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Scheduling in reconfigurable manufacturing system for uncertainty in decision variables
Available online at www.sciencedirect.com
ScienceDirect Materials Today: Proceedings 5 (2018) 18451–18458
www.materialstoday.com/proceedings
ICMPC_2018
Scheduling in reconfigurable manufacturing system for uncertainty in decision variables Durga Prasada*, S.C. Jayswalb
a,b
Mechanical Engineering Department, Madan Mohan Malaviya University of Technology, Gorakhpur-273010 (U.P.), India
Abstract Reconfigurable manufacturing system is a new type of responsive manufacturing system which can adjust its setup to adjust its capacity and functionality with least effort and time when the demand for the product changes. Reconfigurable manufacturing system (RMS) has the exact capacity and functionality whenever is required. In the present work, an integrated approach of Shannon entropy and multi-attribute range evaluation (MARE) has been used for scheduling of the products. Weights of criteria have been calculated using Shannon entropy and ranking is obtained using MARE. MARE calculates the uncertainty of decision variables into the uncertainty of ranking. For scheduling of products, three criteria have been considered; reconfiguration effort, profit over cost and due date. © 2018 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of Materials Processing and characterization. Keywords: reconfigurable manufacturing system; reconfiguration effort; scheduling; shannon entropy, multi-attribute range evaluation
1. Introduction and literature review Reconfigurable manufacturing system is a new type of manufacturing system which can change its capacity and functionality very easily and quickly whenever required. RMS (reconfigurable manufacturing system) has capacity and functionality exactly what is required. RMS is adjustable to the fluctuating demands and it can be easily upgraded with new process technology. Reconfigurable manufacturing systems (RMSs), which possess the advantages of both dedicated serial lines and flexible manufacturing systems, were introduced in the mid-1990s to
* Corresponding author. Tel.: +915516050030. E-mail address: [email protected] 2214-7853 © 2018 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of Materials Processing and characterization.
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Durga Prasad et al./ Materials Today: Proceedings 5 (2018) 18451–18458
address the challenges initiated by globalization. The principal goal of an RMS is to enhance the responsiveness of manufacturing systems to unforeseen changes in product demand [1]. RMS has six key characteristics which are modularity, integrability, scalability, convertibility, customization, and diagnosability. The key characteristics customization, scalability, and convertibility are essential RMS characteristics, while the other three (modularity, integrability, and diagnosability) reduce the system configuration time and its ramp-up time [2-4]. Reconfigurable manufacturing system has been evolved from dedicated manufacturing system. With the concept of using the modular machine, the concept of reconfiguration arises. But it is not limited to modular machines. Some researchers have given the concept of reconfiguration by material handling systems [5], reconfiguration by relocation [6], reconfiguration process plan [7] etc. Koren et al. [8] has given the concept of practical reconfigurable manufacturing system using cell gantry and spine gantry. It is a special type of layout of flexible manufacturing system. Later reconfigurable machines were added in manufacturing system [9]. Reconfigurability has been reviewed in mining industry [10], mold and die making industry [11], Arvin Meritor [12], Powertrain industry [9], Continental Automotive [3, 13] etc. Scheduling is the one of the most important steps in production control. Scheduling may be defined as “Fitting specific job into a general time-table so that orders may be manufactured in accordance with contracted liability or in mass production, so that each component may arrive and enter to assembly in order and at time it is required. In other words, scheduling is that phase of production control which rates the work in order of its priority and provide for its release to the plant at the proper time and in correct sequence.” Thus, scheduling is concerned with when work shall be performed on a product or part. Scheduling in manufacturing system can be done on the basis of some rules such as, FCFS (First come first serve), LCFS (Last come first serve), SPT (Shortest processing time), LPT (Longest processing time), EDT Earliest due date, Maximum profit over cost, Reconfiguration cost/ Reconfiguration effort, Random (on the choice of manager). Scheduling can be done for one criterion as mentioned above or more than one criterion. If more than one criterion is considered, MCDM can be used. Prasad et al. used integrated approach of Shannon entropy and TOPSIS [14] and integrated approach of Shannon entropy and RIM (reference ideal method) [3] for scheduling in reconfigurable manufacturing system. In this paper integrated approach of Shannon entropy and MARE (Multi Attribute Range Evaluation) has been used for scheduling in reconfigurable manufacturing system. The main advantage of using Shannon entropy is that it calculates the weights of the criteria by solving the mathematical model and weights depend on the variance of the decision variables. The advantage of MARE is that it calculates the uncertainty of decision variable into uncertainty of alternatives so that alternatives can be selected on the basis of alternative score and alternative’s uncertainty [15]. This paper also discusses the concept of total reconfiguration effort. 