A general framework on the simulation-based optimization under fixed computing budget

In many real world problems, the design space is huge and the estimation of performance measure has to rely on simulation which is time-consuming. Hence, to find the optimal design in the design space based on the simulation output is not trivial. It is important to have a computing time allocation rule to decide how much effort to spend in sampling the design space, how many designs to sample, and how long to run for each design alternative within a given computing budget. In this paper, we propose a framework for making these allocation decisions. We use the problem of assemble-to-order (ATO) systems to demonstrate how this framework can be applied. The sample average approximation (SAA) method is chosen as the sampling method used in this application example. The numerical results show that this framework provides a good basis for allocation decisions.

[1]  Mark S. Hillier.  Component commonality in multiple-period, assemble-to-order systems , 2000 .

[2]  Xiaolan Xie.  Dynamics and convergence rate of ordinal comparison of stochastic discrete-event systems , 1997, IEEE Trans. Autom. Control..

[3]  Barry L. Nelson,et al.  A fully sequential procedure for indifference-zone selection in simulation , 2001, TOMC.

[4]  Chun-Hung Chen,et al.  New development of optimal computing budget allocation for discrete event simulation , 1997, WSC '97.

[5]  Chun-Hung Chen,et al.  Computing efforts allocation for ordinal optimization and discrete event simulation , 2000, IEEE Trans. Autom. Control..

[6]  Y. Rinott.  On two-stage selection procedures and related probability-inequalities , 1978 .

[7]  Mahmoud H. Alrefaei,et al.  Selecting the best stochastic system for large scale problems in DEDS , 2004, Math. Comput. Simul..

[8]  Loo Hay Lee,et al.  A new approach to discrete stochastic optimization problems , 2006, Eur. J. Oper. Res..

[9]  Chun-Hung Chen,et al.  Simulation Budget Allocation for Further Enhancing the Efficiency of Ordinal Optimization , 2000, Discret. Event Dyn. Syst..

[10]  Stephen E. Chick,et al.  New Two-Stage and Sequential Procedures for Selecting the Best Simulated System , 2001, Oper. Res..

[11]  M. J. Rosenblatt,et al.  Component commonality effects on inventory costs , 1996 .

[12]  M. Magazine,et al.  Component Commonality with Service Level Requirements , 1988 .

[13]  K. R. Baker,et al.  The Effect of Commonality on Safety Stock in a Simple Inventory Model , 1986 .

[14]  W. David Kelton,et al.  Sequential selection procedures: Using sample means to improve efficiency , 2005, Eur. J. Oper. Res..

[15]  Susan H. Xu,et al.  Joint Inventory Replenishment and Component Allocation Optimization in an Assemble-to-Order System , 2004, Manag. Sci..

[16]  Chun-Hung Chen,et al.  A gradient approach for smartly allocating computing budget for discrete event simulation , 1996, Winter Simulation Conference.

[17]  Ek Peng Chew,et al.  A simulation study on sampling and selecting under fixed computing budget , 2003, Proceedings of the 2003 Winter Simulation Conference, 2003..

[18]  David H. Wolpert,et al.  No free lunch theorems for optimization , 1997, IEEE Trans. Evol. Comput..

[19]  R. Caflisch.  Monte Carlo and quasi-Monte Carlo methods , 1998, Acta Numerica.

[20]  Alexander Shapiro,et al.  Monte Carlo simulation approach to stochastic programming , 2001, Proceeding of the 2001 Winter Simulation Conference (Cat. No.01CH37304).

[21]  Barry L. Nelson,et al.  Ranking and Selection for Steady-State Simulation: Procedures and Perspectives , 2002, INFORMS J. Comput..

[22]  Yigal Gerchak,et al.  Component commonality in assemble-to-order systems: Models and properties , 1989 .

[23]  Leyuan Shi,et al.  Nested Partitions Method for Global Optimization , 2000, Oper. Res..

[24]  Enver Yücesan,et al.  Discrete-event simulation optimization using ranking, selection, and multiple comparison procedures: A survey , 2003, TOMC.

[25]  Stephen E. Chick.  Selecting the best system: a decision-theoretic approach , 1997, WSC '97.

[26]  Alexander Shapiro,et al.  The Sample Average Approximation Method for Stochastic Discrete Optimization , 2002, SIAM J. Optim..

[27]  YücesanEnver,et al.  Discrete-event simulation optimization using ranking, selection, and multiple comparison procedures , 2003 .

[28]  Loo Hay Lee,et al.  Explanation of goal softening in ordinal optimization , 1999, IEEE Trans. Autom. Control..

[29]  Chun-Hung Chen,et al.  Optimal computing budget allocation for Monte Carlo simulation with application to product design , 2003, Simul. Model. Pract. Theory.

[30]  Yigal Gerchak,et al.  An inventory model with component commonality , 1986 .

[31]  S. Tayur.  Computing Optimal Stock Levels for Common Components in an Assembly System , 1994 .

[32]  Julie L. Swann,et al.  Simple Procedures for Selecting the Best Simulated System When the Number of Alternatives is Large , 2001, Oper. Res..

[33]  Yu-Chi Ho,et al.  Ordinal optimization of DEDS , 1992, Discret. Event Dyn. Syst..

[34]  P. Camerini,et al.  Review of recent development: The matroidal knapsack: A class of (often) well-solvable problems , 1984 .

[35]  Barry L. Nelson,et al.  Selecting the best system: theory and methods , 2003, Proceedings of the 2003 Winter Simulation Conference, 2003..

[36]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[37]  Mark S. Hillier.  COMPONENT COMMONALITY IN A MULTIPLE-PERIOD INVENTORY MODEL WITH SERVICE LEVEL CONSTRAINTS , 1999 .

[38]  L. Dai.  Convergence properties of ordinal comparison in the simulation of discrete event dynamic systems , 1995 .

[39]  Barry L. Nelson,et al.  Ranking, selection and multiple comparisons in computer simulation , 1994, Proceedings of Winter Simulation Conference.

[40]  Chun-Hung Chen,et al.  Computing budget allocation for simulation experiments with different system structures , 1998, 1998 Winter Simulation Conference. Proceedings (Cat. No.98CH36274).