Single Model Assembly Line Balancing for Newly Recruited Employees Sandeep Choudhary 1 *, Sunil Agrawal 2 1*,2 PDPM Indian Institute of Information Technology, Design and Manufacturing, Jabalpur, 482005, E-mail: 1 mech10165@gmail.com, 2 sa@iiitdmj.ac.in Abstract There is a class of assembly line balancing problems in management science that helps finding out the optimum production rate of the line. In this paper new constraint is developed for the newly recruited employees that are under training period considering a simple assembly line balancing problem of type-2 (SALBP-2). Further, an algorithm is proposed which will allow the supervisor to take the proper decision during the allocation of task to the newly recruited employees with the least effect on the production rate. According to the algorithm, out ofthe total number of tasks in an assembly line, few tasks are manually assigned to newly recruited employees and the rest of the tasks are assigned to the senior employees in such a way that production rate does not suffer. The mathematical model is solved by Branch and Bound method using Lingo 10 software package. Keywords: Single model assembly line, Branch & Bound algorithm, Newly recruited employees 1 Introduction A simple assembly line is a typical flow-oriented production system that consists of a number of workstations (m 2) aligned in a serial manner along a conveyer belt without buffers between them (Gurevskyet al., 2012).Workstations are interconnected with each other through a conveyer belt whose speed depends on the total task time of the bottleneck station (known as cycle time). The simple assembly line balancing problem (SALBP) consists of assigning tasks to stations in such a way that the precedence relationships among the tasks are satisfied, the sum of performance task times assigned to each station does not exceed the cycle time and each task is assigned to one and only one station. The ultimate goal of every company is to improve production rate. At the same time it also has to look after their employees who are actually responsible for carrying out the production especially in company with manual assembly line.generations by generation new employees are being recruited in the job shops. These newly recruited employees are initially being trained in job shops to make them efficient in carrying out the task. Out of total tasks in an assembly line, few tasks are assigned to newly recruited employees in traditional the way.the rest of the tasks are assigned to the senior employees in such a way that production rate does not suffer a lot. When new employees are recruited in a company, they are not much efficient to handle the task assigned to them. They are being trained to so that they become more productivein their work. In spite of the fact that the company suffers with their production at initial stage but it is also mandatory to train these new employees. In the literature, several versions of assembly line balancing problem(albp) arising from different objectiveare as follows(lapierreet al., 2006 and Fathiet al., 2011). SALBP-F is a feasibility problem which is to establish whether or not a feasible line balance exists for a given combination of number of stations and cycle time. SALBP-1 and SALBP-2 have a dual relationship, because the first one minimizes the number of stations with a given fixed cycle time, while the second one minimizes the cycle time (maximizes the production rate) with a given number of stations. SALBP-E is the most general problem version maximizing the line efficiency thereby simultaneously minimizing cycle time and the number of stations considering their interrelationships. The methods used for solving an assembly line balancing problem can be classified as exact methods and approximated methods. Most of the exact techniques fall into following two categories dynamic programming and branch and bound methods (Baybars, 1986). Scholl and Becker (2006), Erel and Sarin (1998) discussed about exact and heuristic solution methods for simple assembly line balancing problem. Talbot et al. (1986) divided heuristics for SALBP into four categories: single pass, composite, backtracking and time trapped optimizing approaches. In this paper, exact method based on branch and bound is being used to solve the simple assembly line balancing problem-2 (SALBP-2) with the help of LINGO 10 software package.the rest of the paper is organized as follows: In Section 2, mathematical formulation is given by an objective function of minimization of cycle time. Section 3 describes 584-1