2. Methodology In this paper methodology to calculate reconfiguration has been discussed and scheduling has been done by integrated approach of Shannon entropy and MARE. Therefore, methodology section has been divided into two subsections; (i) Criteria considered. (ii) Integrated approach of Shannon entropy and MARE 2.1. Criteria considered In present work, three criteria have been considered, reconfiguration effort, profit over cost and due date. 2.1.1. Reconfiguration effort Reconfiguration effort (RE) is the effort for changing the set-up of the manufacturing system from one product/product family to another product/product family whether it is for hardware component or for the software component. Reconfiguration effort can be at three levels, market level reconfiguration effort, system level reconfiguration effort, and machine level reconfiguration effort. The market level reconfiguration effort (MKRE) is associated with the activities that are performed outside the boundaries of the manufacturing system such as financial activities, shipping activities, bidding activities, logistic activities etc., that are associated with purchasing new machines or machine modules, selling old machines or modules and renting machines or modules. System level reconfiguration effort (SRE) is associated with the activities
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that are performed within the boundaries of the manufacturing system but at a level higher than machines. These activities include adding, removing or adjusting the machines in the system, relocating the machines and changing the material flow path. Machine level reconfiguration effort (MRE) is associated with the activities that are performed inside the boundaries of the manufacturing system and are all within the limits at the machine level. These activities include the adding, removing or adjusting machine modules and adding, removing or adjusting operation clusters. For all the activities reconfiguration effort is calculated separately by considering machines and/or modules added, removed or adjusted. Total reconfiguration effort (TRE) can be calculated as the weighted sum of the all three level reconfiguration efforts, Equation 1. + + (1) = where , , are weights assigned to the all three types of reconfiguration effort. + + =1 In present case, only two types activities have been considered, (i) addition/removal of machines (system level) and (ii) addition and removal of modules (machine level) System level reconfiguration effort can be calculated as / /
.
=
.
+
.
+
(2)
, , are the weights assigned to addition, removal and adjustment respectively.
>
>
and
+
+
=
1. +
= where
,
,
+
(3)
are weights assigned to the all three types of reconfiguration effort.
Machine level reconfiguration effort can be calculated as General formula for reconfiguration effort can be written as, =
′
.
+
′
.
+ ′
.
Where ′, ′, ′ are the weights assigned to addition, removal and adjustment respectively. ′ > ′ + ′ + ′ = 1.
(4) ′ > ′ and
If in a manufacturing system, there are n modular machines which are needed to be reconfigured for another type of product, total number of modules added, removed or readjusted can be calculated by using following formulas. . .
= ∑
(
= ∑
× (
= ∑
. = ∑ = +
(
) ×
(
) ×
)
× +
where N i = number of machine required for ith operation; M i = machine required for ith operation
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Durga Prasad et al./ Materials Today: Proceedings 5 (2018) 18451–18458
2.1.2. Profit over cost Profits are the difference between revenues and costs. Profit over cost can be calculated by multiplying the number of products produced i.e. demand of the product to the profit per product. Profit over cost depends on the demand of the product and demand is an important factor in a manufacturing system. Higher profit is the goal of an industry, hence it has been considered as a criterion for scheduling. 2.1.3. Due date Another criterion which has been considered is due date. If due date is close i.e. there are fewer days left for delivery, then its priority should be high. 2.2. Integrated approach of Shannon entropy method and multi attribute range evaluation In the problem integrated approach of Shannon entropy method and MARE (Multi Attribute Range Evaluation) have been used. Weights of each criterion have been determined by using Shannon entropy method and ranking of the alternatives has been obtained by MARE, Figure 1. Since each criterion has different meaning, equal weights of each criterion can’t be considered. Weights can be determined by two ways. First, by preference of decision maker, for example AHP method, Delphi method and weighted least square method, etc. Second, by solving mathematical model, for example entropy method, principal element analysis, multiple objective programming, etc. [3,14]. In present work entropy method has been used to determine the weights
