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Ch Venkatadri Naidu et al. / International Journal of Engineering Science and Technology Vol. 2(6), 2010, 2321-2327 Optimization of Service Operations Sequence in a Four-Wheeler Service Center Ch Venkatadri Naidu1, P Madar Valli2, A V Sita Rama Raju3 Abstract In India, automobile service sector occupies a strategic position in the economic development. Although, sales rate of auto vehicles have been continually and rapidly increasing, a similar growth has not been in the growth of auto service sector leads to customer dissatisfaction. A pilot study has been carried out in a four wheeler service centers and recognizes the need for improve existing process sequence of the service activities those have been fallowed for serviceing the vehicles. This paper proposes improved sequence leading to an optimial sequence which to minimize the total time. The optimal solution was generated as formulating the given problem as a travelling salesman problem (TSP) and solving by employing a novel lexicographic approach. Key words: Service sector, Four-wheeler service center, Optimal sequencing and Lexiserach approach. 1. Introduction The objective of the servicing centre policy could be that it is to arrive at a framework of service operations during the period planned. In general, the major service activities comprise unloading, setups, processes, operations and loading. The major repairs includes Clutch& transmission system, Brake system ,gear box over haul, Suspension system, Wheel Balancing and alignment. Hence, changeover from one service operation to other service operation with minimum total optimum set up time is very important. The sequence of changeover from one operation to another requires some time for preparation. This time is different for different combinations of service operations changeovers. An optimum sequence for change of operations is necessary so that the resulting total changeover time is kept as low as possible. This problem is of practical interest in situations where such changeover time is quite considerable compared to operation time. The situation resembles a TSP, where it is necessary to find an optimal path for a commercial traveler who wishes to visit a set of cities from one city visiting all other cities in the set and return to the starting city at the end such that the total distance travelled or the time taken is minimum. For the design problem of a service line, the vehicle parts to be serviced are analogous to the cities to be visited. The literature reveals that the automobile vehicles sales growth is increasing and expected to grow exponentially in the future. As a result, there is a need to establish and develop service centers to meet the customer demands. Most of the vehicle manufacturers are establishing their service centers in proportion to their sales growth. However, to the author’s knowledge, no scientific studies or methods have been developed on improving the service rate of the existing centers. The questionnaire survey on the Indian auto service sector brings out that there are many issues to be tackled to enhance service rate/delivery of the vehicles. For instance, some of the issues like: (i) optimal allocation of work force for various activities (ii) optimizing the sequence of various models (iii) optimizing the maintenance activities suitably This paper focuses on the issue of studying the various servicing operations involved in a service centre and developing an optimal sequence for it. Taillard (1989) compared the best heuristic method for flow shop sequencing problem and to improve the complexity of the best one. Next applied to this problem taboo search, a new technique to solve optimization problems, and reported computational experiments. Choi and Korkmaz (2002) presented an efficient heuristic procedure that finds a minimum make span for a job shop scheduling with sequence dependent setup times (JSST) problem. Beaty (1995) presented the application of genetic algorithms approaches to different types of sequencing and scheduling problems. Kim et al. (1996) considered the sequencing problem in mixed model assembly lines. A new approach using an artificial intelligence search technique, called genetic algorithm, is used The results show that the algorithm greatly reduces the computation time and, its solution is very close to the optimal solution. Hwang et al. (1997) addressed shop scheduling problem for the side ramp press shop in a truck manufacturing company. In the problem, a set of n jobs is to be scheduled on two machines. To deal flow shop- ISSN: 0975-5462 2321 Ch Venkatadri Naidu et al. / International Journal of Engineering Science and Technology Vol. 2(6), 2010, 2321-2327 sequencing problems Gao and Liu (2007) introduced a novel artificial immune algorithm to efficiently deal with flow shop problems. Hirakawa and Yasuhiro (1999) proposed a quick optimal algorithm for sequencing jobs processed on one machine to minimize total tardiness. The