Mohammad Behbahani

Abstract

Although a considerable number of problems whose analysis depends on a set of complex mathematical relations exist in the literature due to recent developments in the field of decision making, still very simplified and unrealistic assumptions are involved in many. Simulation is one of the most powerful tools to deal with this kind of problems and enjoys being free of any restricting assumptions which may generally be considered in a stochastic system. In addition, simulation optimization techniques are categorized into two broad classes of model-based and meta-model-based methods. In the first class, simulation and optimization component interact with each other causing an increase in simulation times and costs. To cope with this problem, a third component defined as a meta-model that estimates the relationships between the inputs and outputs of the system being simulated comes to the picture in the second class problems. Besides, optimization of semi-expensive simulation optimization problems needs a numerous simulation run in model-based methods. However, as the validation cost increases at a rapid rate in each iteration of the meta-model-based methods, a new method which consists of two phases has been introduced in the literature to solve semi-expensive simulation optimization problems in less computational time. In the first phase, similar to a model-based algorithm, the simulation output is used directly in the optimization stage. In the second phase, the simulation model is changed with a validated meta-model. In this paper, an artificial neural network is employed as the meta-model in order to compare its performance to the ones of the original algorithm that uses a Kriging meta-model in five popular test problems as well as an (s, S) inventory problem.

Keywords: Semi-expensive simulation problems; Simulation optimization; Meta-model-based algorithm; Artificial neural network

Supervisor:

Seyed Taghi Akhavan Niaki, Ph.D., Distinguished Professor

- Table 1

- The flowchart of the ANN semi-meta-model-based algorithm

- (s, S) the simulation of inventory model is developed in MATLAB!

This functions is based on the (s, S) inventory model Biles et al. (2007) (Biles,W. E.,Kleijnen, J. P., van Beers,W.,VanNieuwenhuyse, I. (2007,December) Kriging metamodeling in constrained simulation optimization: An explorative study. Paper presented at the Proceedings of the 39th conference onWinter simulation, Piscataway, NJ, USA.)

Download the code!

Input: (the size of "small s", the size of "Big S") Output: totalcost of the simulation

The parameters of this (s, S) inventory control model are as follows: (You can change for your problem)
- The holding cost is charged $1 per day per item
- The shortage cost is charged $5 per day per item
- The simulation period is 4,000 days per replicate
- The ordering cost is $32 plus $3 per unit ordered
- The order arrival time follows an exponential distribution with a mean of 6 days
- The inventory position is reviewed at the end of each day
- The customer demand is exponentially distributed with the mean of 90
- The number of units demanded per customer is 1.

Input and Output Example (Article Results):

- input(s,S):[s=741, S=845] --> output(totalcost)=604.58
- in code: [Totalcost]=invmodel([741, 845])

This simulation model is not a semi-expensive model
- In fact the effeciency of the proposed algorithm is shown based on
"The nubmer of Simulation Evaluations"

- download previous version of its article

- download the main file (Thesis)