Figure 1 Integrated approach of Shannon Entropy and MARE
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where, = Performance value of alternative i when it is evaluated in terms of criterion j, i = 1,2,…,m and j = 1,2,…, Integrated approach of Shannon Entropy and MARE has following steps Step 1: Establish the decision matrix Step 2: Normalize the decision matrix =
∑
Step 3: Compute entropy ℎ = −ℎ
. ln
Where ℎ is the entropy constant and is considered equal to: ℎ = (ln ) = 0, if =0 and . ln Step 4: Set = 1 − ℎ , as the degree of diversification. Step 5: Set
=∑
as the degree of importance of attribute j
Step 6: Establish the decision matrix. Each criterion has three values; minimum maximum Step 7: Normalize the decision matrix*. If max value is desired, ∗ = If min value is desired,
∗
=
, most likely
, and
( ) ( )
Max and min values are selected for min, most likely and max values for each criterion. ∗ ∗ and are interchanged. If min value is desired for jth criterion, Step 8: Calculate alternative score separately for min, most likely, and max decision variables. ∗ = ∑ ∗ = ∑ ∗ = ∑ Step 9: Calculate the uncertainty in alternatives i as = − Step 10: Calculate ratio of most likely alternative to uncertainty, Select the alternative which has the highest ratio. 3. Problem Formulation Problem used in the illustrative example is inspired by the research work done by the author in Continental Automotive Components (India) Pvt. Ltd and given in [3]. It is also extended form of [14]. In this problem, there are seven machines. Machines have been grouped as group 1, group 2 and group 3 as shown in Table 1. Machine M2 are and and M4 are modular machines which can change their configurations. Configurations of machine . Configurations of machine are , and . Auxiliary modules are {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Four types of product families are manufactured named as product family A, B, C and D. = 0, = 0.7, = 0.3, = 0.6 , = 0.3 , = 0.1 , = 0.5, = 0.4, = 0.1 , ′ = 0.5, ′ = 0.4, ′ = 0.1 . Most likely values of profit over cost and due date are given in Table 2 and minimum, most likely and maximum values of these criteria have been shown in Table 3. If initially product family A is running in manufacturing system, then system can be reconfigured for product family B, product family C and product family D.
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Durga Prasad et al./ Materials Today: Proceedings 5 (2018) 18451–18458
Reconfiguration effort for changing the configuration from A to B, Group-1 machine added ={ }=0; machine removed ={M1 }=1; machine adjusted ={M2, M4 }=2; 0.5 × 0 0.4 × 1 0.1 × 2 = + + = 0.2 3 3 3 Similarly, = 0.4, = 0.45 = 0.6 × 0.2 + 0.3 × 0.4 + 0.1 × 0.45 = 0.285 modules added = {2,10}=2; modules removed = {1,4,5,9}=4; modules adjusted = {3,8}=2; 0.5 × 2 0.4 × 4 0.1 × 2 + + = 0.35 8 8 8 =0
=
= 0.7 × 0.285 + 0.3 × 0.35 = 0.305 = 0.242,
Similarly,
= 0.237
Table 1. Machine configurations for Product families A, B, C , and D
Machines
Machine configurations
Group 1 Group 1
Auxiliary modules {1,3,4} {2,3}
Group 2 Group 1
A
B
C
{5,8,9} {8,10} {5,10}
Group 3 Group 2 Group 3
D
Table 2 shows the alternatives with criteria most likely. Weights of the alternatives have calculated with this table. Table 3 shows the Alternatives with criteria minimum, most likely and maximum. Since TRE is evaluated, it has been considered same for min, most likely, and max values. Profit over cost and due date have been assumed for min and max values for the calculation of alternatives as shown in Table 3. Table 2. Alternatives with criteria most likely
Alternatives 1. Product family B 2. Product family C 3. Product family D
Profit over cost (103 INR) 1500 1300 1700
TRE 0.305 0.242 0.237
Due date (days) 22 28 20
Table 3. Alternatives with criteria minimum, most likely and maximum
Alternatives
1. Product family B 2. Product family C 3. Product family D
Profit over cost (103 INR)
min
TRE most likely
max
min
0.305 0.242 0.237
0.305 0.242 0.237
0.305 0.242 0.237
1400 1250 1500
most likely 1500 1300 1700
Due date (days)
max
min
most likely
1550 1350 1800
15 22 18
22 28 20
max 27 32 22
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Figure 2 Alternatives with uncertainties
