ASSESSMENT OF A COMPLEX MACHINE MIX PROBLEM BY INTEGRATED SIMULATION AND AHP MODELING

1. ASSESSMENT OF A COMPLEX MACHINE MIX PROBLEM BY INTEGRATED SIMULATION AND AHP MODELING A. Azadeh, M. Haghnevis and Y. Khodadadegan Department of Industrial Engineering and Research Institute of Energy Management and Planning Faculty of Engineering, University of Tehran

2. Objectives and Features • The objectives : • Introduce an integrated simulation AHP model for modeling • Assessment and improvement of a machine mix problem with complex queue priorities and service times • The unique feature : • Integrated simulation AHP modeling of a production system with complex service times and queue priorities • The integrated simulation AHP approach of this study may be applied for other similar production systems • There is no closed form expression for such situations, as previous studies show no mathematical models exists for machine mix with such complex service times and queue priorities • Introduction of a hybrid simulation AHP approach for alternative analysis. The hybrid approach of this study for such complex settings may be easily extended to other similar production systems • The hybrid approach of this study is applied to actual production system discussed in the next section

3. Introduction • Queuing systems require controlling and maintaining a list of events to determine next occurrences. • Most of queuing problems can be modeled and solved by closed form mathematical methods (Gross & Harris, 1984; Kleinrock, 1975; White, Schmidt and Bennett, 1975; Ross, 1983; Jaiswal, 1968) but in few cases because of severe complexity and variety of constraints does not have closed form expressions. Therefore, computer simulation approach can be used in these rare cases (Shannon, 1975). • Priority queues have been studied since the early days of queuing theory Stidham (2002). The monograph on queues by Cox and Smith (1961) gives a concise summary of the early works. The book by Jaiswal (1986) provides a compendium of known result as of the late `60s. Most of the research until then concerned single-server queues with fixed priorities. Operating under preemptive or nonpreemptive disciplines.

4. Identify a production system with n order types, and complex service and queue disciplines Compare existing system with other alternatives by AHP Verify and validate simulation model Identify a meaningful set of performance measures Develop a simulation model for simulation model The general hybrid simulation AHP model Can be used for different kinds of productions with various orders and complex service and queue priorities (chemical, military and food industries).

5. General Model • The entity (order):determined with that has just received service • The priority : entities which have the same order as the entity being serviced • If the waiting entities have different orders than the entity being serviced, the priority is with the entity with the highest rank • The arriving entities are ranked numerically from 1 to n depending on the priority of the order • To prevent severe waiting times of entities, the maximum time allotted for a particular order type is ta for a = 1,...,n representing the n orders, respectively • If ta is reached, the entity with higher ranking is prepared for production immediately after service completion

6. General Model • The complex service and queue priorities for such systems are defined as: • Orders are classified with respect to their type (The orders are numbered from a= 1 to n) • Orders are then placed in the queue according to the order which is being processed and current positioning of orders in the queue (the services turn over moves clockwise) • Each order type has a limited total production time • Different setup times are required between order type changes

7. a: Order type (Atrib[6]) i: Manufacturing priority (Atrib[8]) Arrival of orders Set priority by Order type a i ..... Set priority by Manufacturing n 5 3 n 1 2 5 3 2 1 2 5 3 2 1 n 3 2 2 n 3 5 2 3 n+2 n 5 5 n+1 n+2 1 2 3 n+2 n n n+3 n n+2 n+1 3 5 3 5 ..... Machine Production time control If total production time is less than ta Production process of existing order is ended and a new order is initiated Customer ..... If a order is continuously produced and total production time is grater than or equal to ta The production priority will be given to the next prioritized order and remove all entitiesto be re-ordered for prioritization in the queue Schematic Diagram

8. Start K Is the priority of a new entity greater than or equal to entity which is being serviced? Adding to entity priority equal to order type number (entity is placed at the end of the queue) • No • Yes Arrangement of entities in a queue with particular length Occupation of a particular machine "i"(save machine number) Implement of production process Expiring the production time Saving the priority and type of produced entity A General Logical Chart

9. A Saving the priority and type of produced entity Is the order type of present entity equal to order type of previous entity? (Is a particular order continuously produced?) Saving new time as production time of the particular entity and saving order type number of new production • no • yes Adding the process time of present entity to length of total production time Expiring of the set up time of production change Production priority will be given to the next prioritized order Is the production time of the entity with particular order type (total production time) greater than determined constraint ta? • yes Expiring of the set up time of production change • no Remove all entities in queue of machine "i" to be re-ordered for prioritization in the queue (transfer to K) Release machine i Collect required information Finish General Logical Chart

10. Attributes and Variables The simulation model was developed by Visual SLAM (Pritsker, Oreilly & LaVal, 1997; Pritsker, 1990; Pritsker, Sigal, & Hammesfahr, 1989).

