Simulation Budget Allocation Research Articles

Simulation Budget Allocation for Improving Scheduling and Routing of Automated Guided Vehicles in Warehouse Management

Simulation Budget Allocation for Improving Scheduling and Routing of Automated Guided Vehicles in Warehouse Management

Practical Simulation Budget Allocation for Ranked Subset Partitioning

Practical Simulation Budget Allocation for Ranked Subset Partitioning

Optimal budget allocation policy for tabu search in stochastic simulation optimization

Tabu search (TS) is a powerful method for solving combinatorial optimization problems. However, when TS is adopted for stochastic simulation optimization, the simulation noises may mislead the search direction and prevent TS from converging to high-quality solutions. This issue can be mitigated by increasing the number of simulation samples used for solution evaluation, however, real-world applications are generally constrained by a finite computing budget. Therefore, it is critical to reducing the noise effect by an efficient simulation budget allocation, i.e., splitting the total number of samples on solutions. Studies on the budget allocation problem of TS are sparse. Most of the works employ equal allocation or simple policies which are not optimal. Based on the large deviations framework, we propose a new budget allocation policy to enhance the performance of TS under stochastic settings. The proposed allocation policy, provided in closed-form formulas, is asymptotically optimal for maximizing the probability that TS performs the correct move in a single iteration. The efficiency of the proposed method is validated by solving different problems from manufacturing and healthcare scenarios, including an inventory control problem, a throughput maximization problem for the production line, and a physician scheduling problem for the radiotherapy center. The numerical results show that, with the proposed method, TS can obtain better results using the same amount of computational efforts.

Managing hospital inpatient beds under clustered overflow configuration

Inpatient beds represent one of the most critical resources in hospitals, of which the availability has been under increasing pressure in China. Such beds are usually to be either used exclusively (“dedicated”) by each department or shared (“pooled”) among departments. This paper considers a generalized bed configuration known as the clustered overflow configuration. The departments are partitioned and managed as clusters. Each department has its dedicated beds and can also admit patients to overflowed beds shared among the departments in the same cluster. A mixed-integer stochastic programming model is developed to optimize the partition and bed-allocation decisions. The objective is to minimize the weighted total cost of rejecting patients, holding patients waiting, nursing cost, and partitioning cost. A simulation-based metaheuristic approach (SMA) is proposed to solve the problem. A niching genetic algorithm (NGA) framework is first proposed to optimize the partitions, and then each partition is evaluated by optimizing the underlying bed-allocation plan through adaptive hyperbox algorithm-based local search (AHA-LS). In AHA-LS, two speeding mechanisms are proposed to effectively identify promising partitions and discard the worst ones. One is an original sequential simulation budget allocation (SSBA) mechanism to sequentially allocate the simulation iteration to evaluate the bed allocation decisions for a given partition; the other is optimal computing budget allocation (OCBA) to allocate the simulation budget to evaluate the bed-allocation plans. The elite clusters form a cluster pool, based on which a set covering model is proposed and solved to obtain a better solution. Case studies are conducted based on real data collected from a public hospital in Shanghai, China. The numerical results collectively demonstrate the applicability and efficiency of the proposed method. Sensitivity analyses are also performed to gain managerial insights.

Efficient estimation of a risk measure requiring two-stage simulation optimization

This paper is concerned with the efficient estimation of the risk measure of a system where the estimation requires solving a two-stage simulation optimization problem. The first stage samples risk factors that specify a second stage simulation optimization problem. The second stage solves a simulation optimization problem and outputs the best performance of the system under the realized risk factors, which are then aggregated across all first stage samples to produce an estimate of the risk measure. Applications of such an estimation scheme arise frequently in important industries such as financial, healthcare, logistics, and manufacturing. Because a large number of first stage samples are typically needed, each of which requires solving a computationally expensive simulation optimization problem, the two-stage simulation optimization approach faces a major computational efficiency challenge. In response to this challenge, this paper proposes a sequential simulation budget allocation procedure that determines the allocation of simulation budget based on a score known as revised probability of sign change for each decision under each scenario. The consistency of the proposed procedure is proved and the computational efficiency gain of the proposed is demonstrated using both benchmark test functions and two test cases in the context of financial portfolio risk estimation and healthcare system resilience estimation.