1. Results and discussion Using Shannon entropy, weights of the criteria have been calculated as 0.2952, 0.2564 and 0.4484. It shows that weight of due date is the highest. Reason of this is that there is more variation in the due date in comparison to reconfiguration effort and profit over cost. Normalized values of alternatives of reconfiguration effort, profit over cost, and due date for alternatives have been calculated and shown in Table 4. Alternative scores of the product families have been calculated using MARE and shown in Table 5. Figure 2 shows the uncertainty in alternatives. It shows that product family B has the highest uncertainty and product family C has the lowest uncertainty. Product family D has the highest most likely alternative score while product C has the lowest most likely score. If the part families are scheduled for most likely alternatives, schedule will be D – B – C. If part families are scheduled for the less uncertainty, schedule will be C – D – B. If part families are scheduled considering the ratio of most likely to uncertainty, schedule will be D – C – B. Table 4. Normalized values of reconfiguration effort, profit over cost and due date
Alternatives 1. Product family B 2. Product family C 3. Product family D
Profit over cost
Due date
min
TRE most likely
max
min
most likely
max
min
most likely
0.7770
0.7770
0.7770
0.7778
0.8333
0.8611
0.5556
0.6818
1.0000
0.9793
0.9793
0.9793
0.6944
0.7222
0.7500
0.4688
0.5357
0.6818
1.0000
1.0000
1.0000
0.8333
0.9444
1.0000
0.6818
0.7500
0.8333
Table 5. Alternative scores of part families
Alternatives 1. PRODUCT B 2. PRODUCT C 3. PRODUCT D
Min 0.6779 0.6773 0.8146
Most likely 0.7488 0.7145 0.8737
Maximum 0.8986 0.7871 0.9253
Uncertainty
Ratio
Rank
0.2207 0.1089 0.1107
3.3934 6.5082 7.8940
3 2 1
max
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2. Conclusions In the present work, an integrated approach of Shannon entropy and MARE has been used for the scheduling of the products. Methodology has been validated by means of illustrative example. Illustrative example is inspired by the research work done by the author in Continental Automotive industry. On the basis of work done, following points can be concluded. 1. In the present work methodology for calculating reconfiguration effort for a multi-product line has been discussed. 2. Shannon entropy method has been discussed and weights of the criteria have been calculated using this method. It shows that for problem considered, weight of due date is the highest. Weights of the criteria have been determined as 0.2952, 0.2564, and 0.4484. 3. MARE method has been discussed and ranking of the alternatives have been calculated using this method. It provides not only the ranking of the alternatives but also the uncertainty in the alternatives. If the part families are scheduled for most likely alternatives, schedule will be D – B – C. If part families are scheduled for the less uncertainty, schedule will be C – D – B. If part families are scheduled considering the ratio of most likely to uncertainty, schedule will be D – C – B. References [1] Koren Y, Gu X, Guo W (2017). Reconfigurable manufacturing systems: Principles, design, and future trends. Frontiers of Mechanical Engineering DOI: 10.1007/s11465-018-0483-0 [2] Koren Y (2006) General RMS characteristics. comparison with dedicated and flexible systems. In: Dashchenko AI (ed) Reconfigurable Manufacturing Systems and Transformable Factories, Springer Berlin Heidelberg, Berlin, Heidelberg, pp 27-45, DOI 10.1007/3-540-293973_3 [3] Prasad D, Jayswal SC (2017) Reconfigurability consideration and scheduling of products in a manufacturing industry. International Journal of Production Research DOI 10.1080/00207543.2017.1334979 [4] Prasad D, Jayswal SC (2017) Design of reconfigurable manufacturing system. In: National conference on Futuristics in Mechanical Engineering (FME-2016), Madan Mohan Malaviya University of Technology, Gorakhpur, India [5] Oke A, Abou-El-Hossein K, Theron NJ (2011) The design and development of a reconfigurable manufacturing system. South African Journal of Industrial Engineering 22(2):121-132 [6] Lee GH (1997) Reconfigurability consideration design of components and manufacturing systems. The International Journal of Advanced Manufacturing Technology 13(5):376-386 [7] Youssef AM, ElMaraghy HA (2006) Assessment of manufacturing systems reconfiguration smoothness. The International Journal of Advanced Manufacturing Technology 30(1-2):174-193 [8] Koren Y, Shpitalni M (2010) Design of reconfigurable manufacturing systems. Journal of manufacturing systems 29(4):130-141 [9] Koren Y (2013) The rapid responsiveness of rms. International Journal of Production Research 51(23-24):6817-6827 [10] Makinde O, Mpofu K, Popoola A (2014) Review of the status of reconfigurable manufacturing systems (RMS) application in south africa mining machinery industries. Procedia CIRP 17:136-141 [11] Oke A, Abou-El-Hossein KA, Theron NJ (2011) Reconfigurability approach in manufacture of moulds and dies. In: Advanced Materials Research, Trans Tech Publ, vol 264, pp 1708-1713 [12] Abdi MR, Labib AW (2003) A design strategy for reconfigurable manufacturing systems (RMSs) using analytical hierarchical process (ahp): a case study. International Journal of production research 41(10):2273-2299 [13] Prasad D, Jayswal SC (2017) Case study of a reconfigurable manufacturing industry. In: Chauhan AK (ed) International Conference on Innovations and Developments in Mechanical Engineering (IDME17), KNIT Sultanpur, India, pp 32-36 [14] Prasad D, Jayswal SC (2017) Scheduling of Products for Reconfiguration Effort in Reconfigurable Manufacturing System.
