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In this paper, we investigate the properties of the sampled version of the fictitious play algorithm, familiar from game theory, for games with identical payoffs, and propose a heuristic based on fictitious play as a solution procedure for discrete optimization problems of the form max {u(y) y = (y1,…yn ∈ y1 x … x yn} i.e., in which the feasible region is a Cartesian product of finite sets y1 i ∈ N = (1, …, n). The contributions of this paper are twofold. In the first part of the paper, we broaden the existing results on convergence properties of the fictitious play algorithm on games with identical payoffs to include an approximate fictitious play algorithm that allows for errors in players 'best replies. Moreover, we introduce sampling-based approximate fictitious play that possesses the above convergence properties, and at the same time provides a computationally efficient method for implementing fictitious play. In the second part of the paper, we motivate the use of algorithms based on sampled fictitious play to solve optimization problems in the above form with particular focus on the problems in which the objective function u(·) comes from a "black box," such as a simulation model, where significant computational effort is required for each function evaluation. [ABSTRACT FROM AUTHOR]

One approach to coping with the apparent difficulty of many schedule-optimization problems, such as occur in machine shops and computer processing, is to devise efficient algorithms that find schedules guaranteed to be "near-optimal." This paper presents an introduction to this approach by describing its application to a well-known multiprocessor scheduling model and illustrating the variety of algorithms and results that are possible. The paper concludes with a brief survey of what has been accomplished to date in the area of scheduling using this approach. [ABSTRACT FROM AUTHOR]

Model reference adaptive search (MRAS) for solving global optimization problems works with a parameterized probabilistic model on the solution space and generates at each iteration a group of candidate solutions. These candidate solutions are then used to update the parameters associated with the probabilistic model in such a way that the future search will be biased toward the region containing high-quality solutions. The parameter updating procedure in MRAS is guided by a sequence of implicit probabilistic models we call reference models. We provide a particular algorithm instantiation of the MRAS method, where the sequence of reference models can be viewed as the generalized probability distribution models for estimation of distribution algorithms (EDAs) with proportional selection scheme. In addition, we show that the model reference framework can also be used to describe the recently proposed cross-entropy (CE) method for optimization and to study its properties. Hence, this paper can also be seen as a study on the effectiveness of combining CE and EDAs. We prove global convergence of the proposed algorithm in both continuous and combinatorial domains, and we carry out numerical studies to illustrate the performance of the algorithm. [ABSTRACT FROM AUTHOR]

We study the classical multistage lot sizing problem that arises in distribution and inventory systems. A celebrated result in this area is the 94% and 98% approximation guarantee provided by power-of-two policies. In this paper, we propose a simple randomized rounding algorithm to establish these performance bounds. We use this new technique to extend several results for the capacitated lot sizing problems to the case with submodular ordering cost. For the joint replenishment problem under a fixed base period model, we construct a 95.8% approximation algorithm to the (possibly dynamic) optimal lot sizing policy. The policies constructed are stationary but not necessarily of the power-of-two type. This shows that for the fixed based planning model, the class of stationary policies is within 95.8% of the optimum, improving on the previously best known 94% approximation guarantee. [ABSTRACT FROM AUTHOR]

This paper proposes an optimization model of incorporating competence sets of group decision makers to maximize the total benefit of the whole group. Such an incorporation model is formulated as finding a deduction graph linked from the nodes of existing competencies to the nodes of desired competencies. Compared with other methods treating competence set problems (Yu and Zhang 1991, Li and Yu 1994, and Shi and Yu 1996), the proposed model can solve problems involving multiple decision makers; in addition it allows the network to be cyclic and to contain compound nodes. [ABSTRACT FROM AUTHOR]

This paper presents a method for finding optimal flows in a dynamic network with random inputs into the system and congestion limits on flow. This model has been used in deterministic settings to represent dynamic traffic assignment and job shop routing. This paper builds on the deterministic results to show that a globally optimal solution in the stochastic problem may be obtained by a sequence of linear optimizations. A decomposition algorithm for this procedure is presented that efficiently solves problems with large-scale deterministic equivalents of up to 66,000 variables. [ABSTRACT FROM AUTHOR]

We consider a production/distribution system represented by a general directed acyclic network. Each node is associated with a specific "product" at a given location and/or production stage. An arc (i, j) indicates that item i is used to "produce" item j. External demands may occur at any of the network's nodes. These demands occur continuously at item-specific constant rates. Components may be assembled in any given proportions. The cost structure consists of inventory carrying, variable, and fixed production/distribution costs. The latter depend, at any given replenishment epoch, on the specific set of items being replenished, according to an arbitrary set function merely assumed to be monotone and submodular. It has been shown that a simply structured, so-called power-of-two policy is guaranteed to come within 2% of a lower bound for the minimum cost. In this paper, we derive efficient algorithms for the computation of an optimal power-of-two policy, possibly in combination with this lower bound. These consist of a limited number of polymatroidal maximum flow calculations in networks closely associated with the original production/distribution network. [ABSTRACT FROM AUTHOR]

This paper presents a branch-and-bound algorithm for solving fixed charge transportation problems where not all cells exist. The algorithm exploits the absence of full problem density in several ways, thus yielding a procedure which is especially applicable to solving real world problems which are normally quite sparse. Additionally, streamlined new procedures for pruning the decision tree and calculating penalties are presented. We present computational experience with both a set of large test problems and a set of dense test problems from the literature. Comparisons with other codes are uniformly favorable to the new method, which runs more than twice as fast as the best alternative. [ABSTRACT FROM AUTHOR]

We study echelon-stock (R, nQ) policies in a multistage, serial inventory system with compound Poisson demand. We provide a simple method for determining near-optimal control parameters. This is achieved in two steps. First, we establish lower and upper bounds on the cost function by over- and under-charging a penalty cost to each upstream stage for holding inadequate stock. Second, we minimize the bounds, which are simple, separable functions of the control parameters, to obtain heuristic solutions. We also provide an algorithm that guarantees an optimal solution at the expense of additional computational effort. A numerical study suggests that the heuristic solutions are easy to compute (even for systems with many stages) and are close to optimal. It also suggests that a traditional approach for determining the order quantities can be seriously suboptimal. All the results can be easily extended to the discrete-time case with independent, identically distributed demands. [ABSTRACT FROM AUTHOR]