A simulation–optimization method: Its convergence and utility

An optimization method is given for solving problems where a portion of the explicit mathematical form is unknown but can be evaluated. The solution scheme is an iterative process utilizing optimization and subsystem evaluation (such as via simulation). Conditions for the convergence of the iterative process are given. Several published application articles are noted as using this basic methodology. The method is superior to most other numerical optimization procedures. However, the class of problems for which the method is applicable is restricted to problems with enough known structure to generate a convergent iterative procedure. Three numerical examples are given and comparisons made with several other methods of optimizing unknown systems.     

Equivalence relations in the theory of repetitive consumption

Preference for food in the function of the time since last consumption and total preference in the function of eating frequency are equivalent mathematical representations of attitudes governing food consumption. The observed and postulated properties of these functions imply a formal correspondence between preference maximizing and variety seeking behavior.     

Reformulating zero-sum games with multiple goals

This paper investigates the two-person zero-sum multiple payoff game in which the objective is to minimize a player's total underachievement from a fixed set of goals. It is demonstrated that a previous formulation of this problem can be substantially simplified.     

Optimal ordering policies when anticipating parameter changes in EOQ systems

The classical Economic Order Quantity Model requires the parameters of the model to be constant. Some EOQ models allow a single parameter to change with time. We consider EOQ systems in which one or more of the cost or demand parameters will change at some time in the future. The system we examine has two distinct advantages over previous models. One obvious advantage is that a change in any of the costs is likely to affect the demand rate and we allow for this. The second advantage is that often, the times that prices will rise are fairly well known by announcement or previous experience. We present the optimal ordering policy for these inventory systems with anticipated changes and a simple method for computing the optimal policy. For cases where the changes are in the distant future we present a myopic policy that yields costs which are near-optimal. In cases where the changes will occur in the relatively near future the optimal policy is significantly better than the myopic policy.     

Optimal set partitioning,matchings and lagrangian duality

We formulate the set partitioning problem as a matching problem with simple side constraints. As a result we obtain a Lagrangian relaxation of the set partitioning problem in which the primal problem is a matching problem. To solve the Lagrangian dual we must solve a sequence of matching problems each with different edge-weights. We use the cyclic coordinate method to iterate the multipliers, which implies that successive matching problems differ in only two edge-weights. This enables us to use sensitivity analysis to modify one optimal matching to obtain the next one. We give theoretical and empirical comparisons of these dual bounds with the conventional linear programming ones.     

The queueing system MX/G/1 and its ramifications

This paper deals with the bulk arrival queueing system M^X/G/1 and its ramifications. In the system M^X/G/1, customers arrive in groups of size X (a random variable) by a Poisson process, the service times distribution is general, and there is a single server. Although some results for this queueing system have appeared in various books, no unified account of these, as is being presented here, appears to have been reported so far. The chief objectives of the paper are (i) to unify by an elegant procedure the relationships between the p.g.f.'s

     

Interval estimation of a global optimum for large combinatorial problems

Consider an “intractable” optimization problem for which no efficient solution technique exists. Given a systematic procedure for generating independent heuristic solutions, we seek to obtain interval estimates for the globally optimal solution using statistical inference. In previous work, accurate point estimates have been derived. Determining interval estimates, however, is a considerably more difficult task. In this paper, we develop straightforward procedures which compute confidence intervals efficiently in order to evaluate heuristic solutions and assess deviations from optimality. The strategy presented is applicable to a host of combinatorial optimization problems. The assumptions of our model, along with computational experience, are discussed.     

Explicit steady state solutions for a particular M(x)/M/1 queueing system

An explicit steady state solution is determined for the distribution of the number of customers for a queueing system in which Poisson arrivals are bulks of random size. The number of customers per bulk varies randomly between 1 and m, m arbitrary, according to a point multinomial, and customer service is exponential. Queue characteristics are given.     

Flowshop sequencing problem with ordered processing time matrices: A general case

The ordered matrix flow shop problem with no passing of jobs is considered. In an earlier paper, the authors have considered a special case of the problem and have proposed a simple and efficient algorithm that finds a sequence with minimum makespan for a special problem. This paper considers a more general case. This technique is shown to be considerably more efficient than are existing methods for the conventional flow shop problems.     

几种带补偿功能的三光纤传感器的分析

在单光纤对光耦合模型的基础上 ,研究了三种带补偿功能的三光纤反射式位移传感器 ,建立了通用的光耦合的数学模型。仿真研究了它们的位移特性 ,并比较了它们的优缺点。研究结果表明 ,采用三光纤的光纤位移传感器不但线性范围、位移灵敏度和线性度等特性得到较好改善 ,而且可以有效地消除光源功率波动和反射面的反射率变化等因素对位移测量的影响