands in V_2 are, respectively, independent vectors of the polymatroids on V_1 and V_2 ・ The independent-flow problems considered in the present paper are the following two: (1) to find a maximum independent flow; and (2) to find an optimal independent flow, i,e,, a maximum independent flow of the minimum cost when a cost is given to each arc, We present several theorems which algorithmically characterize optimal independent flows and we propose algorithms for solving the independent-flow problems based on the theorems.

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This paper considers the interval reliability of a repairable system for the time interval [T, T+x], Optimum preventive maintenance policies maximizing (i) the limiting interval reliability when T is constant, and (ii) the interval reliability when T is exponential, and minimizing (iii) the expected cost per unit of time, are derived, It is shown that under suitable conditions there exist optimum policies which are given by unique solutions of equations, Further this paper treats discrete case.

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Zero-one programming can be effectively used to formulate and help resolve many commonly encountered management decision problems, However, the formulation itself often takes on a large-scale that cannot easily be solved by current optimization methods, The most common approach for obtaining an a,pproximate solution is to stop the calculations after a fixed time period and to use the best known solution at that time, even though only a small number of iterations may have been performed. This paper presents an improved algorithm for solving zero-one programming problems, especially those of large-scale, based on implicit enumeration, The algorithm results in a good initial feasible solution, and in rapid convergence to the optimal solution in a small number of It can also be used to obtain close approximate solutions by stopping the calculation after very few iterations.

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The effect of the various design factors on the production rate in a parallel line is discussed by a Markov model and the difference of the effect between parallel lines and series lines is represented, A simple and effective scale is proposed to evaluate the availability of a parallel line and the production rate of a parallel line is approximately estimated by the scale and the relation between the production rates and the buffer capacities in a series line.

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We discuss some of the concepts related to the flow problems in a discrete-continuous compound system, and propose an approximation method as well as a numerical algorithm for the maximum-flow problem in a network which is assumed to be locally uniform and sufficiently dense, The algorithm is derived by means of the finite-element technique, and is tested by taking up as an example the maximum-flow problems on the road network of Tokyo Metropolitan Area.

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A combined overhaul/replacement policy is developed for a class of deteriorating equipment, where operating costs increase with age, It is assumed that the effect of an overhaul is to reduce these costs by a fixed amount, from the time of overhaul onwards, Two possible assumptions as to the dependence of overhauling effects on equipment age and two functional forms the this dependence are explored, Discounting considerations are omitted from the analysis and the possible effect of this omission on outcomes is investgated.

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In this paper, sufficient conditions to decide the precedence relation between neighboring two jobs are presented by means of an adjacent pairwise interchage method for minimizing mean flow-time in flow-shop scheduling, On the bases of the sufficient conditions, a computational algorithm is proposed for an optimal or near optimal solution, The mean flow-time by this algorithm puts 90% of the optimal value as an average of over one hundred problems, The algorithm can be executed even by manual calculations within the time proportional to nxm^2, where n and m are the number of jobs and machines respectively.

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This paper examines the distance r between two points that are randomly distributed over a bounded area, First, with respect to circular and quadrate areas, the probability density functions of r are obtained, After standard-izing these two functions by making each expected value equal, next their forms are compared, From this comparison, it is revealed that these forms are almost the same, This fact may imply that the probability density function of r is almost independent of the form of an area, It may hence be not inappropriate to con-sider rectangular areas as a representative of various forms of areas , Based upon this result, two kinds of approximation to the expected value of r are obtained, Let L be the perimeter of the minimum convex covering of an area. Then the first approximation is given by E(r) 〜 c _1 l , where c_1 is constant. The second approximation is given by E(r) 〜 c_2R , where R is the diameter of the area and c_2 is constant. These results are tested by using the forms of the 23 wards In Tokyo. Then c_1= 0.13 and c_2=0.33 are obtained.

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