11. Visual SLAM Network

12. The Case Study • The above phenomena are used as production planning and scheduling of a spray coatings manufacturer. • The manufacturer is capable of producing different spray coatings (from faint color to dark color). • The faintest and darkest colors are ranked one and n, respectively. • There is a set-up time if a new order must be started for any of the machines. • There is no set-up time as long as the same order is prepared by any machines.

13. Arrival of orders a i Set priority by Order type a: Order type (Atrib[6]) i: Manufacturing priority (Atrib[8]) Set priority by Manufacturing Machine Production time control If total production time is less than 600 Production process of existing order is ended and a new order is initiated Customer If a order is continuously produced and total production time is grater than or equal to 600 4 3 4 6 6 6 4 5 3 6 5 3 5 4 6 6 5 4 5 4 5 5 The production priority will be given to the next prioritized order and remove all entitiesto be re-ordered for prioritization in the queue 4 4 3 6 6 5 5 8 8 7 6 6 5 5 5 6 7 8 6 8 5 5 The Case Study ta = 600 a = 3 to 6 n=4 C=15

14. 4 4 4 4 5 6 4 6 4 18 16 16 17 16 16 16 18 16 Machine Machine Example • After passing some of simulation time, below state may be occurred I: In this state if order type of arrival entity was 4 (a=4) then manufacturing priority became 16 (i=16) and if a=5 or 6 then i =17 and 18 sequentially and if order type of arrival entity was 3 (a=3) then manufacturing priority became 19 (i=19) 3+4+4+4+4>16 • Also in below state if order type of arrival entity was 3 (a=3) then manufacturing priority became 19 (i=19). II: • In all state if entities have similar manufacturing priority earlier arrival entity was product.

15. Verification and Validation • Verification: • The movements of entities compared with the movement of orders in the actual production system. • Validation: • The most important performance measure of the production system which is number of completed orders in a two weeks period was selected and verified by the management. • Run for two working weeks and replicated twenty times. • The results compared with 20 random samples of the actual system. • Independent t-test has been used to compare the production system with simulation model with respect to total number of completed orders. • H0: µ1 = µ2 at α = 0.01 level of significance.

16. Results of production planning alternatives • The verified and validated simulation model was used as production planning and scheduling tool to identify the optimum alternatives (lowest set-up and waiting times).

17. AHP rankings • Analytic Hierarchical Process (AHP). • The decision maker models a problem as hierarchy of criteria, sub criteria, and alternatives. After the hierarchy is constricted, the decision maker assesses the importance of each element at each level of the hierarchy. • By generating entries in a pair wise comparison matrix where elements are compared to each other. • For each pair wise, the decision maker typically uses the eigenvector method (EM) to generate a priority vector hat gives the estimated, relative weights of the elements at each level of hierarchy. • Weights across various levels of the hierarchy are then aggregated using the principle of hierarchic composition to produce a weight for each alternative (Chandrana et al, 2005).

18. Value Analysis • By noting value performance = (worth)/ (cost) in context of value engineering • VE (Value engineering) is an organized, creative technique directed at analyzing the functions of a product, service or system with the requirements which comprise its value-such as performance, reliability, maintainability, appearance, etc. • VE is not constrained to produce the same design at least cost but rather to search out methods of achieving a superior product at least cost (Parker 1998 and Shellito 1992). • Low performance alternatives are discarded from further considerations and the results of value analyze analysis shows thesuperiority of alternative "c" over all other alternatives.

19. Conclusion • The bottlenecks and sensitive points of the system are identified. • Sensitivity analysis could be easily performed. • Customer satisfaction may be enhanced due to introduction of an optimum model with lowest set-up and waiting times

20. ASSESSMENT OF A COMPLEX MACHINE MIX PROBLEM BY INTEGRATED SIMULATION AND AHP MODELING A. Azadeh, M. Haghnevis and Y. Khodadadegan Department of Industrial Engineering and Research Institute of Energy Management and Planning Faculty of Engineering, University of Tehran FINISH