Route Planning for Two Wafer Fabs with Capacity-Sharing Mechanisms - Essay Example

Route planning for two wafer fabs with capa sharing mechanisms Journal International Journal of Production Research Volume: 47 Year: 2009 Course Title: Instructor Name: Name: Date of submission: Introduction The industrial sector dealing with the manufacture of semiconductor materials must take into consideration some two very fundamental factors anytime they may have a desire to expand the capacity of their manufacturing plants. These factors are: 1. The cost of equipment is quite high probably about an estimated value of one billion dollars per every 12 inch of water fab. 2. The lead time for acquisition of equipment this is quite long and ranges between 3 and 9 months. However, to solve this problem and take care of the ever rising demand for the semi conductors in the manufacturing industry, the company may consider expanding its plant and thus adopting a dual fab strategy. Avont & Wassenhove, (1988) argue that this would involve a factory space in large scale that is able to hold two fabs and one condition that must be met; it is a must that this space be established in advance. The equipment that is required for the two fabs is then moved into the space over a given period of time. This movement is dependent on the market demand. A dual fab of this nature the most appropriate approach is running each fab separately and this will lead to underutilisation of equipment available and to solve this problem, a cross fab production paradigm for production and this should give a problem that gives a route. Toba et al (2005) proposed a real time solution for this problem. Motivation This research arises from the increasing demand for semi conductor materials in the manufacturing industry. In order to fill this gap, there is needed to come up with a system that allows for full utilization of the available space and equipment. Problem definition To define the problem at hand, we have to define the two available fabs as fab_A and fab_B. The following assumptions will be made to define the problem. 1. Each of the fabs is equipped in a comprehensive way and it is capable of handling the manufacture of the semi conductors by itself and does not require any input from other fabs. 2. Each product has at least four available routes of production. These routes are divided into two sections whereby the cutoff point of the routes exists. These two routes can be manufactured in two different fabs and this results into two possible routes for use in cross fab production. One of the routes is represented by and this means that the first part of the route is manufactured at fab_A and the second part is manufactured at fab_B. The other part denotes the first part of the route being manufactured at fab_B while the second part of the route being manufactured at fab_A. We are thus left with the four routes which are: and. 3. The path of transport that is available between any two stations is very unique. To reduce the complexity of controlling the traffic, we must define a fixed path. If we let the cutoff point and route and the route ratios of the product I be represented by. If we define as a set of cut off points and. The route planning problem will then be given by. Background concepts Before we get into the proposed model structure, it is important to understand some of the important concepts that will recur in this approach. 1. Operations management: This refers to the administration of all activities in the function of the production system. 2. Cross fab route: This refers to the path followed by each module during the process of implementing the algorithms. 3. Operations strategy: This is the chosen mode of carrying out all the activities involved in production of semi conductors. 4. LP-GA method: This refers to a combination of linear programming and genetic algorithm when implementing the proposed algorithm. 5. Operations planning: This is the strategy put into place so as to ensure that all the processes are running in an efficient way. Model A model proposed by Binh & Lan (2007), has the framework for the route planning of the two wafer fabs with capacity-sharing mechanisms is designed as below: Figure 1: Diagram showing the solution framework (courtesy of International Journal of Production Research) query According to Binh & Lan (2007, Module 1 deals with the static capacity allocation whereby each path of transportation is assumed to be equipped with infinite capacity and the time of transportation between any two available workstations is zero. We must find the optimum value of. To solve this problem, we must use an iterate use of a linear program model. To find the optimum, we must use a binary search algorithm. Module 2 is used to find the time phase’s capacity allocation. Having determined the value of *, we must handle the variables. There are two sub models that exist. The first sub model develops a performance evaluation for a particular. The second sub model searches for R* so that we have the best performance. To solve this