optimal algorithm relies upon the branch-and-bound method applied directly to Lawler's (1977) decomposition theorem and gives an optimal solution. Xiaobo et al. (1997) proposed two algorithms branch-and-bound method and simulated annealing method for finding an optimal or sub-optimal sequence of mixed models that minimizes the total conveyor stoppage time. Shukla et al. (2009) developed a mathematical model for the batch sequencing problem in a multistage supply chain by taking into account three practically important objectives, viz. minimization of lead time, blocking time and due date violation. A meta heuristic, artificial immune system is employed to find an optimal/near optimal solution. Xiaobo and Zhou (1999) dealt with Toyotas goal of sequencing mixed models on an assembly-line with multiple work stations. The sequencing problem with Toyotas goal is formulated. Two algorithms based on different mechanisms, respectively modified goal chasing and simulated annealing, are developed for solving the sequencing problem. Mondal and Sen (2000) developed a new heuristic for the single machine job sequencing problem where the objective is to minimize the weighted sum of quadratic completion times of jobs is introduced Literature presents various approaches presented which needs to develop and formulate a function in terms of variables and also constraints with the same variables. In fact, it is difficult to frame objective functions and constraints for many practice problems. For such problems it is impractible to employe any of the method described in the review.This work is concerned with use of a search technique, lexicographic search approach, for generating an optimal sequence for maintenance activities of a generic service centre. 3. Application of Lexicographic Search Approach The lexicographic search approach, a combinatorial optimization was developed by Pandit in 1962. In the first instance, for the knapsack problem and has since been applied to many other combinatorial programming problems like job scheduling (Gupta, 1976). He has applied this approach for finding an optimal sequence of jobs and schedules them accordingly. In addition to this, it has been applied even to the assignment problem and travelling salesman problem (Das., 1976). It has also been applied to a travelling salesman problem with precedence constraints (Ahmed and Pandit., 1976). The travelling salesman problem with precedence constraints is the usual travelling salesman problem with the restriction that the salesman should start from a prescribed node (a headquarters) and each admissible turn is to satisfy a precedence relation denoted by ir < jr and r = 1, 2, 3 ……, i.e. the node jr should not be visited unless node ir is already visited. This approach has also been applied to a bulk transportation problem (Sundara Murthy). In this application, there is a set I = (1, 2, 3……., m) of m sources which produce a particular product and set J = (1, 2, 3……., n) of n places which require this product. The requirement of each place, the capacity of each source and the bulk transportation cost are given; the objective is to find the least transportation cost satisfying the requirement of all the places. Concepts involved in the lexicographic search are so natural that the exact definitions connected with these concepts appear almost academic, if not pedantic. A detailed explanation (Ravi Kumar., 1995) of these concepts is described below. 3.1 The Lexisearch Methodology The lexicographic search approach to combinatorial optimization, as already pointed out, was developed by Pandit in the first instance for the knapsack problem and has since been applied to many other combinatorial programming problems like job scheduling etc., in addition to assignment problem and travelling salesman problem. Concepts involved in lexicographic search are so natural that the exact definitions connected with these concepts appear almost academic if not pedantic. The lexisearch derives its name from lexicography, the science of effective storage and retrieval of information. The basis for this approach is the possibility of defining a structure in the solution space on the following lines: Elements in the solution space of the problem are arranged in a hierarchical order as blocks and sub blocks within blocks, etc., like the words in a dictionary. For instance, many combinatorial programming problems admit of representing the set of all possible ‘solutions’ as ‘words’, say (1, 2, 3, ……., n) based on a alphabet, so that the first few letters define a block of solutions, all having the specified ‘leader/incomplete word’ in common. Thus, the entire set of ‘words’ in this ‘dictionary’ words (viz., the elements in the solution space) are partitioned/arranged into blocks. The number of letters in a block (i.e. the number of letters of the leader which defines the block) is called length of the ISSN: 0975-5462 2322 Ch Venkatadri Naidu et al. / International Journal of Engineering Science and Technology