In 7th
International Conference of Materials Processing and Characterization (ICMPC 2017), (GRIET Hyderabad, India), 17-19 March 2017. [15] Hodgett RE, Martin EB, Montague G, Talford M (2014) Handling uncertain decisions in whole process design. Production Planning & Control. 25(12):1028-38.
ScienceDirect Materials Today: Proceedings 5 (2018) 18451–18458
www.materialstoday.com/proceedings
ICMPC_2018
Scheduling in reconfigurable manufacturing system for uncertainty in decision variables Durga Prasada*, S.C. Jayswalb
a,b
Mechanical Engineering Department, Madan Mohan Malaviya University of Technology, Gorakhpur-273010 (U.P.), India
Abstract Reconfigurable manufacturing system is a new type of responsive manufacturing system which can adjust its setup to adjust its capacity and functionality with least effort and time when the demand for the product changes. Reconfigurable manufacturing system (RMS) has the exact capacity and functionality whenever is required. In the present work, an integrated approach of Shannon entropy and multi-attribute range evaluation (MARE) has been used for scheduling of the products. Weights of criteria have been calculated using Shannon entropy and ranking is obtained using MARE. MARE calculates the uncertainty of decision variables into the uncertainty of ranking. For scheduling of products, three criteria have been considered; reconfiguration effort, profit over cost and due date. © 2018 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of Materials Processing and characterization. Keywords: reconfigurable manufacturing system; reconfiguration effort; scheduling; shannon entropy, multi-attribute range evaluation
1. Introduction and literature review Reconfigurable manufacturing system is a new type of manufacturing system which can change its capacity and functionality very easily and quickly whenever required. RMS (reconfigurable manufacturing system) has capacity and functionality exactly what is required. RMS is adjustable to the fluctuating demands and it can be easily upgraded with new process technology. Reconfigurable manufacturing systems (RMSs), which possess the advantages of both dedicated serial lines and flexible manufacturing systems, were introduced in the mid-1990s to
* Corresponding author. Tel.: +915516050030. E-mail address: [email protected] 2214-7853 © 2018 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of Materials Processing and characterization.
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Durga Prasad et al./ Materials Today: Proceedings 5 (2018) 18451–18458
address the challenges initiated by globalization. The principal goal of an RMS is to enhance the responsiveness of manufacturing systems to unforeseen changes in product demand [1]. RMS has six key characteristics which are modularity, integrability, scalability, convertibility, customization, and diagnosability. The key characteristics customization, scalability, and convertibility are essential RMS characteristics, while the other three (modularity, integrability, and diagnosability) reduce the system configuration time and its ramp-up time [2-4]. Reconfigurable manufacturing system has been evolved from dedicated manufacturing system. With the concept of using the modular machine, the concept of reconfiguration arises. But it is not limited to modular machines. Some researchers have given the concept of reconfiguration by material handling systems [5], reconfiguration by relocation [6], reconfiguration process plan [7] etc. Koren et al. [8] has given the concept of practical reconfigurable manufacturing system using cell gantry and spine gantry. It is a special type of layout of flexible manufacturing system. Later reconfigurable machines were added in manufacturing system [9]. Reconfigurability has been reviewed in mining industry [10], mold and die making industry [11], Arvin Meritor [12], Powertrain industry [9], Continental Automotive [3, 13] etc. Scheduling is the one of the most important steps in production control. Scheduling may be defined as “Fitting specific job into a general time-table so that orders may be manufactured in accordance with contracted liability or in mass production, so that each component may arrive and enter to assembly in order and at time it is required. In other words, scheduling is that phase of production control which rates the work in order of its priority and provide for its release to the plant at the proper time and in correct sequence.” Thus, scheduling is concerned with when work shall be performed on a product or part. Scheduling in manufacturing system can be done on the basis of some rules such as, FCFS (First come first serve), LCFS (Last come first serve), SPT (Shortest processing time), LPT (Longest processing time), EDT Earliest due date, Maximum profit over cost, Reconfiguration cost/ Reconfiguration effort, Random (on the choice of manager). Scheduling can be done for one criterion as mentioned above or more than one criterion. If more than one criterion is considered, MCDM can be used. Prasad et al. used integrated approach of Shannon entropy and TOPSIS [14] and integrated approach of Shannon entropy and RIM (reference ideal method) [3] for scheduling in reconfigurable manufacturing system. In this paper integrated approach of Shannon entropy and MARE (Multi Attribute Range Evaluation) has been used for scheduling in reconfigurable manufacturing system. The main advantage of using Shannon entropy is that it calculates the weights of the criteria by solving the mathematical model and weights depend on the variance of the decision variables. The advantage of MARE is that it calculates the uncertainty of decision variable into uncertainty of alternatives so that alternatives can be selected on the basis of alternative score and alternative’s uncertainty [15]. This paper also discusses the concept of total reconfiguration effort. 