The alternative procedure of lot size determination in flexible manufacturing systems.

Vazan, Pavel ; Moravcik, Oliver

Abstract: The paper presents the way how to use simulation optimization for determination of lot size in FMS. It provides the basic methods and procedures. The simulation optimization can be alternative procedure to classic analytical methods. This procedure involves more factors that influence lot size, than analytical methods. Therefore it is more accurate.

Key words: Batch production, lot size, simulation, simulation optimization

1. INTRODUCTION

The lot size is the number of pieces which is processed at the same time at one workplace with one-off (time) and at the same costs investment for its set up. (Tomek, 1999) The lot size is one of the directions of production which markedly influences production costs. There are several known methods for determination of lot size in the world. Many of them have attribute "optimal" directly in their name but the problem of correct lot size determination remains the problem. The authors will demonstrate the possibility of usage of simulation optimization for calculation of lot size.

2. STATE-OF-THE-ART

There are mainly used analytical methods for determination of lot size. These methods try to express lot size by mathematical relation in dependence on time used to set up workplace and piece of time, for example the method of so called capacitance of lot size. The lot size, so called economically optimal lot size is often used. This lot size is expressed by mathematical model. The solution of compromise between the reduction of fixed costs per piece and increasing of lot size and on the other side increasing of the storage costs (Gregor, 2000).

The other methods are based on empirically found variables with many defects. There are used different approaches, e.g. optimal lot size is defined in many possibilities and chosen is the one with its own minimal costs. There is included e.g. optimal lot size according to Teplov or Bankovsky (Gregor, 2000).

Management attempts to set up the same lot size in the same planning periods. The lot size is calculated as a part of annual capacity suitable for relevant planning period. This is a simple principle of periodical lot size.

In spite of the fact that classic calculation methods of lot size have optimal size in their title, they usually consider only few factors which influence lot size. That is why the attribute "optimal" is applied only for strictly defined conditions. The necessary input values set up costs or storage costs are in fact qualified approximations but not exact values. These calculated optimal lot size are at least approached to optimal values (Potoradi,1999).

Lot size is also influenced by other factors not only by considered classic methods of calculation. Here belong: production type, orientation of material flow, system flexibility, organization of manufacturing process etc. Of course, these factors do not include analytical methods (Habchi, 1995). During the determination of lot size it is necessary to take into consideration also conceptions which are used in planning and control of production. Systems coming out from MRP expect constant lot size through the production process. Conceptions coming out from JIT philosophy consider lot size as one piece in ideal case (Khan, 2002). But systems using OPT accept changeable lot size.

Contemporary approaches of determination of lot size are focused on mathematical models that minimize costs. Such approach is used for determination of so called Economic Manufacturing Quantity. The reason of high costs is not solved. Many authors accept that the best method to verify optimal lot size is simulation way (Gregor, 2000, Habchi, 1995) Potoradi, 1999, Ramaswami, 2006). Software tools for simulation model design of production system reached such level of development that the simulation model design lasts few days. The simulation models of production system have high accuracy and they allow to test the behaviour of production system for chosen lot size. It is possible by the simulation way to follow many factors that influence correct lot size. The results of simulation experiments may totally follow the chosen production goals. These goals are not only costs but also flow times, work in process, usage of capacities, number of produced parts etc. The simulation connected with simulation optimization may be appropriate method for determination of optimal lot size in dynamically changeable conditions of flexible manufacturing systems.

3. DESIGN OF SOLVING PROCEDURE

3.1 Methods

The authors propose to use the simulation optimization for determination of lot size in production systems. The existence of the simulation model is necessary assumption for the usage of the simulation optimization. It means that simulation model of FMS have to be created. The most appropriate simulation method is the discrete-event simulation for manufacturing model building. Rapid expansion of simulation tools for manufacturing allowed the usage of this procedure very effectively. The model building takes a short time and the model is very detailed. The authors use the Witness simulator.

Simulation optimization is defined as optimization of outputs from simulation experiments. It is based on optimization of outputs from discrete event simulation models (Fu, 2001).

Simulation optimization provides a structured approach to determine optimal input parameter values, where optimal is measured by a function of output variables associated with a simulation model. (Swisher, 2000)

The simulation optimization problem is defined as well as ordinary optimization problem by primary methods. (Fu. 2001):

* input and output variables;

* objective function;

* constraints.

[FIGURE 1 OMITTED]

The value of objective function cannot be evaluated directly but it must be estimated as output from simulation run. It means that optimization via simulation is computationally very expensive. On the other side the definition of objective function is very simple without complicated mathematical formula.