Vol. 2(6), 2010, 2321-2327 block. The block ‘B’ with a leader (1, 2, 3…) of length three consists of all the words beginning with (1, 2, 3) as the first three letters. The block A with leader (1, 2, 3) of length 2, is the immediate ‘super block’ of B and includes B as one of its sub blocks. The block C with leader (1, 2, 3) is a sub block of ‘B’. This block ‘B’ consists of many sub blocks (1, 2, 3), one for each different. The block B is the immediate super block of block C. Similarly, A is the immediate super block of block B. By the structure of the problem, it is often possible to get bounds to the values of all the words in a block (i.e. the bound for the block) by an examination of its leader. The possible three cases are: Case 1: In case the block contains a better word (i.e. when the bound is less than the trial solution value) one has to go into super blocks. Case 2: In case the value of this bound is greater than or equal to the trial solution value, jump over to the next block within the present super block. If the current block happens to be the last super block, of course, one goes to the first block of the next super block. Case 3: When the value of the partial word is greater than or equal to the trial solution, jump out to the next super block. Further, when the exact values of the leaders of the same size within the block are non-decreasing in this case, the exact value of a ‘current’ leader is always greater than the trial value; one need not check the subsequent blocks within this super block at all but can move over to the next super block. This property of monotonic in the leaders of the same size is not always present, for instance the travelling salesman problem, with ‘usual’ alphabet table, shows this structure. However, the quadratic assignment does not allow this possibility. The above concepts and approach are illustrated below, in the case of the well known travelling salesman problem: Let a, b, c, d be four cities to be covered by a salesman. Then the set of possible partial words and complete words is illustrated lexicographically as follows: a ab abc abcd abdc ac acb acbd acdb ad adb adbc adcb b ba bac bacd badc bc bcd bcad bcda bd bda bdac bdca c ca cab cabd cadb cb cba cbad cbda cd cda cdab cdba d da dab dabc dacb db dba dbac dbca dc dca dcab dcba Applying the above procedure described earlier, an optimum sequence for maintenance activities can be obtained with minimal effort. The words starting with ‘a’ can be grouped together; such a group is called ‘a’ block and activity ‘a’ is called the leader of the block. In a block there can be sub blocks; for instance, block of words with leader ‘b’ has sub blocks ba, bc, and bd. While the words bacd and badc are the two words which constitute the sub block ‘ba’ of the block ‘b’. There would be blocks having only one word, for example, the block with the leader bac contains only the word bacd. All the incomplete words can be used as leaders to define the blocks. For the blocks of the size 2, with leaders ab, ac, and ad the block with the leader ‘a’ is the immediate super block. The logical flow of the lexisearch procedure at each step is mentioned under the remarks table of the alphabet table; the notations used are described below: GS: Go to sub block i.e. add the first available free letter of the remaining ones; GS for dc is dca. JB: Jump block, to go to the next block of the same length i.e., replace the last letter of the current block by the letter next to it in the alphabet table; JB at abd is abe. JO: Jump out to the next higher order block, i.e. remove the last letter of the current leader and then jump block; JO for cdbe is cde. ISSN: 0975-5462 2323 Ch Venkatadri Naidu et al. / International Journal of Engineering Science and Technology Vol. 2(6), 2010, 2321-2327 The search is started with the first letter ‘a’ as the leader. As the search is for the optimum solution, one can jump the current block if its bound is greater than or equal to the current trial solution. No complete word in the block can be better than the current one. Bound Calculations Bound is the sum of the times/costs of the nodes (which is not in the word excluding the latest city) to the first reachable node (excluding latest node) within the first (m-1) nodes. Bound calculations are illustrated in the study. The details of this can be seen elsewhere (Pundit., 1962) 3.2 The Algorithm The out line of the lexisearch algorithm is illustrated below. Let C = [cij] be the given n X n time matrix denotes the change over times from one activity to another and cij the changeover time of activity j from activity i, and node 1 be the starting node. Step 0: For the precedence constraints, say, ir < jr; r = 1, 2, 3, …, k put c (jr, ir) = c (1, jr) = c (ir, 1) = (as large as possible). Remove the bias. This bias removal reduces the matrix to a non negative matrix with at least one zero in each row and in each column. Obviously, it is enough to solve the problem with respect to this matrix. Sort each row