2. Methodology In this paper methodology to calculate reconfiguration has been discussed and scheduling has been done by integrated approach of Shannon entropy and MARE. Therefore, methodology section has been divided into two subsections; (i) Criteria considered. (ii) Integrated approach of Shannon entropy and MARE 2.1. Criteria considered In present work, three criteria have been considered, reconfiguration effort, profit over cost and due date. 2.1.1. Reconfiguration effort Reconfiguration effort (RE) is the effort for changing the set-up of the manufacturing system from one product/product family to another product/product family whether it is for hardware component or for the software component. Reconfiguration effort can be at three levels, market level reconfiguration effort, system level reconfiguration effort, and machine level reconfiguration effort. The market level reconfiguration effort (MKRE) is associated with the activities that are performed outside the boundaries of the manufacturing system such as financial activities, shipping activities, bidding activities, logistic activities etc., that are associated with purchasing new machines or machine modules, selling old machines or modules and renting machines or modules. System level reconfiguration effort (SRE) is associated with the activities
Durga Prasad et al./ Materials Today: Proceedings 5 (2018) 18451–18458
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that are performed within the boundaries of the manufacturing system but at a level higher than machines. These activities include adding, removing or adjusting the machines in the system, relocating the machines and changing the material flow path. Machine level reconfiguration effort (MRE) is associated with the activities that are performed inside the boundaries of the manufacturing system and are all within the limits at the machine level. These activities include the adding, removing or adjusting machine modules and adding, removing or adjusting operation clusters. For all the activities reconfiguration effort is calculated separately by considering machines and/or modules added, removed or adjusted. Total reconfiguration effort (TRE) can be calculated as the weighted sum of the all three level reconfiguration efforts, Equation 1. + + (1) = where , , are weights assigned to the all three types of reconfiguration effort. + + =1 In present case, only two types activities have been considered, (i) addition/removal of machines (system level) and (ii) addition and removal of modules (machine level) System level reconfiguration effort can be calculated as / /
.
=
.
+
.
+
(2)
, , are the weights assigned to addition, removal and adjustment respectively.
>
>
and
+
+
=
1. +
= where
,
,
+
(3)
are weights assigned to the all three types of reconfiguration effort.
Machine level reconfiguration effort can be calculated as General formula for reconfiguration effort can be written as, =
′
.
+
′
.
+ ′
.
Where ′, ′, ′ are the weights assigned to addition, removal and adjustment respectively. ′ > ′ + ′ + ′ = 1.
(4) ′ > ′ and
If in a manufacturing system, there are n modular machines which are needed to be reconfigured for another type of product, total number of modules added, removed or readjusted can be calculated by using following formulas. . .
= ∑
(
= ∑
× (
= ∑
. = ∑ = +
(
) ×
(
) ×
)
× +
where N i = number of machine required for ith operation; M i = machine required for ith operation
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Durga Prasad et al./ Materials Today: Proceedings 5 (2018) 18451–18458
2.1.2. Profit over cost Profits are the difference between revenues and costs. Profit over cost can be calculated by multiplying the number of products produced i.e. demand of the product to the profit per product. Profit over cost depends on the demand of the product and demand is an important factor in a manufacturing system. Higher profit is the goal of an industry, hence it has been considered as a criterion for scheduling. 2.1.3. Due date Another criterion which has been considered is due date. If due date is close i.e. there are fewer days left for delivery, then its priority should be high. 2.2. Integrated approach of Shannon entropy method and multi attribute range evaluation In the problem integrated approach of Shannon entropy method and MARE (Multi Attribute Range Evaluation) have been used. Weights of each criterion have been determined by using Shannon entropy method and ranking of the alternatives has been obtained by MARE, Figure 1. Since each criterion has different meaning, equal weights of each criterion can’t be considered. Weights can be determined by two ways. First, by preference of decision maker, for example AHP method, Delphi method and weighted least square method, etc. Second, by solving mathematical model, for example entropy method, principal element analysis, multiple objective programming, etc. [3,14]. In present work entropy method has been used to determine the weights