Improved Penalty Function with Memory for Stochastically Constrained Optimization via Simulation

Penalty function with memory (PFM) in Park and Kim [2015] is proposed for discrete optimization via simulation problems with multiple stochastic constraints where performance measures of both an objective and constraints can be estimated only by stochastic simulation. The original PFM is shown to perform well, finding a true best feasible solution with a higher probability than other competitors even when constraints are tight or near-tight. However, PFM applies simple budget allocation rules (e.g., assigning an equal number of additional observations) to solutions sampled at each search iteration and uses a rather complicated penalty sequence with several user-specified parameters. In this article, we propose an improved version of PFM, namely IPFM, which can combine the PFM with any simulation budget allocation procedure that satisfies some conditions within a general DOvS framework. We present a version of a simulation budget allocation procedure useful for IPFM and introduce a new penalty sequence, namely PS 2 + , which is simpler than the original penalty sequence yet holds convergence properties within IPFM with better finite-sample performances. Asymptotic convergence properties of IPFM with PS 2 + are proved. Our numerical results show that the proposed method greatly improves both efficiency and accuracy compared to the original PFM.

Optimal computing budget allocation for the vector evaluated genetic algorithm in multi-objective simulation optimization

Motivated by the vector evaluation genetic algorithm (VEGA), this research develops simulation budget allocation rules for the VEGA in solving simulation optimization problems. We formulate the selection problem of the VEGA using the optimal computing budget allocation approach, and derive the asymptotically optimal allocation rule and an easily implementable approximated allocation rule. The efficiency of the propose simulation budget allocation rules is demonstrated via comparing with some existing allocation rules. Furthermore, the proposed allocation rule is integrated with the VEGA to solve the multi-objective simulation optimization problems. The numerical experiments on the benchmarking test problems indicate that the proposed allocation rule can improve the search efficiency of the VEGA in stochastic environment by reducing the average distance towards the true Pareto front and improving the purity of the estimated Pareto front.

Technical Note—Bootstrap-based Budget Allocation for Nested Simulation

Nested simulation (also referred to as two-level simulation) finds a variety of applications such as financial risk measurement, and a central issue of nested simulation is how to allocate a finite amount of simulation budget to achieve the highest accuracy. In “Bootstrap-based Budget Allocation for Nested Simulation”, Zhang, Liu, and Wang propose a bootstrap-based rule for simulation budget allocation for nested simulation. By utilizing the asymptotically optimal inner- and outer-level sample sizes that are typically unknown, the proposed method employs bootstrap sampling on a small amount of initial samples to estimate the unknown optimal sample sizes, thus providing a reasonably good allocation rule for the main simulation. An allocation rule to ensure the asymptotic validity of confidence intervals is also given.

A Study on Efficient Computing Budget Allocation for a Two-Stage Problem

We consider how to allocate simulation budget to estimate the risk measure of a system in a two-stage simulation optimization problem. In this problem, the first stage simulation generates scenarios that serve as inputs to the second stage simulation. For each sampled first stage scenario, the second stage procedure solves a simulation optimization problem by evaluating a number of decisions and selecting the optimal decision for the scenario. It also provides the estimated performance of the system over all sampled first stage scenarios to estimate the system’s reliability or risk measure, which is defined as the probability of the system’s performance exceeding a given threshold under various scenarios. Usually, such a two-stage procedure is very computationally expensive. To address this challenge, we propose a simulation budget allocation procedure to improve the computational efficiency for two-stage simulation optimization. After generating first stage scenarios, a sequential allocation procedure selects the scenario to simulate, followed by an optimal computing budget allocation scheme that determines the decision to simulate in the second stage simulation. Numerical experiments show that the proposed procedure significantly improves the efficiency of the two-stage simulation optimization for estimating system’s reliability.