Single Model Assembly Line Balancing for Newly Recruited Employees numerical example.the results obtained after solving the numerical problem are discussed in section 4. Finally some conclusions are drawn in Section 5. 2 Mathematical model The mathematical model used in this paper has been modification over the already existing formulation (commonly found in most of the work on ALB) proposed by Miralleset al. (2007). The objective function and constraints of their model are presented below from equation 1 to 7. An additional constraint (8) on newly recruited employees has been added in this work. Indices i, j w s C N W t S p wi D j I w M : Index of task ( =1,2 ) : Index of employees : Index of workstation ( =1,2... ) : Cycle time of assembly line : set of tasks : set of employees : set of newly recruited employee ( t) W : set of workstations :processing time for task when executed by employee : set of tasks that immediately precede task in the precedence graph : set of tasks that has to be assigned to newly recruited employees :Constant such that Decision variables x swi = y sw = 1, if task is assigned to employee at workstation 0, otherwise 1, if employee is assigned to workstation 0, otherwise Objective function M pwi Min = C (1) xs wi ysw ysw i N s S (2) (3) (4) s xs s xswj i,j N i (5) D wi j pwi xswi C xswi Mysw xsti y sw x swi s S, w(6) W w W, (7) s S (8) (9) (10) Model (Eqs.1-10) focuses on minimizing the cycle time for a given number of workstations. First constraints(eq.2) guarantees that each task is executed, and that it is done by a single employee, at a single workstation. Constraints (Eq.3 and Eq.4) establish bisection between employees and workstation at a feasible solution, i.e., every employee isassigned to a single workstation and vice versa. Constraints (Eq. 5) defining the precedence relations. Constraints (Eq.6 and Eq.7) ensured that the sum of the execution times of the tasks at the most charged workstations does not exceed the cycle time. Constraints (Eq.8) indicate that particular task is to be assigned to the new employees in order to give him training. Constraints (Eq.9) and constraints (Eq.10) are usual integrity restrictions. 3 Numerical Illustration t W, i I w { 01, } s S, w W { 01, } s S,, i N The data for numerical illustrationshas been taken from Zhang and Gen (2011). There are total 10 tasks that are to be performed by 4 employees having 4 workstations to produce the single model product. These set of tasks follow the precedence relation. Its precedence diagram and task times taken by individual employees aregiven in figure 1 and table 1respectively. The fourth employee shown in the table ( 4) is a newly recruited employee while the rest three employees ( 1, 2and 3) are old one. The problem is to assign the tasks to newly recruited employee and the rest of the three old employees in such a way that the production rate least affected. 1 6 8 3 5 7 Figure 1 Precedence diagram 9 10 584-2
Table 1 Data set of task time (sec) performed by each employees Task Precedence 1 2 3 4 (new) 1 Ø 17 23 17 13 2-0 0 0 0 3 Ø 22 15 27 25 4-0 0 0 0 5 {3} 21 25 16 32 6 {1} 28 18 20 21 7 Ø 42 28 23 34 8 {6} 17 23 40 25 9 Ø 19 18 17 34 10 {7,8,9} 16 27 35 26 4 Results and Discussion The mathematical model of ALBP, discussed in the previous section, for newly recruited employees is solved using Lingo 10 software with an objective to minimize cycle time.the results are summarized in the table 2. Table 3 shows the results in detail. The algorithm for finding the complete solution in this table is explained as follows. First, the task(s) to be assigned to the newly recruited employeeis(are) chosen arbitrarily, starting from 1st task, as shown in the second column of the table.further,each time the tasks are added in the previous set of tasks till the cycle time of the problem is minimized. The set of tasks for which the minimum cycle time is obtained is considered as the first set of best combinations of tasks (tasks 1, 3 in the first iteration).the rest of the tasks are assigned to older employees as obtained in the solution. This