Figure 1 Integrated approach of Shannon Entropy and MARE
Durga Prasad et al./ Materials Today: Proceedings 5 (2018) 18451–18458
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where, = Performance value of alternative i when it is evaluated in terms of criterion j, i = 1,2,…,m and j = 1,2,…, Integrated approach of Shannon Entropy and MARE has following steps Step 1: Establish the decision matrix Step 2: Normalize the decision matrix =
∑
Step 3: Compute entropy ℎ = −ℎ
. ln
Where ℎ is the entropy constant and is considered equal to: ℎ = (ln ) = 0, if =0 and . ln Step 4: Set = 1 − ℎ , as the degree of diversification. Step 5: Set
=∑
as the degree of importance of attribute j
Step 6: Establish the decision matrix. Each criterion has three values; minimum maximum Step 7: Normalize the decision matrix*. If max value is desired, ∗ = If min value is desired,
∗
=
, most likely
, and
( ) ( )
Max and min values are selected for min, most likely and max values for each criterion. ∗ ∗ and are interchanged. If min value is desired for jth criterion, Step 8: Calculate alternative score separately for min, most likely, and max decision variables. ∗ = ∑ ∗ = ∑ ∗ = ∑ Step 9: Calculate the uncertainty in alternatives i as = − Step 10: Calculate ratio of most likely alternative to uncertainty, Select the alternative which has the highest ratio. 3. Problem Formulation Problem used in the illustrative example is inspired by the research work done by the author in Continental Automotive Components (India) Pvt. Ltd and given in [3]. It is also extended form of [14]. In this problem, there are seven machines. Machines have been grouped as group 1, group 2 and group 3 as shown in Table 1. Machine M2 are and and M4 are modular machines which can change their configurations. Configurations of machine . Configurations of machine are , and . Auxiliary modules are {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Four types of product families are manufactured named as product family A, B, C and D. = 0, = 0.7, = 0.3, = 0.6 , = 0.3 , = 0.1 , = 0.5, = 0.4, = 0.1 , ′ = 0.5, ′ = 0.4, ′ = 0.1 . Most likely values of profit over cost and due date are given in Table 2 and minimum, most likely and maximum values of these criteria have been shown in Table 3. If initially product family A is running in manufacturing system, then system can be reconfigured for product family B, product family C and product family D.
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Reconfiguration effort for changing the configuration from A to B, Group-1 machine added ={ }=0; machine removed ={M1 }=1; machine adjusted ={M2, M4 }=2; 0.5 × 0 0.4 × 1 0.1 × 2 = + + = 0.2 3 3 3 Similarly, = 0.4, = 0.45 = 0.6 × 0.2 + 0.3 × 0.4 + 0.1 × 0.45 = 0.285 modules added = {2,10}=2; modules removed = {1,4,5,9}=4; modules adjusted = {3,8}=2; 0.5 × 2 0.4 × 4 0.1 × 2 + + = 0.35 8 8 8 =0
=
= 0.7 × 0.285 + 0.3 × 0.35 = 0.305 = 0.242,
Similarly,
= 0.237
Table 1. Machine configurations for Product families A, B, C , and D
Machines
Machine configurations
Group 1 Group 1
Auxiliary modules {1,3,4} {2,3}
Group 2 Group 1
A
B
C
{5,8,9} {8,10} {5,10}
Group 3 Group 2 Group 3
D
Table 2 shows the alternatives with criteria most likely. Weights of the alternatives have calculated with this table. Table 3 shows the Alternatives with criteria minimum, most likely and maximum. Since TRE is evaluated, it has been considered same for min, most likely, and max values. Profit over cost and due date have been assumed for min and max values for the calculation of alternatives as shown in Table 3. Table 2. Alternatives with criteria most likely
Alternatives 1. Product family B 2. Product family C 3. Product family D
Profit over cost (103 INR) 1500 1300 1700
TRE 0.305 0.242 0.237
Due date (days) 22 28 20
Table 3. Alternatives with criteria minimum, most likely and maximum
Alternatives
1. Product family B 2. Product family C 3. Product family D
Profit over cost (103 INR)
min
TRE most likely
max
min
0.305 0.242 0.237
0.305 0.242 0.237
0.305 0.242 0.237
1400 1250 1500
most likely 1500 1300 1700
Due date (days)
max
min
most likely
1550 1350 1800
15 22 18
22 28 20
max 27 32 22
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Figure 2 Alternatives with uncertainties