Ranking and selection for terminating simulation under sequential sampling

This research develops an efficient ranking and selection procedure to select the best design for terminating simulation under sequential sampling. This approach enables us to obtain an accurate estimate of the mean performance at a particular point using regression in the case of a terminating simulation. The sequential sampling constraint is imposed to fully utilize the information along the simulation replication. The asymptotically optimal simulation budget allocation among all designs is derived concurrently with the optimal simulation run length and optimal number of simulation groups for each design. To implement the simulation budget allocation rule with a fixed finite simulation budget, a heuristic sequential simulation procedure is suggested with the objective of maximizing the probability of correct selection. Numerical experiments confirm the efficiency of the procedure relative to extant approaches.

An extended Two-Stage Sequential Optimization approach: Properties and performance

This paper looks into nonlinear non convex stochastic unconstrained optimization with finite simulation budget. Our work builds upon the Two-Stage Sequential Optimization (TSSO) algorithm that addresses the class of problems of interest by using the modified nugget effect kriging (MNEK) meta-model and proposing a budget allocation followed by a two-stage sequential procedure. Despite its efficiency and performance, we have observed that, given a finite budget, the choice of the number of replications per iteration, currently left to the user, is particularly critical for the algorithm performance. A fixed a-priori assignment can affect the ability to control the algorithm making it particularly sensitive to the initial settings. In this paper, we propose the extended TSSO (eTSSO). Specifically, a general simulation budget allocation scheme is proposed with the objective to balance the need of accurate function estimations to improve the selection in the search stage, with the need to explore the solution space. The new scheme adaptively, and recursively, increases the simulation budget based upon information iteratively returned by the optimizer itself. We analyze the asymptotic properties of eTSSO. Subsequently, we propose four alternative variants of the general allocation that we empirically analyze by comparing the quality of the estimated optimum input combination and the corresponding estimated optimum output against TSSO and other state of the art algorithms.

Efficient Simulation Budget Allocation With Bound Information

This paper proposes a bound-based simulation budget allocation (BSBA) procedure for solving ranking and selection (R&S) problems in simulation optimization. For many practical applications, strict bounds on system performances can be obtained through empirical and theoretical approaches. These bounds provide additional information which may help solve R&S problems. In this paper, a new method of objective function estimation is proposed using both bound information and simulation outputs. This new estimation method is demonstrated to be particularly effective. To solve R&S problems, several asymptotic optimal allocation rules are also derived. Using these allocation rules, a BSBA procedure is proposed to achieve high efficiency in identifying the best design. Numerical experiments are provided to examine the performance of the proposed BSBA procedure. The computational results show that BSBA outperforms three compared allocation procedures, especially when bounds are tight or the simulation budget is small.

Enhancing the Noise Robustness of the Optimal Computing Budget Allocation Approach

Since an optimal computing budget allocation (OCBA) approach maximizes the efficiency of the simulation budget allocation to correctly find the optimal solutions, various OCBA-based procedures, such as OCBA, OCBAm+, and MOCBA+, have been widely applied to solve simulation-based optimization problems. Recently, it has been found that the stochastic noise in a simulation model increases due to the increasing complexity of modern industrial systems. However, the OCBA approach may be inefficient for these practical problems. That is, it is very likely to waste a lot of budget on other candidates that are not truly optimal due to the abnormal simulation results, which occurs frequently in noisy environments. In this paper, we intuitively analyze the causes of this efficiency deterioration of the OCBA approach, and then a simple heuristic adjustment is proposed to enhance the noise robustness of the OCBA approach based on our analysis results. The proposed adjustment allows the OCBA approach to further consider the precision of the simulation results, thereby significantly reducing the wasted budget and increasing the efficiently. In addition, it can be applied to the existing allocation rules without modification and does not require additional computational costs. Many experimental results for the eight OCBA-based procedures clearly demonstrate the effectiveness of this adjustment. In particular, the results of practical problems emphasize its necessity.

