Simulation Budget Allocation for Further Enhancing the Efficiency of Ordinal Optimization

Ordinal Optimization has emerged as an efficient technique for simulation and optimization. Exponential convergence rates can be achieved in many cases. In this paper, we present a new approach that can further enhance the efficiency of ordinal optimization. Our approach determines a highly efficient number of simulation replications or samples and significantly reduces the total simulation cost. We also compare several different allocation procedures, including a popular two-stage procedure in simulation literature. Numerical testing shows that our approach is much more efficient than all compared methods. The results further indicate that our approach can obtain a speedup factor of higher than 20 above and beyond the speedup achieved by the use of ordinal optimization for a 210-design example.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45045/1/10626_2004_Article_264696.pd

Novel Approaches to Feasibility Determination

The article of record as published may be found at https://doi.org/10.1145/3426359This article proposes two-stage Bayesian and frequentist procedures for determining whether a number of systems—each characterized by the same number of performance measures—belongs to a set Γ defined by a finite collection of linear inequalities. A system is “in (not in) Γ” if the vector of the means is in (not in) Γ, where the means must be estimated using Monte Carlo simulation. We develop algorithms for classifying the systems with a user-specified level of confidence using the minimum number of simulation replications so the probability of correct classification over all r systems satisfies a user-specified minimum value. Once the analyst provides prior values for the means and standard deviations of the random variables in each system, an initial number of simulation replications is performed to obtain current estimates of the means and standard deviations to assess whether the systems can be classified with the desired level of confidence. For any system that cannot be classified, heuristics are proposed to determine the number of additional simulation replications that would enable correct classification. Our contributions include the introduction of intuitive algorithms that are not only easy to implement, but also effective with their performance. Compared to other feasibility determination approaches, they also appear to be competitive. While the algorithms were initially developed in settings where system variance is assumed to be known and the random variables are independent, their performance remains satisfactory when those assumptions are relaxed

A fuzzy newsvendor approach to supply chain coordination

In the absence of a clear command and control structure, a key challenge in supply chain management is the coordination and alignment of supply chain members who pursue divergent and often conflicting goals. The newsvendor model is typically used as a framework to quantify the cost of misalignment and to assess the impact of various coordination initiatives. The application of the newsvendor framework, however, requires the specification of some probability distribution for the sources of uncertainty, and in particular, for the market demand. The specification of an adequate demand distribution becomes difficult in the absence of statistical data. We therefore consider a fuzzy approach to the newsvendor problem. We use several fuzzy parameters in the model for the demand, the wholesale price, and the market sales price. We solve the fuzzy newsvendor problem to study three coordination policies: quantity discounts, profit sharing, and buyback. For each coordination policy, the optimal order quantity of the retailer is computed. The possible profits of the members in the supply chain are calculated with minimum sharing of private information. We further extend the fuzzy newsvendor model to a setting with a single manufacturer and multiple retailers under the assumption of ample capacity for the manufacturer. Detailed numerical examples are also provided.Fuzzy sets Inventory Logistics Supply chain management

Using Accessibility To Assess The Performance Of Generalized Hill Climbing Algorithms

The search problem, ACCESSIBILITY, asks whether a finite sequence of events can be found such that, starting with a specific initial event, a particular state can be reached. This problem is intractable, indicating the need for heuristics to address it. One difficulty when applying heuristics to ACCESSIBILITY is assessing a priori their effectiveness, and knowing how to best adjust them to improve performance. This paper introduces the false negative probability as a performance measure for generalized hill climbing algorithms applied to discrete optimization problems, using ACCESSIBILITY as the analysis framework. The false negative probability is also used to obtain necessary convergence conditions. The implications of these results on how GHC algorithms can be effectively applied are discussed