in ascending order and store the corresponding indices in another matrix, say X. Initialize the ‘current trial solution value’ to a large number. Since our starting node is 1, we start from 1st row. Put k = 1. Step 1: Go to the Kth element of the row (say node p) and compute the changeover time. If the time is greater than or equal to the current trial solution value, go to Step 8, else go to Step 2. Step 2: If the (incomplete) word forms a sub-tour or if any prescribed restriction is violated, drop the node added in Step 1 and increment k by 1, and then to Step 6; else go to Step 3. Step 3: If one full cycle is generated, then replace the time associated as the current trial solution value and go to Step 8, else go to Step 4. Step 4: Calculate the bound. Step 5: If the (bound + time) is greater than or equal to the trial solution, drop the node added in Step 1 and increment K by 1, and then go to Step 6, else go to Step 7. Step 6: If k is less than n (total number of nodes), go to Step 1, else go to Step 8. Step 7: Go to sub block, i.e. go to Pth row and then put k = 1; go to Step 1. Step 8: Jump this block i.e. go to previous row (i.e. node) and increment k by 1 where k is the column number of that row. This will automatically reject all the subsequent words from this block as solutions worse (at least not better) than the current trial value. If the present node is the starting node and k = n, go to Step 9 else go to Step 1. Step 9: Current word gives the optimal sequence with current trial solution value as the optimal changeover time respective to the reduced time matrix. Step 10: Add the bias to the optimal solution value obtained above and stop. 4. Case Study The approach is shown witha numerical example of a leading automobile four wheeler service center in India for all models in all segments of most popular company Maruthi Suzuki Ltd. The service center services on an average 12000 operations of various model vehicles of 15 models/month. This service center has to deliver every month on an average two thosand vehicles. The technical advisors after fillingup the jobcards they issue job orders to shopfloor people. It is noticed that maximum time was lost, while processing in the present sequences. In the survey analysis, one section covers purely covers the detailed study on the different maintainance activities generally carried out in a service centre and their durations. Basically in all the service centers, the total activities are carried out in two stages. In the first stage, job cards are filled and accordingly mantenance activities are carried out. This first stage consists of two group of activities. It depends on the criticality of activities needed. They are critical and non critical group of activities. In the second stage vehicles are checked and tested on a trial run basis. Later in case of any further problems, the ncessary corrective actions will be taken. Based on the survey data the list of activities are summerized and shown in Table 1. ISSN: 0975-5462 2324 Ch Venkatadri Naidu et al. / International Journal of Engineering Science and Technology Vol. 2(6), 2010, 2321-2327 Table 1: Servcicing Opeartions Activity Average Time (in hours) Basic Operations Waiting in queue 0.6 Inspection and job card entry 0.4 Water washing 1.0 Group I Engine testing 0.5 Fueling system 0.2 Steering check and setups 0.3 Lighting and battery system 0.5 Body repairs 1.0 Air conditioner testing 0.3 Ignition timings 0.4 Trail runs 0.4 Rectifications (1) 0.5 Rectifications (2) 0.5 Group II (Critial Activities) Gear box overhaul 2.5 Wheel balancing and alignment 1.0 Clutch and transmission system 1.0 Brake system 1.0 Suspension system 1.5 In the critical opearation(group two) of activities, it consists of five opeartions shown. Based on the critical examination and the discussion had with the various service center personel, it was concluded that the crtical activities are the dependent, and hence the activities processing times would vary. Accordingly the dependent activity and based on the feed back its duartions are presented in Table 3. All the five activities are arranged in an order covering all the activities. Table 2: Time Data Matrix 1 2 3 4 5 1 - 16 4 13 7 2 3 - 8 9 10 3 6 5 - 13 9 4 8 7 10 - 11 5 9 10 13 8 - The lsit of activities and the processing times are in below. For example each cell value indicates the required time to copmplete the operation . For example the processing time 16 indicates the activity ‘2’ takes 160 minutes if it starts after activity ‘1’. It would be optimal if starts the activity number 3 after completion of 1 and takes 40 minutes to complete the actvity 1-3 . The corresponding activity times are shown in Table 3. (presented in 10: 1 ratio values) For the processing times (Table 2), an alphabet table is prepared by arranging the processing times in increasing order, accordingly the corresponding activities are also indiacted.The generated alphabet table is shown in Table 3. ISSN: 0975-5462 2325 Ch Venkatadri