A Simulation Budget Allocation Procedure for Finding Both Extreme Designs Simultaneously in Discrete-Event Simulation

Although discrete-event simulation has been widely used in various engineering fields, its efficiency remains an issue. Ranking and selection (R&S) procedures can solve this efficiency problem by allocating a limited simulation budget intelligently. While the existing R&S procedures mostly aim to find only the best simulation input design, practitioners sometimes require the worst design as well to analyze systems requiring high reliability, such as military systems, municipal waste management, etc. Motivated by these practical needs, we propose a simulation budget allocation procedure for selecting both extreme designs simultaneously in the presence of large stochastic noise. To maximize the accuracy of the selections under a limited budget, the proposed procedure sequentially allocates a small budget and updates the simulation results such that they can be used as significant evidence for the correct selections. Our experimental results on benchmark and practical problems demonstrate improved efficiency compared to previous works. It is expected that the proposed procedure will be effectively utilized in the fields of the fourth industrial revolution, such as digital twins that demand quickly finding both extreme designs to maintain synchronization with the corresponding real systems.

Outpatient appointment scheduling problem considering patient selection behavior: data modeling and simulation optimization

In medical outpatient services, due to patients’ imbalanced selection for doctors of different levels and for different visiting periods, inefficiency of resource utilization and dissatisfaction of patients have become the main problems faced by hospital managers. For the first time, this research has considered patients’ preference between high-ranking professional titles of general doctor and expert doctor. Through analyzing real data of the outpatient clinic at Dalian City Dermatology Hospital, the behavioral pattern of patients’ patience limit adjusted with expected waiting time was obtained. This research also established a data-driven discrete event simulation model that takes into account walk-in patients’ time preferences, appointment patients’ no-shows and cancellations, and considers complex patient flow caused by unbalanced selection of doctor resources and patience limit of waiting time. To optimize scheduling for appointment patients with two types of doctors, this research put forward a simulation optimization framework that maximized hospital benefit and minimized patients’ dissatisfaction. At the same time, simulation budget allocation based on multi-objective optimization and genetic algorithm were combined to obtain the approximate Pareto joint capacity plan of multi-servers and a patient scheduling scheme. The simulation model was validated through a case study based on real data of outpatient service for the whole year, and the proposed optimization method can comprehensively improve performance of outpatient service scheduling system. The simulation optimization framework can provide an effective scheduling scheme for all multi-server service systems involving consumer selection and impatient behavior.

Optimal computing budget allocation for complete ranking with input uncertainty

Existing research in ranking and selection has focused on the problem of selecting the best design, subset selection and selecting the set of Pareto designs. Few works have addressed the problem of complete ranking. In this research, we consider the problem of ranking all alternatives completely with consideration of input uncertainty. Given a fixed simulation budget, we aim to maximize the probability of correct ranking among all designs based on their worst-case performances. The problem is formulated as an optimal computing budget allocation model. To make this optimization problem computationally tractable, we develop an approximated probability of correct ranking and derive the asymptotic optimality condition based on it. A sequential ranking procedure is then suggested to implement the proposed simulation budget allocation rule. The high efficiency of the proposed simulation procedure is demonstrated via a set of numerical experiments. In addition, useful insights and analysis on characterizing the optimality condition and implementing the efficient budget allocation rule are provided.

