Monte Carlo simulation is a commonly used tool for evaluating the performance of complex stochastic systems. In practice, simulation can be expensive, especially when comparing a large number of alternatives, thus motivating the need to intelligently allocate simulation replications. Given a finite set of alternatives whose means are estimated via simulation, we consider the problem of determining the subset of alternatives that have means smaller than a fixed threshold. A dynamic sampling procedure that possesses not only asymptotic optimality, but also desirable finite-sample properties is proposed. Theoretical results show that there is a significant difference between finite-sample optimality and asymptotic optimality. Numerical experiments substantiate the effectiveness of the new method. Summary of Contribution: Simulation is an important tool to estimate the performance of complex stochastic systems. We consider a feasibility determination problem of identifying all those among a finite set of alternatives with mean smaller than a given threshold, in which the means are unknown but can be estimated by sampling replications via stochastic simulation. This problem appears widely in many applications, including call center design and hospital resource allocation. Our work considers how to intelligently allocate simulation replications to different alternatives for efficiently finding the feasible alternatives. Previous work focuses on the asymptotic properties of the sampling allocation procedures, whereas our contribution lies in developing a finite-budget allocation rule that possesses both asymptotic optimality and desirable finite-budget properties.

Electron beam inspection (EBI) with high resolution is a promising technique to improve the defect inspection on the surface of patterned wafer. However, high resolution usually means long inspection time, which results in the low throughput and limitation of EBI applied in practice. This study aims to optimize the inspection time of EBI by reducing the total number of inspection regions without loss of the accuracy. We first refine this defect inspection optimization problem as a partial congruent square cover problem. Then, we propose two novel mixed-integer linear programming models for this problem. To deal with the large-scale problems, an approximation algorithm is developed to obtain the high-quality solutions. This approximation algorithm efficiently utilizes the linear programming (LP) rounding technique and greedy strategy based on the proposed model. Compared with the existing algorithms in the literature, numerical results show the superiority of the proposed model and algorithm.Note to Practitioners—Defect inspection is a key process in wafer fabrication for identifying and inspecting the patterning defects generated during the complicated fabrication processes. Electron beam inspection (EBI) takes place of optical inspection gradually as the design rules keep shrinking and the circuits are more susceptible to nanoscale killer defects. Low throughput is the main drawback of EBI and the improvements on throughput have far-reaching significance on the high volume manufacturing of semiconductor products. This study aims to reduce the number of inspection regions to improve the total inspection time in the EBI process. Considering that the inspection time for each inspection region is constant, less inspection regions means less total inspection time. However, the positions of inspection regions are arbitrary across the continuous planar space, putting pressure on modeling and solving the problem. A preprocessing algorithm is designed to discover a limited number of candidate positions of inspection regions without loss of optimality, which greatly simplifies the problem. For dealing with large-scale instances, an approximation algorithm combining linear programming (LP)-rounding technique and greedy strategy is designed to get near optimal solutions. Since the number of inspection regions is one key factor determining the total inspection time, the proposed optimization methods have a potential to be applicable to enhance the efficiency of advanced EBI platforms, such as ASML HMI eP series.

This article investigates a hybrid flow shop scheduling problem that consists of a batch processor in the upstream and a discrete processor in the downstream. Limited waiting time between the batch processor and discrete processor is taken into consideration. Such a scheduling problem is commonly seen as bottlenecks in the production of precision parts, back-end process of semiconductor products, and glass and steel industries. A mixed-integer linear programming model is presented to minimize the makespan. Considering the complexity of this problem and the imperative requirement in real-time optimization, we first develop a constructive heuristic together with the worst case analysis by exploiting the key decision structure of the problem. Based on the decision structure, we then develop a learning-based scheduling approach via customized genetic programming to automatically generate effective heuristics for this problem. Lower bounds are also developed to provide a measurement for the performance of proposed algorithms. Numerical results show that our proposed algorithms outperform the existing metaheuristics and are capable of providing high-quality solutions using less computational time. Note to Practitioners-The production system consisting of a batch processor in the upstream and a discrete processor in the downstream is common in practice. The batch processor first handles a group of jobs simultaneously. Then, the jobs are released to a buffer to wait for the process on the discrete processor one by one. However, the waiting time of the jobs in the buffer is often required to be limited according to the production requirements. For example, after being heated in the heat-treatment oven, the aerospace precision parts have to be processed on the machining equipment in limited waiting time to improve the processability in subsequent manufacturing. The semiconductor chips have to be packed in limited waiting time after baking to avoid getting wet. The incongruous production modes between the batch processor and discrete processor, together with the limited waiting time constraint, make such operations always the bottleneck in manufacturing. Efficient heuristics, providing high-quality solutions with low time complexity, are much preferred in practice for most of the complicated scheduling problems, such as the scenarios described earlier. However, the designing process of an effective heuristic is tedious, and the heuristic is usually deeply customized for a certain production scenario. Genetic programming (GP) provides an inspiring approach to automatically generate sophisticated heuristics for complicated scheduling problems through evolutionary learning processes. By customizing a GP-based approach, the designing process of heuristics is automated, and some undetectable knowledge relations can be obtained to enhance the quality of heuristics. Such an approach facilitates to obtain more sophisticated schedules by analyzing valuable knowledge for smart manufacturing. The superiority of the heuristic learned by GP is shown in the computational experiment, and it has great potential to be applied to the practical scheduling.

Ranking and selection (R&S) procedures are powerful tools to enhance the efficiency of simulation-based optimization. In this paper, we consider the R&S problem subject to stochastic constraints and seek to improve the selection efficiency by incorporating the information from across the domain into quadratic regression metamodels. To better fulfill the quadratic assumption of the regression metamodel used in this paper, we divide the solution space into adjacent partitions such that the underlying functions of both the objective and constraint measures in each partition are approximately quadratic with homogeneous noise. Using the large deviations theory, we characterize the asymptotically optimal allocation rule by maximizing the rate at which the probability of false selection tends to zero. Numerical experiments demonstrate that our approach dramatically improves the selection efficiency by 50%-90% on some typical selection examples compared with the existing approaches.

In this study, the customer order scheduling problem is investigated to minimize total weighted completion time. A quadratic formulation is proposed to address this problem. This formulation is converted into an equivalent mixed-integer linear programming model by applying the linearization technique and the special structure of the problem. The problem size that can be solved to optimality is then investigated and reported based on the final linearized formulation. Furthermore, a hybrid nested partitions algorithm is developed to solve large-scale problems. Numerical results illustrate the advantages of the proposed model and demonstrate that the proposed algorithm can obtain high-quality solutions within a reasonable computational time.

In this paper, we study the radiation treatment planning optimization for Volumetric-Modulated Arc Therapy (VMAT). A nonlinear mixed integer programming model is formulated, then the linearization technique is used, and the resulting mixed integer programming model is solved by a heuristic approach based on the Nested-Partitions framework. The approach partitions the feasible region iteratively and constructs a feasible solution by solving the LP relaxation of the original problem. We design two partition strategies: partition by column and expansion from center of aperture. Numerical results with clinical cases show the efficiency of the proposed model and algorithm.