1. Results and discussion Using Shannon entropy, weights of the criteria have been calculated as 0.2952, 0.2564 and 0.4484. It shows that weight of due date is the highest. Reason of this is that there is more variation in the due date in comparison to reconfiguration effort and profit over cost. Normalized values of alternatives of reconfiguration effort, profit over cost, and due date for alternatives have been calculated and shown in Table 4. Alternative scores of the product families have been calculated using MARE and shown in Table 5. Figure 2 shows the uncertainty in alternatives. It shows that product family B has the highest uncertainty and product family C has the lowest uncertainty. Product family D has the highest most likely alternative score while product C has the lowest most likely score. If the part families are scheduled for most likely alternatives, schedule will be D – B – C. If part families are scheduled for the less uncertainty, schedule will be C – D – B. If part families are scheduled considering the ratio of most likely to uncertainty, schedule will be D – C – B. Table 4. Normalized values of reconfiguration effort, profit over cost and due date
Alternatives 1. Product family B 2. Product family C 3. Product family D
Profit over cost
Due date
min
TRE most likely
max
min
most likely
max
min
most likely
0.7770
0.7770
0.7770
0.7778
0.8333
0.8611
0.5556
0.6818
1.0000
0.9793
0.9793
0.9793
0.6944
0.7222
0.7500
0.4688
0.5357
0.6818
1.0000
1.0000
1.0000
0.8333
0.9444
1.0000
0.6818
0.7500
0.8333
Table 5. Alternative scores of part families
Alternatives 1. PRODUCT B 2. PRODUCT C 3. PRODUCT D
Min 0.6779 0.6773 0.8146
Most likely 0.7488 0.7145 0.8737
Maximum 0.8986 0.7871 0.9253
Uncertainty
Ratio
Rank
0.2207 0.1089 0.1107
3.3934 6.5082 7.8940
3 2 1
max
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2. Conclusions In the present work, an integrated approach of Shannon entropy and MARE has been used for the scheduling of the products. Methodology has been validated by means of illustrative example. Illustrative example is inspired by the research work done by the author in Continental Automotive industry. On the basis of work done, following points can be concluded. 1. In the present work methodology for calculating reconfiguration effort for a multi-product line has been discussed. 2. Shannon entropy method has been discussed and weights of the criteria have been calculated using this method. It shows that for problem considered, weight of due date is the highest. Weights of the criteria have been determined as 0.2952, 0.2564, and 0.4484. 3. MARE method has been discussed and ranking of the alternatives have been calculated using this method. It provides not only the ranking of the alternatives but also the uncertainty in the alternatives. If the part families are scheduled for most likely alternatives, schedule will be D – B – C. If part families are scheduled for the less uncertainty, schedule will be C – D – B. If part families are scheduled considering the ratio of most likely to uncertainty, schedule will be D – C – B. References [1] Koren Y, Gu X, Guo W (2017). Reconfigurable manufacturing systems: Principles, design, and future trends. Frontiers of Mechanical Engineering DOI: 10.1007/s11465-018-0483-0 [2] Koren Y (2006) General RMS characteristics. comparison with dedicated and flexible systems. In: Dashchenko AI (ed) Reconfigurable Manufacturing Systems and Transformable Factories, Springer Berlin Heidelberg, Berlin, Heidelberg, pp 27-45, DOI 10.1007/3-540-293973_3 [3] Prasad D, Jayswal SC (2017) Reconfigurability consideration and scheduling of products in a manufacturing industry. International Journal of Production Research DOI 10.1080/00207543.2017.1334979 [4] Prasad D, Jayswal SC (2017) Design of reconfigurable manufacturing system. In: National conference on Futuristics in Mechanical Engineering (FME-2016), Madan Mohan Malaviya University of Technology, Gorakhpur, India [5] Oke A, Abou-El-Hossein K, Theron NJ (2011) The design and development of a reconfigurable manufacturing system. South African Journal of Industrial Engineering 22(2):121-132 [6] Lee GH (1997) Reconfigurability consideration design of components and manufacturing systems. The International Journal of Advanced Manufacturing Technology 13(5):376-386 [7] Youssef AM, ElMaraghy HA (2006) Assessment of manufacturing systems reconfiguration smoothness. The International Journal of Advanced Manufacturing Technology 30(1-2):174-193 [8] Koren Y, Shpitalni M (2010) Design of reconfigurable manufacturing systems. Journal of manufacturing systems 29(4):130-141 [9] Koren Y (2013) The rapid responsiveness of rms. International Journal of Production Research 51(23-24):6817-6827 [10] Makinde O, Mpofu K, Popoola A (2014) Review of the status of reconfigurable manufacturing systems (RMS) application in south africa mining machinery industries. Procedia CIRP 17:136-141 [11] Oke A, Abou-El-Hossein KA, Theron NJ (2011) Reconfigurability approach in manufacture of moulds and dies. In: Advanced Materials Research, Trans Tech Publ, vol 264, pp 1708-1713 [12] Abdi MR, Labib AW (2003) A design strategy for reconfigurable manufacturing systems (RMSs) using analytical hierarchical process (ahp): a case study. International Journal of production research 41(10):2273-2299 [13] Prasad D, Jayswal SC (2017) Case study of a reconfigurable manufacturing industry. In: Chauhan AK (ed) International Conference on Innovations and Developments in Mechanical Engineering (IDME17), KNIT Sultanpur, India, pp 32-36 [14] Prasad D, Jayswal SC (2017) Scheduling of Products for Reconfiguration Effort in Reconfigurable Manufacturing System.
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