This paper investigates an m-product inventory system (m ≧ 3) with a capacity constraint where products can have individual order intervals and orders be phased to reduce the maximum stock level of all the products on hand. The objective is then to find the optimal order quantity of each product by considering staggering time and order interval which minimizes the system cost per unit time. The problem is described in a non-linear integer programming problem which shows a very complicated nature to derive the solution analytically. Therefore, a, heuristic algorithm is proposed and tested for its efficiency with various numerical examples as being superior to either the Lagrangian multiplier method or the fixed cycle method.

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Minoux considered the maximum balanced flow problem of a two-terminal network, which is the problem of finding a maximum flow f in the network such that each arc-flow f(a) (a ∈ A) is bounded by a fixed proportion of the total flow value from the source to the sink, where A is the arc set of the network. He also proposed an algorithm for finding a maximum integral balanced flow, i.e., a maximum balanced flow satisfying that the value of each arc-flow of the network is integral. Integral balanced flows defined by Minoux can be regarded as one way to balance flows in the network. In this paper, we propose another way to balance flows in a two-terminal network N. To be exact, we consider the maximum vertex-balanced flow problem in network N, i.e., the problem of finding a, maximum flow f' in N such that for each vertex v ∈ V any arc-flow f'(a) (a ∈ δ^-(v)) entering v is bounded by a fixed proportion of the total flow Σ{f'(a) : a ∈ δ^-(v)} entering v, where V is the vertex set of N and δ^-(v) is the set of the arcs entering v. We intended to propose an algorithm for finding a maximum integral vertex-balanced flow in network N, but we found that the maximum integral vertex-balanced flow problem (IVBP) is difficult. Our main purpose in this paper is to prove that problem (IVBP) is NP-complete and to propose a polynomial-time approximation algorithm for (IVBP).

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In this paper a heuristic algorithm is presented for scheduling in flowshops with the objective of minimizing the sum of completion times or total flowtime of jobs. The algorithm is developed by considering the lower bound on completion times of jobs for various stages of flowshop. Since the proposed lower bound will also hold for the flowshop with no job-waiting constraint at some or all stages of processing, the heuristic can as well be applied to such flowshop problems. The performance of the heuristic algorithm in all types of flowshop problems has been evaluated. It is found to be consistently good and superior to the existing flowshop scheduling algorithms.

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In this paper, we consider a dynamic stochastic inventory model with fixed inventory holding and shortage costs in addition to a fixed ordering cost. We discuss a sufficient and necessary condition for an (s, S) policy to be optimal in the class of such stochastic inventory models. Furthermore, we explore how such a sufficient and necessary condition can be rewritten when the demand distribution is specified. Several examples such as uniform, exponential, normal and gamma distribution functions are treated. The main purpose of this paper is to show that the (s, S) policy is still optimal under a simple condition even if fixed inventory costs are involved. Although Aneja and Noori [1] consider a similar model only with fixed inventory shortage cost, our proof for the optimality of an (s, S) policy in the multi-period model is different from and much simpler than theirs.

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The coefficients of linear programming problems have been assumed to be determined as crisp values by the experts. However, the knowledge of the experts is not always so accurate to determine them as crisp values. The experts often have vague or imprecise knowledge of the coefficients. In such cases, it is not sufficient to fix the coefficients definitely. It is more sufficient to determine them only as regions in which the coefficients possibly take. From this point of view, the inexact linear programming, the interval linear programming and possibilistic linear programming have been proposed. In multiobjective linear programming, the ones with interval coefficients or with fuzzy coefficients have been proposed and the concept of efficiency is extended. Bitran directly extended the efficiency to multiobjective linear programming problem with interval objective functions : [numerical formula] where A is an m by n matrix, b and x are respectively m and n vectors. Φ is a set of p by n matrices with components c<ij> In the interval [l<ij> , u<ij>], i := 1, 2, . . . , p and j =: 1, 2, . . . , n By Bitran, it was pointed out that two kinds of efficient solutions can be considered. In this paper, the solution concepts for the interval multiobjective linear program are proposed in a different manner from Bitran's approach. First, given a reflective domination relation in the objective space, a strong (nonreflective) domination relation is defined. The domination relations in the decision space are composed from the domination relations in the objective space and using them the nonreflective domination relations are defined. The properties of nonreflective domination relations are investigated. Next, four concepts of nondominated solutions for the interval multiobjective linear programming problem, i.e. possibly nondominated solutions, necessarily nondominated solutions, strong possibly nondominated solutions and weak necessarily nondominated solutions, a,re defined using four nonreflective domination relations. The properties of these nondominated solutions are discussed and it is shown that an arbitrary element of each nondominated solution set can be expressed by a convex combination of the corresponding nondominated extreme points. Moreover, the relationships with Bitran's two efficient solutions are clarified. Two of four nondominated solutions are equivalent to Bitran's two efficient solutions and the others are intermediated ones between them.

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This is a single-period single-product inventory model with several individual sources of demand. It is a multi-location problem wit,h an opportunity for centralization. The holding' and penalty cost functions, at each location, are assumed to be linear and identical. Two types of inventory system are considered in this paper: The decentralized system and the centralized system. The decentralized system is a system in which a separate inventory is kept to satisfy the demand at each source of demand and there is no reinforcement between locations; i.e., the surplus supplied location is not, allowed to supply the deficient supplied location. Therefore, the total expected cost of the decentralized system is the sum of the expected cost of individual locations, as the holding cost, or penalty cost of each location depends only on its own inventory level and is unrelated to any other location's inventory level. The centralized system is a system in which the surplus location is allowed to supplement the deficient one by transportation. Therefore, the holding cost or penalty cost is calculated by the net surplus or net deficient after the reinforcement. The total expected cost of the centralized system should therefore include the expected holding cost, the expected penalty cost and the expected transportation cost. Let h^^- > 0,p^^- > 0 and t^^- ≧ O be the unit holding cost, the unit penalty cost and the unit transportation cost, respectively. This pa,per demonstrates that, for any probability distribution of a location's demand, the following two properties are always true: (1) t^^- < h^^-+p^^- if and only if the total expected cost in a decentralized system exceeds those in a centralized system. (2) For all i, j, i ≠ j,p<ij> , the coefficient of correlation between the i-th location's demand and the j-th location's demand, is equal to 1, then for any t^^- , the total expected cost in a, decentralized system is equal to those in a, centralized system.

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In this paper, the batch arrival cyclic service multiqueue system is studied. For a compound Poisson arrival cyclic service multiqueue system, we derive useful equalities with respect to the weighted sum of the mean waiting times for E-limited and G-limited service disciplines. Using these equalities, the upper bound of the mean waiting time at each queue is derived for symmetric system. Further, for general batch arrival cyclic service multiqueue system, an approximate formula with respect to the weighted sum of the mean waiting times is derived. For symmetric system, this approximate formula reduces to the approximate formula of the mean waiting time for exhaustive, gated, E-limited and G-limited service disciplines. In numerical results, these characteristic quantities are evaluated by comparing those to simulation results and other approximate results.

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