W e consider a class of the subset selection problem in ranking and selection. The objective is to identify the top m out of k designs based on simulated output. Traditional procedures are conservative and inefficient. Using the optimal computing budget allocation framework, we formulate the problem as that of maximizing the probability of correctly selecting all of the top-m designs subject to a constraint on the total number of samples available. For an approximation of this correct selection probability, we derive an asymptotically optimal allocation and propose an easy-to-implement heuristic sequential allocation procedure. Numerical experiments indicate that the resulting allocations are superior to other methods in the literature that we tested, and the relative efficiency increases for larger problems. In addition, preliminary numerical results indicate that the proposed new procedure has the potential to enhance computational efficiency for simulation optimization.

Ordinal optimization offers an efficient approach for simulation optimization by focusing on ranking and selecting a finite set of good alternatives. Because simulation replications only give estimates of the performance of each alternative, there is a potential for incorrect selection. Two measures of selection quality are the alignment probability or the probability of correct selection (P{CS}), and the expected opportunity cost E[OC], of a potentially incorrect selection. Traditional ordinal optimization approaches focus on the former case. This paper extends Chen's optimal computing budget allocation (OCBA) approach, which allocated replications to improve P{CS}, to provide the first OCBA-like procedure that optimizes E[OC] in some sense. The procedure performs efficiently in numerical experiments.

We propose to improve the efficiency of simulation optimization by integrating the notion of optimal computing budget allocation into the Cross-Entropy (CE) method, which is a global optimization search approach that iteratively updates a parameterized distribution from which candidate solutions are generated. This article focuses on continuous optimization problems. In the stochastic simulation setting where replications are expensive but noise in the objective function estimate could mislead the search process, the allocation of simulation replications can make a significant difference in the performance of such global optimization search algorithms. A new allocation scheme is developed based on the notion of optimal computing budget allocation. The proposed approach improves the updating of the sampling distribution by carrying out this computing budget allocation in an efficient manner, by minimizing the expected mean-squared error of the CE weight function. Numerical experiments indicate that the computational efficiency of the CE method can be substantially improved if the ideas of computing budget allocation are applied.

Safety stocks are set to minimize inventory costs-the cost function in problem (15)-using as input the buyer's demand model, the service level agreement-the constraint in problem (15)-and (a model of) the production capacities B i n . We will explore how demand parameters can be adjusted according to both supplier and buyer cost structures so that any generated savings can be shared among them.We assume that the buyer's demand is an m-state Markov-modulated process (MMP), with transition probability matrix PD and demand levels at each state given by the vector rD. The supplier's production capacity at each node i of the assembly network is modeled by an m i -state MMP with transition probability matrix P B and capacities at each state given by the vector r B , i = 1; . . . ; N . We assume that any mutually agreed adjustments in r D keep the mean demand E [D] constant; otherwise, the buyer would be unable to satisfy demand in the long term. We denote by E[D] this constant value. Let C R (r D ), the buyer cost associated with any change of r D , bewhere i expresses the buyer's cost for changing the demand level in the i th state of the demand process. rD is the vector of demand levels initially determined and to which the buyer associates zero cost. The supplier's inventory cost function, CM (rD), is the optimal value function of problem (15). Our objective is to find the vector rD that solves the following problem:Problem (17) is a nonlinear optimization problem over a convex set and can be solved using the conditional gradient method. To that end, we need the cost function gradient. The gradient of the buyer's cost can be easily derived from (16). We can evaluate the gradient of the supplier inventory costs using finite differences. It is interesting to observe that the above algorithm can be used in a distributed fashion. In particular, the buyer can take charge of finding new demand vectors on feasible descent directions. At each iteration, the buyer presents the supplier with the new demand levels r k D and the supplier responds with the gradient rC M (r k D ) of its cost function.This gradient information can be provided in the form of appropriate incentives to the buyer. The buyer uses this gradient information to find a feasible direction and compute r k+1 D . Note that neither the supplier nor the buyer need to know each other's cost structures. V. CONCLUSIONWe studied the inventory control problem for a single class assembly network which operates under a modified echelon base-stock policy. We developed an approach to find close-to-optimal echelon stock levels that minimize inventory costs while guaranteeing stockout probabilities stay below some predefined levels. Relying upon large deviations techniques, we reduced the safety stock selection to a deterministic nonlinear optimization problem.We also used our inventory control approach to analyze how a supplier can interact with a buyer to reach a mutually beneficial mode of operations. This interaction takes the form of a supply contract that enforces...

We present a simulation run allocation scheme for improving efficiency in simulation experiments for decision making under uncertainty. This scheme is called Optimal Computing Budget Allocation (OCBA). OCBA advances the state-of-the-art by intelligently allocating a computing budget to the candidate alternatives under evaluation. The basic idea is to spend less computational effort on simulating non-critical alternatives to save computation cost. In particular, OCBA is employed to intelligently provide the smallest number of simulation runs for a desired accuracy. In this paper, we present a new and more general OCBA scheme which can consider cases that users are interested not only the best design, but also any one in a good design set. In addition, this paper also presents the application of our OCBA to a design problem in US air traffic management. The national air traffic system in US is modeled as a large, complex, and stochastic network. The numerical examples show that the computation time can be reduced by 54% to 88% with the use of OCBA.