A new medical staff allocation via simulation optimisation for an emergency department in Hong Kong

Whether triage targets can be achieved has been an imperative assessment of service qualities for an emergency department in healthcare management. In this research, we focus on triage targets and try to fully meet the target of fast emergency response for critical patients subject to triage requirements for other category patients by optimising the medical staff allocation in the emergency department. Main challenges stem from multiple stochastic constraints and the time-consuming simulation. To solve the stochastically constrained discrete optimisation via simulation problem, we develop a discrete-event simulation model and propose a simulated-annealing-based algorithm called ConSA that adopts a special searching mechanism and an efficient simulation budget allocation rule to find a high-quality configuration of medical staff. A case study based on the data from a public hospital in Hong Kong is carried out. Numerical experiments demonstrate that our algorithm leads to a 38.28% improvement in the main performance compared to the current staff allocation and dominates other algorithms in terms of computational efficiency and output accuracy. It indicates that our method is a good decision tool for hospital managers.

Optimal Computing Budget Allocation for Stochastic N–$k$ Problem in the Power Grid System

The $N$ − $k$ problem is very well known in the power industry and it tries to answer the question whether there exists a set of $k$ lines in a power network with $N$ elements whose removal would cause the failure of the system. In practice, it is common to evaluate a system according to an $N$ −1 criterion, i.e., $k = 1$ . While this problem has traditionally been considered in a deterministic setting, stochastic behavior within the system is important especially in the context of extreme events. A number of stochastic Monte Carlo models have been proposed to estimate the probability of cascading failures. In this paper, we deal with simulation budget allocation of the stochastic $N$ –1 problem. More specifically, we assume that a simulation model is able to provide us an estimate of the system failure rate when any line is tripped. It is not difficult to see how simulation of all configurations to some certain accuracy can become computationally expensive with the growth of $N$ . Under such a setting, we transform the $N$ –1 problem into a stochastic selection process with optimal computing budget allocation (OCBA): given $N$ configurations, we would like to sequentially allocate a certain number of simulation replications in order to answer the question whether the system is reliable or not. We show through theoretical analysis and numerical experiments that the probability of correctly identifying the system reliability state can be increased by applying OCBA allocation rules in the simulation budget allocation process.

Adaptive simulation budget allocation in Simulation assisted Differential Evolution algorithm

Recently, the literature on simulation assisted optimization for solving stochastic optimization problems has been considerably growing. In the optimization context, the population based meta-heuristics algorithms, such as, Differential Evolutionary (DE), has shown tremendous success in solving continuous optimization problems. While in the simulation context, Monte-Carlo Simulation for sample average approximation is one of the successful approaches in handling the stochastic parameters of such problems. However, the intertwined computational burden, when combining these two approaches is amplified, and that encourages new research in this topic. In this problem, the challenge is to maintain high quality stochastic solutions by minimizing the computational cost to a reasonable level. To deal with this challenge, we propose a novel Adaptive Segment Based Scheme (ASBS) algorithm, for allocating the MCS budget in a Simulation assisted Differential Evolution (Sim-DE) Algorithm. This allows the algorithm to adaptively control the simulation budget based on a performance measure. The performance of the proposed ASBS algorithm is compared with other simulation budget allocation techniques while using the same base algorithm. The experimental study has been conducted by solving a modified set of IEEE-CEC’2006 test problems and a wind-thermal power systems application. The experimental results reveal that the ASBS algorithm is able to substantially reduce the simulation budget, with an insignificant effect in solution quality.

Efficient simulation budget allocation for subset selection using regression metamodels

This research considers the ranking and selection (R&S) problem of selecting the optimal subset from a finite set of alternative designs. Given the total simulation budget constraint, we aim to maximize the probability of correctly selecting the top-m designs. In order to improve the selection efficiency, we incorporate the information from across the domain into regression metamodels. In this research, we assume that the mean performance of each design is approximately quadratic. To achieve a better fit of this model, we divide the solution space into adjacent partitions such that the quadratic assumption can be satisfied within each partition. Using the large deviation theory, we propose an approximately optimal simulation budget allocation rule in the presence of partitioned domains. Numerical experiments demonstrate that our approach can enhance the simulation efficiency significantly.