Virtual manufacturing cells scheduling considering lotstreaming and sequence dependent setup times

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JIEM

Journal of Vol. 2, No.

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Virtual

stream

A.Ayough

Abstract

In this pape (VMC) is p machines is processing types with type of syst nonlinear p operation, th problems ha Keywords programmin Received: Ma Revised: May Accepted: Aug

1. Intro

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Virtual manufacturing cells scheduling considering lot-streaming…

Journal of Industrial Engineering and Management Studies (JIEMS), Vol. 2, No. 1 Page 62

at the start of each period, cells are reconfigured. When the demand change is high, replacement equipment will cost a lot. Some researchers suggested, virtual manufacturing cell (VMC) to overcome the defects of traditional CMS. In this type of system, the cells are not physical and we can have shared machines between cells. Logical grouping of jobs and machines are only in the production control system and the imagination of workers. A new approach to layout at VMC, is the scattered arrangement in which for increasing the availability, similar machines are scattered throughout the shop floor. This paper addresses the VMC problem with lot-streaming tactic.

Researches have done on the scheduling of virtual manufacturing cells. If, due to performing various operations by each vehicle (machines sharing between cells), at no one, preparation time sequence dependent machinery is not considered. While this can lead to the calculation of real and direct impact on the completion of all jobs. In this study, we focus on the scheduling of operations in VMC with scattered layout and consider sequence dependent setup time to thereby minimize the completion time of all jobs and the distance traveled by the work. We also consider lot streaming strategy that provides the ability to split the jobs.

2. Literature review

MacLean et al. for the first time in 1982 introduced the concept of virtual manufacturing cells. According to them virtual cell is not as a physical grouping of machinery, but it is as data files and processes on a controller computer (MacLean et al. 1982). Irani et al. developed a two-stage flow based approach for formation of VMCs with an objective of minimizing traveling distances (Irani et al. 1993). Kannan and Ghosh in 1996, Kannan in 1997 and 1998 explored the many part-family based scheduling rules in process layout (Kannan VR. 1997). In 2003, Ko and Egbelu presented a methodology for designing VMCs. They carried out a comparative study of dynamic and static manufacturing systems at the intent of examining the influence of variations in the product mix on the shop performance. The total preparation time and total distance transport components were considered as a measure of performance (Ko K-C and Egbelu PC. 2003). Mak et al. provided a non-linear programming for scheduling VMCs and ant colony optimization algorithm is presented (Mak et al. 2007). Kesen et al. in 2009 compared three types of cell systems, processes and virtual cells using simulation (Kesen et al. 2009). Kesen et al. gave mixed integer linear programming model with objective function for minimizing job completion time and distance jobs profiting (Kesen et al. 2010). In 2012 its previous models developed so that the job could be divided into smaller tasks (lot streaming) (Kesen SE. and Gungor Z. 2012).

3. Problem description and model formulation

3.1. Virtual manufacturing cells

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successive operations can be overlapped. Since machines are positioned in different locations in the layout, after the operation ojh is completed on machine i and before the operation oj,h+1 is started on machine k, dik unit of travelling time occurs for job j. Sifj is setup time for machine i while it is working for job f and now it wants to do job j. so sij is setup time for machine i while it is standby and now it wants to do job j. As a result, according to the amount of operations Sifj or Sij, setup time between two sequence for machine i must be considered.

Problem of VMC scheduling includes:  Assigning proper machine to each operation  Obtain the sub lot size for each job

 Calculated the starting time of each operation  Determine the time to start the job in any order

All of the above should be selected so that all jobs will be done in the shortest time possible. The following assumptions should be considered:

 Operations must be performed one after another according to the problem input  Each machine can only perform one operation at a single time.

 Sequence of operations, setup time depends on the sequence, process time, batch size and the travelling time between the machines are pre-determined.

 The machines are fixed and do not change their location.  Number of sub-lot for all jobs is fixed and known in advance.

 All job must be available at time zero and is not acceptable in any new work.  Each job can visit any machine at most once.

 There is no preference for doing Jobs.

 Machine Breakdown and maintenance activities are not considered.

Parameters:

i,k: indices for machine (i, k=1, . . . ,m) where m is the number of machines in the system j,f: indices for job ( j=1, . . . , n) where n is the number of jobs in the system

h,r: indices for operation (h=1, . . . , hj) where hj is the number of operations to be performed for job j

p,q: indices for sub-lot (p=1, . . . ,L) where L is the number of sub-lots

l: indices for order on each machine (l=1, . . . , li) where li is the number of operations assigned to machine i

Nj: lot size for job j

Pijh: unit processing time of operation ojh on machine i dik: travelling time between machine i and k

Sij: machine i setup time for doing job j while machine i was standby

Sifj: machine i setup time for doing job j while machine i was do job f in previous order. SQjhi: 1 if machine i capable of doing jth operation of job j to be, 0 otherwise.

