Continuous optimization via simulation using Golden Region search

Simulation Optimization (SO) is the use of mathematical optimization techniques in which the objective function (and/or constraints) could only be numerically evaluated through simulation. Many of the proposed SO methods in the literature are rooted in or originally developed for deterministic optimization problems with available objective function. We argue that since evaluating the objective function in SO requires a simulation run which is more computationally costly than evaluating an available closed form function, SO methods should be more conservative and careful in proposing new candidate solutions for objective function evaluation. Based on this principle, a new SO approach called Golden Region (GR) search is developed for continuous problems. GR divides the feasible region into a number of (sub) regions and selects one region in each iteration for further search based on the quality and distribution of simulated points in the feasible region and the result of scanning the response surface through a metamodel. The experiments show the GR method is efficient compared to three well-established approaches in the literature. We also prove the convergence in probability to global optimum for a large class of random search methods in general and GR in particular

Optimal computing budget allocation for constrained optimization

Ph.DDOCTOR OF PHILOSOPH

Evaluation and Design of Supply Chain Operations using DEA

Performance evaluation has been one of the most critical components in management. As production systems nowadays consist of a growing number of integrated and interacting processes, the interrelationship and dynamic among processes have create a major challenge in measuring system and process performance. Meanwhile, rapid information obsolescence has become a commonplace in today’s high-velocity environment. Managers therefore need to make process design decisions based on incomplete information regarding the future market. This thesis studies the above problems in the evaluation and design of complex production systems. Based on the widely used Data Envelopment Analysis models, we develop a generalized methodology to evaluate the dynamic efficiency of production networks. Our method evaluates both the supply network and its constituent firms in a systematic way. The evaluation result can help identify inefficiency in the network, which is important information for improving the network performance. Part II of the thesis covers multi-criteria process design methods developed for situations of different information availability. Our design approaches combine interdisciplinary techniques to facilitate efficient decision-making in situations with limited information and high uncertainty. As an illustration, we apply these approaches to project selection and resource allocation problems in a supply chain

FINDING THE BEST IN THE PRESENCE OF A STOCHASTIC CONSTRAINT

Our problem is that of finding the best system—i.e., the system with the largest or smallest primary performance measure—among a finite number of simulated systems in the presence of a stochastic constraint on a secondary performance measure. In order to solve this problem, we first find a set that contains only feasible or near-feasible systems (Phase I) and then choose the best among those systems in the set (Phase II). We present a statistically valid procedure for Phase I and then propose another procedure that performs Phases I and II sequentially to find the best feasible system. Finally, we provide some experimental results for the second procedure.