completesone iteration. In other words, the constraint 8 is updated each time a new task is added in the previous tasks and the whole problem is run again. Similarly, the second iteration is done by choosing the next candidate task from among the set of remaining tasks. The procedure is continued till newly recruited employee is trained for all the tasks. Table 2 Number of task to be assigned to the newly recruited employees Iteration no 1 Task for New employees (W4) No of task Cycle time (sec) Permitted (1)/ Not permitted (0) 1 1 51 0 1,3 2 39 1 1,3,5 3 70 0 2 5 1 51 1 5,6 2 53 0 3 6 1 50 0 6,8 2 46 1 4 7 1 52 1 7,9 2 68 0 5 9 1 53 1 9,10 2 60 0 6 10 1 50 1 Iteration no 1 2 3 4 5 Table 3 Detail of Task assignment Task Employee Station Cycle Time 1 4 1 3,6,9 2 2 51 5,7 3 3 1,3 4 1 6,9 2 2 39 5,7 3 3 1,3,5 4 2 7,9 2 1 70 6,8 3 3 10 1 4 5 4 3 1,7 3 1 51 3,6,9 2 2 5,6 4 2 1,3 2 1 53 7,9 3 3 6 4 3 3,7 2 1 50 1,5,9 3 2 6,8 4 3 3,7 2 1 46 1,5 3 2 9,10 1 4 7 4 2 3,5 3 1 52 1,6 2 3 8,9,10 1 4 7,9 4 3 3,5 3 1 68 1 2 2 6, 9 4 3 3,7 2 1 53 1,5,6 3 2 9,10 4 4 1,3,6 2 1 60 5,8 1 2 7 3 3 584-3
Single Model Assembly Line Balancing for Newly Recruited Employees 6 Manual Task Assignment by supervisor to new employee else 10 4 4 3,7 2 1 1,5,9 3 2 6,8 1 3 Start Read Data (Precedence Diagram, no. of old employees and new employee) Obtain cycle time for iteration i AddTask for assignment to new employee manually Optimizationm odel Optimizationm odel Obtain cycle time for iteration i+1 Comparison if Cycle Time i < Cycle Time i+1 yes Computer basedremaining Task Computer basedremaining Task Finally allow the task (cycle time found in iteration i) to be assign to new employee by supervisor employee Figure 2 Flow chart of Algorithm for single iteration 50 The whole procedure can be summarized as follows. Every task is to be assigned to newly recruited employees in order to train him/her. The cycle time depends on the number of tasks to be assigned to the newly recruited employees. The supervisor will crosscheck the cycle time with the number of tasks assigned to newly recruited employees within the iteration. The least cycle time will be selected and corresponding task is going to be assigned to the newly recruited employee also. This process is also shown in figure 2 for single iteration. After gaining the experience, new employees are shifted to the next task by the supervisor and the process follow. There is least difference between the cycle times of all permitted task when compared among all the combination of permitted task. 5 Conclusions In this work we have proposed an algorithm which tries to optimize assignment of tasks to the newly recruited employee, also to the remaining employees, such that the newly recruited employee is trained on all the tasks on the assembly line. These tasks will be done at different workstations based on precedence diagram. The objective here is to find out the optimal assignment so that the total production rate/cycle time is least affected. A numerical study is done to show the optimal station-worker-task assignment in the case of SALBP-2 including the assignment of newly recruited worker. The minimum cycle time in this example is obtained as 39 Sec which is the optimized result. However, there is need to train the newly recruited employee on all the tasks.therefore, when the same employee is assigned another task (other than optimized assignment), the cycle time for the new assignment is higher than the 39 Sec.But since the whole problem is solved again, the algorithm gives the optimized result by assigning the remaining task to the older employees accordingly. This will improve the production rate of the whole plant in comparison to the arbitrary assigning the tasks to the new worker. Therefore, in case of training the new workers on the assembly line, the proposed algorithm finds out the assignmentsuch that there is a least fall in production rate. Reference Scholl, A. and Becker, B. (2006), State-of-the-art exact and heuristic solution procedures for simple assembly line balancing, European Journal of Operational Research, 168(3), pp.663-693. Lapierre, S.D., Ruiz, A. and Soriano, P. (2006), Balancing assembly lines with tabu search, European Journal of Operational Research 168, pp.826 837. 584-4
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