Naidu et al. / International Journal of Engineering Science and Technology Vol. 2(6), 2010, 2321-2327 Table 3: Alphabet Table 1 2 3 4 5 3→4 1→3 2→5 2→7 4→8 5→7 3→8 1→6 1→8 1→9 4→13 4→9 5→9 3→10 2→10 2→16 5→10 4→13 5→11 3→13 1→10000 2→10000 3→10000 4→10000 5→10000 The bounds are calculated for each step according to the algorithm and the final serach matrix obtained is presented in Table 4. From the table it can be interpreted that the minimum total time required to complete all the 5 activities are 31 time units (310 minutes). The corresponding optimal sequence is 1-3-5-4-2-1. Implementaion of this sequence would lead to minimizing the overall service time. Table 4: Search Table 1→1 1→2 2→3 3→4 4→5 Bounds Status 1→3 (4) 4+34=38 GS 3→2=5 (9) 9+29=38 GS 2→4=9 18+20=38 GS (18) 4→5=11 29+9=38 GS (29) (NTRV) 5→1=9 NTRV=38 JO (38) 3→5=9 13+18=31 GS (13) 5→4=8 21+10=31 GS (21) 4→2=7 28+3=31 GS (28) 2→1=3 NTRV=31 JO (31) 3→4=13 17+26=43 GS (17) 4→2=7 24+19=43 GS (24) 2→5=10 34+9=43 GS (34) 5→1=9 NTRV=43 JO (43) 1→5=7 (7) 7+29=36 GS 5→4=8 15+21=36 GS (15) 4→2=7 22+14=36 GS (22) ISSN: 0975-5462 2326 Ch Venkatadri Naidu et al. / International Journal of Engineering Science and Technology Vol. 2(6), 2010, 2321-2327 2→3=8 30+6=36 GS (30) (NTRV) 3→1=6 NTRV=36 JO (36) 1→4=13 13+33=46 JO (13) 1→2=16 16+33=49 JO (16) (Stop) 5. Results The sequence of existing activities carried out in many of the service centers and time to taking to complete are varying from center to center. No center has been following scientific approaches to minimize the throughput time of all the activities involved. For instance, the time taken in the studied centers was 420 minutes and also it is varying from center to center. All the activities are critically examined and proper sequence has been proposed in this chapter. It shows that all the activities could be completed within 310 minutes duration. It shows, approximately 110 minutes of the existing total time can be reduced and it accounts for a minimization of 26% of time over the existing one. Obviously, it leads enhanced service rate and thus customer satisfaction. 6. Conclusions The conclusions from the paper are summerized as below 1. Improving the rate of delivery of vehicles in a service center enhances the customer satisfaction. Minimizing the delay time between the activities, and proper sequencing of the activities are the two important factors to be taken care off. Indian automobile service sector reveals that importance of optimizing the sequencing of the activities would enhance the delivery rate of the vehicles. 2. In this paper, a novelstic search approach lexicographic methodology has been used to optimize the sequencing of maintenance activities in a service centre. The major advantage of this approach is that it requires simple bound calculations and no operating parameters are involved. The results show that the critical operations in the process can be carried out within 310 minutes thus it reduces the activity completion time and leads to enhance the faster delivery of the vehicles. 3. The algorithm presented here was used to optimize the sequence of a simple 5 servicing activitites. However, for copmlex problems for instance, beyond 10 models manually calculations are very difficult and becomes a labourous process. Hence, for such problems, it is necessiates the need of a progrmme in a machine. References: [1] Beaty, S.J, Genetic Algorithms for Instruction Sequencing and Scheduling. .(1995), [2] Choi, I. C. and Korkmaz, O. (2002), Job Shop Scheduling With Sequence and Time Dependent Setup Times. [3] Gao,H. and Liu, X. (2007), Improved Artificial Immune Algorithm and Its Application On The Permutation Flow Shop Sequencing Problems, The Information Technology Journal, Vol. 6, pp 929-93 [4] Hirakawa and Yasuhiro. (1999), A Quick Optimal Algorithm for Sequencing on one Machine to Minimize Total Tardiness, An International Journal of Production Economics, Vol.60-61, pp 549-555. [5] Hwang., Hark., Sun. and Ung, J.(1997), Production Sequencing Problem with Reentrant Work Flows and Sequence Dependent Setup Times, A Journal of Computers and Industrial Engineering, Vol. 33, pp 773-776. [6] Mondal, S.A. and Sen, A.K. (2000), An Improved Precedence Rule for Single Machine Sequencing Problems with Quadratic Penalty, A European Journal of Operational Research, Vol. 125, pp 425-436. [7] Pandit, S. N. N, Operations Reseasrch, (1976), Vol 10, pp 633-646. [8] Taillard, E. (1989), Some Efficient Heuristic Methods for the Flow Shop Sequencing Problem. [9] Xiaobo, Z. and Zhou, Z. (1999), Algorithms for Toyota’s Goal of Sequencing Mixed Models on an Asembly Line with Multiple Workstations, The Journal of the Operational Research Society, Vol. 50, pp 704-715. [10] Xiaobo., Zhao., Ohno. And Katsuhisa. (1997), Algorithms for Sequencing Mixed Models on an Assembly Line in a JIT production system, A Journal of Computers and Industrial Engineering, Vol. 32, pp 47-56. ISSN: 0975-5462 2327

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