The computational cost of simulation optimization causes that the practical usage of simulation optimization without software support is impossible. The software packages are solved as plug-in modules which are added in the basic simulation platform. The approach to simulation optimization is based on viewing the simulation model as a black box function evaluator. Figure 1 shows this black-box approach to simulation optimization. The optimizer chooses a set of values for the input parameters and uses the responses generated by the simulation model to make decisions regarding the selection of the next trial solution.

3.2. Procedure

The critical step of solving was the definition of objective function. As it was mentioned, the lot size is influenced by more factors not only by costs. The authors in the process of definition of objective function went out of production goals. There were also included number of finished parts, machine utilization and flow time in objective function besides of the costs which represents the important goals of production. The function for cost calculation involved not only the set up costs and storage costs but also operation costs and transport costs. The objective function calculates costs per unit.

All variables and functions are set and calculated in elements of FMS in simulation model. Partial values of objective function are always calculated when specific element of FMS is finishing its activity. Total cost sum is calculated at the same time.

Discrete-event simulation allows this process. The objective function can be defined in a simple way and it does not need to contain input values. Its final value is given as a result of simulation run.

Selection of inputs parameters is realized by optimizing module. The right values of input variables also have to be connected. It is very important to constrain the input parameters meaningfully. We recommend the constraints of input parameters to set up through special designed preparatory simulation experiments.

The algorithm selection is a very important step for simulation optimization usage. The software tools give more algorithms. These algorithms do not need to search all set of possible combinations but they have to find the global extreme of objective function. Here arises a question if these algorithms do not find only local extreme. It is typical for Hill climb algorithm.

The selection of algorithm has to respect mainly two basic factors:

* what data will include individual sets of variables;

* time of optimization process.

4. ADVANTAGES AND DISADVANTAGES

The simulation optimization is more accurate method for determination of lot size than the classic methods because it is able to respect much more number of factors which influence lot size. But it also requires the existence of simulation model. On the other side the simulation model allows research in the detail way the real manufacturing process. Classic methods are fast and simple. Simulation optimization can take long time according to the restriction of the possible solving combinations. The length of duration seems as the greatest problem of simulation optimization usage. Simulation optimization is definitely proper method for accurate method for determination of lot sizes, especially for FMS where the set up time is markedly reduced.

5. CONCLUSION

There are more areas where simulation optimization would be used. Of course the choice of the procedure for usage in simulation optimization depends on the analyst and the solved problem. The simplicity and good software aid appear as strong assumptions for real using of simulation optimization. We are planning for the next step of our research to realize extensive study. This study will compare proposed procedure with classic methods for determination of lot size in FMS.

6. REFERENCES

Fu C. M. (2001) Simulation Optimization In: Peters B.A., Smith J.S., Medeiros D.J., Rohrer m.W.:Proceedings of the 2001 Winter Simulation Conference. Arlington, USA, pp. 55-61

Gregor, M., Kosturiak, J., Mieieta, B., Bubenik, P., Ruzieka, J. (2000) Dynamicke planovanie a riadenie vyroby, KPI-ZU EDIS, pp. 179-212.

Habchi G.1; Labrune C. (1995) Study of lot sizes on job shop systems performance using simulation. In Simulation Practice and Theory, Volume 2, Number 6, 15 May 1995, pp. 277-289, Springer.

Khan L. R., Sarker R.A. (2002) An optimal batch size for a JIT manufacturing system. In Computers and Industrial Engineering Volume 42, Issue 2-4 26th International conference on computers and industrial engineering, pp. 127-136, ISSN:0360-8352

Potoradi, J.;(1999) Determining optimal lot-size for a semiconductor back-end factory In Proceedings of the 1999 Winter Simulation Conference Volume 1, pp. 720-726

Ramaswamy K.V.(2006) Optimal lot sizing in manufacturing revisited. In: Journal of Information and Optimization Sciences. Vol. 27, 2006 no.1 pp 97-105

Swisher J.R., Jacobson S.H., Hyden P.D., Schruben L.W. (2000) A survey of simulation optimization techniques and procedures. In Joines J.A., Barton R.R., Kang K., Fishwick, P.A.,: Proceedings of the 2000 Winter Simulation Conference. Orlando, USA, pp. 119-128

TOMEK, G.--VAVROVA, V., (1999) Oizeni vyroby. Praha: Grada publishing, 1999. ISBN 80-7169-578-5