se use a genetic algorithm. The solution for the dual fab route planning problem is given as: Module 1: Linear programming model and the search algorithm The LP model uses an iterative linear programming program (Karabuk & Wu, 2003). It computes a minimum number of cross fab transportations for a particular value of The objective is illustrated as (. This equation describes dependent relationships. The next equation below ensures that we use n capacity in each workstation This function minimizes the number of cross fab production lots. Bisection search algorithm This algorithm finds the optimal solution. Initialization Take the whole values of each product ϒ segment. For i=1 to N On the ϒ segment create 2 cut off points on each of the available products Solve the linear program to find the Compute the ϒ segment for the available products based on the value of End for Output cut off points for the products Module 2 for the genetic algorithm Figure 2: Iterative points on the genetic algorithm (courtesy of International Journal of Production Research) Given the target cycle and the and cut off point decision. We therefore find the optimal route ratio decision in order to maximize the total throughout the 2 fabs. The solution for this problem is given by: Query network According to Chiang, et al, 2007 the input output function of the output model is given by In order to determine the objective function of the model, we are going to use the bisection search technique to compute the total throughput The genetic algorithm The genetic algorithm identifies the optimal solution from a space denoted by {R}. Step 1: Initialisation t=0 , state=’not terminate’ Randomly generate, Np valid chromosomes for a population P0 Step 2: genetic search While (status=’not terminate’) do Use cross over operator to create Nc new chromosome Use mutation operator to create Nm new chromosome Form a pool by taking the union of Pt t=t+1 and select the best Np chromosome for the pool to form Pt Check the terminate condition and if met set status =’terminate’ End while Step 3 The cross over operation creates two new chromosomes from two existing ones. According to Bin & Lan 2007, we can use one of the available gene segments to create and this yields chromosomes. In the mutation operation any new chromosome is created by an existing chromosome with a given segment i*. Then . This yields chromosomes Results In order to determine the effectiveness of the method proposed above, we are going to use an LP-GA approach. In order to achieve this we are going to compare the three methods in different circumstances of operation using two different product mixes RA and RB. RA=(3:2:5) and RB=(5:4:1) Table 1: comparison for the three products Product 1 Product 2 Product 3 Total number of steps 172 172 150 RA 85th step 85th step 129th step RB 84th step 84th step 78th step Table 2: comparison of the mean cycle for different algorithms RA=QA(128 slots) RB=QB(169 slots) Algorithm CT(min) Gap (%) CT(min) GAP (%) LP-GA 11080 0 11639 0 M-GA 12175 9.88 12811 10.06 N-GA 12463 12.48 14075 20.9 Table 3: Comparison of the mean cycle time RA(CT0=11081 m) RB(CT0=11445 m) Algorithm Throughout Gap (%) Throughout GAP (%) LP-GA 128 0 169 0 M-GA 125 2.34 165 2.37 N-GA 124 3.12 161 4.13 Table 4: Comparison of the two modules performance Route ratio Module 1(s) Module 2(s) RA 3.5 95.578 RB 4.2 103.265 From the results obtained above, it is observed that the LP-GA method performs much better than the other methods used as the benchmark for the comparison. Conclusion The research paper focuses on the implementation of a dual fab system for semiconductors. Each of the final products is manufactured in one of the two fabs. Each product has four routes of production whereby each one of them is defined by a cutoff point. The LP-GA method has been proposed as the most appropriate way of solving this problem. This method has also been tested and its performance compared to other methods and the results supports the method as it performs much better than all the other methods. Through more extensive research, this system can be made more efficient and further improvements can be done on the system. References Avonts, L.H. and Wassenhove, L.N.V., 1988. The part mix and routing mix problem in FMS: a coupling between an LP model and a closed queueing network. International Journal of Production Research, 26 (12), 1891–1902. Binh, Q.D. and Lan, P.N., 2007. Applications of a genetic algorithm to the fuel reload optimization for a research reactor. Applied Mathematics and Computation, 187, 977–988. Chiang, D.,et al., 2007. Optimal supply chain configurations in semiconductor manufacturing. International Journal of Production Research, 45 (3), 631–651. Toba, H.,et al., 2005. Dynamic load balancing among multiple fabrication lines through estimation of minimum inter-operation time. IEEE Transactions on Semiconductor Manufacturing, 18 (1), 202–213. Karabuk, S. and Wu, S.D., 2003. Coordinating strategic capacity planning in the semiconductor industry. Operations Research, 51, 839–849. Read More