M: sufficiently big number Decision variables

Cmax: makespan or maximum completion time of jobs to leave the system Vjp: number of parts to be produced for job j in lot p

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A. Ayough, A. Alem Tabriz, A. Javani

Journal of Industrial Engineering and Management Studies (JIEMS), Vol. 2, No. 1. Page 65

Xijhlp: 1 if operation ojh for lot p is performed on machine i in order l, 0 otherwise

Zikjhp: 1 if operation ojh is performed on machine i and operation oj,h+1 is performed on machine k, 0 otherwise.

tjhp: starting time of operation ojh for the pth lot Tmil: starting time of work on machine i in order l

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Objective function is to minimize the make span value that is used in order to minimize the total completion time of jobs. Constraint (1) ensures that the make span is greater or equal to the completion of all jobs. Constraint number (2) shows that summation of sub-lot size is equal to lot size for each job. Constraint set (3) guarantees that the succeeding operation of any job for any sub-lot can be started only after the preceding operation is completed and transported between respective machines. Constraint set (4 & 5) enforces that between the consecutive operations to be executed on any machine; the succeeding one can only be started after the preceding one is completed and setup time is spend. Constraint sets (6 & 7 & 8 & 9) guarantee that if Xijhlp is equal to 1 , the starting time of ojh for sub-lot p and the starting time of the work on machine i in order l plus setup time are the same. Constraints number (10) ensures that at most one operation will be done on every machine in order l. Also limits the number (11) shows that for machine i until l has not accepted its operation, it will not be able to get it another operation for order l + 1. Constraint (12) ensures that the ojh for the sub-lot p must be assigned to only one machine (Also, it should be allocated to one of the machines). On the constraint number (13) we can say that if machine i has the ability to perform ojh, it can select it.

Constraint set (14) makes sure that if operation ojh for sub-lot p is performed on machine i, this operation must be performed on machine i in any order. Constraint sets (15) and (16) ensure that if operation ojh and operation oj,hþ1 for sub-lot p are performed on machine i and k respectively, Zikjhp can only be equal to 1, 0 otherwise. Constraint set (17) ensures that if operation ojh for sub-lot p is performed on machine i, the number of items to be processed in job j for sub-lot p (ie, sub-lot size) must be greater than zero. The constraints (18) and (19) show that if the machine does not change or is ongoing on the last operation, Zikjhp value is zero. Constraint numbers (20), (21), (22), (23), (24), (25), (26) and (27) indicate that the variables are non-negative.

Kesen and Gunger in 2012 VMC developed a model for the VMC system scheduling so that the work could be divided into smaller tasks (lot streaming). This model has the following problems:

 The main problems are the lack of a parameter that indicates the machine is able to perform which operations. To solve this problem we define the parameter SQjhi and we resolve this problem by taking the Constraints 13.

 Also there is not suitable Constraints that covers all states of Zikjhp and For this purpose, Constraints of 18 and 19 were considered.

 In this model Xijh.l+1,p can be 1 while Xijhlp was 0, that This had a negative impact on Tmil. For example, Tmil value in the first and second order was zero, but in third order, it starts to get value. To solve this problem, Constraint 11 was considered.

4. Numerical examples

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Page 67

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Page 69

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Table 7: Lot sizes, operation sequences and process time of the jobs

job j sequence operation and process time lot size

1 B(25,23) C(18,17) 20

2 A(32,35) B(12,11) C(15,14) 17

3 C(21,24) A(25,22) 27

Table 8: Machine setup time from standby mode (Sij)

Table 9: Sequence dependent setup time (Sifj)

Table 10: The ability of machine i to produce hth operation for each job (SQjhi)

After the example code in Lingo, optimum solution (global optimum) within 19 minutes and 25 seconds was obtained (Refer to Figure 4). The minimum time for completion of Jobs, 644 time units was achieved. Also V11 = 10, V12 = 10, V21 = 9, V22 = 8, V31 = 14, V32 = 13 was calculated.

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number of sub-lot. This study expansion is in some ways. To solve the large size, Time solution is increased highly by methods exact solution. Hence, the use of meta-heuristic algorithms can be useful for this purpose. Also monitor machine Breakdown and maintenance of a system can lead to the development of models and create new research.

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