DESIGN OF ROBUST PLANT LAYOUT FOR DYNAMIC PLANT LAYOUT PROBLEM (cont.…)

SREEPATHY R NAIKIEM 2014-16NIT CALICUT

Simulated annealing methodologyHow simulated annealing works explained using a simple problem

•In 1953 Metropolis created an algorithm to simulate the annealing process

•The algorithm simulates a small random displacement of an atom that results in a change in energy

•If the change in energy is negative, the energy state of the new configuration is lower and the new configuration is accepted

•If the change in energy is positive, the new configuration has a higher energy state

•However, it may still be accepted according to the Boltzmann probability factor:

Example problem Route sheet and demand matrix are given

Route sheet,

Demand matrix,

From these matrices flow matrix can be found out

Example problem(cont.)

Flow matrix =

Now lets consider 3 iterations of the solution using simulated annealing

Initial temperature =464

Sample taken at each temperature=5

Cooling rate=.98

Final temperature=3

Example problem(cont.) Initially a random layout is generated by the algorithm

Initial layout=

Distance matrix= ;MHC matrix=

TMHC=490

Example problem(cont.) New layout=

Distance matrix= ; MHC matrix=

TMHC=435

Example problem(cont.) Check whether to accept or reject the new layout

Calculate Δ=current TMHC- previous TMHC =490-435 =55

If ,then accept the solution (ie. Δ<0)

Else use Metropolis criterion (ie. Δ>0) ,which is the case here

P =exp(-Δ/T) =exp(-55/464) = 0.888Random number is generated ,R= 0.426As P>R it is accepted (else it will be rejected)

Example problem(cont.)

New temperature = cooling rate x previous temperature = 0.98 x 464 = 454.72

The procedure is repeated for various layouts ,here for single temperature 5 sample are takenFinally when the temperature reaches the termination condition ,T=3suppose Δ=55P=exp(-55/3) =1.091 xProbability of selection will be very small such that no alternatives are accepted

NUMERICAL DEMONSTRATION AND ANALYSIS OF RESULTS•Data set used for evaluating the performance of the layout formation method consists of data from case studies from Yaman et al. (1993), Chan et al. (2004) and QAPLIB website (2007).

•Data used from QAPLIB website (2007) consists of problems of Nugent et al. and Wilhelm and Ward (1987). Data from Yaman et al. (1993), Chan et al. (2004)

•Data obtained from Balakrishnan and Cheng (2009) are used to demonstrate the performance of robust layout model

•The cost per unit part movement is taken as 10 (ω = Rs.10/unit traveling score)

•The part transportation quantity per move is taken as 1 ( = 1)

Results of Yaman et al. (1993) case and Chan et al. (2004)•The data set of Yaman et al. (1993) consists of five periods in the planning horizon and five parts to process with nine machines

•For each part in the family, the operational sequence and demand in a five-period planning horizon are provided in Tables 1 and 2, respectively

•Chan et al. (2004) proposed a part-handling factor for Yaman et al. (1993) case and are given in Table 3

•Table 1:Machine operational sequence of Yaman et al. (1993) case

Results of Yaman et al. (1993) case and Chan et al. (2004) (cont..)•Table 2:Demand profiles in Yaman et al. (1993) case

•Table 3:Proposed part-handling factors by Chan et al. (2004) for Yaman et al. (1993) case

Results of Yaman et al. (1993) case•Table 4:Expected demand profile of the parts

•Table 5:Robust layout with SA method and its total traveling score for expected demand profile when =1 and = 1

•Table 6:Robust layout material handling cost of each period () and TMHC of planning horizon when =1 and = 1

Results of Chan et al. (2004) caseThe above problem(Yaman et. al.) is also solved by including part handling factor ()The robust layout procedure suggested in this paper provides less total MHC under dynamic demand. This shows the better performance of the proposed layout model (robust) and relocation of machines from one period to the next is also not necessary

•Table 7:Robust layout with SA method and its total traveling score for expected demand profile when is varying and = 1

Results of Chan et al. (2004) case

•Table 8:Robust layout material handling cost of each period (MHCp) and TMHC of planning horizon when is varying and = 1

•Table 9:Comparison of results of Chan et al. (2004) and the results of robust approach for various problem cases

Results of case study from Balakrishnan and Cheng•The performance of robust layout model using the data obtained from Balakrishnan and Cheng are analyzed

•These data set consists of eight problems in each of the six situations (6 –departments 5 and 10 periods; 15 – departments 5 and 10 periods; and 30 – departments 5 and 10 periods) and thus a total of 48 problems which are solved using proposed robust model for DPLP

•The results of the robust approach solution values are not significantly different compared to the values obtained by Balakrishnan and Cheng, although there is no relocation of facilities and no operational disruptions in any periods of planning horizon in the robust method

Results of case study from Balakrishnan and Cheng(cont.)

•The following research papers on adaptive approach are used for comparison of results of robust approach for Balakrishnan and Cheng’s data set

1. Conway and Venkataramanan (1994) – Conway and Venkataramanan Genetic Algorithm (CVGA)

2. Balakrishnan and Cheng (2000) – Nested Loop Genetic Algorithm (NLGA)

3. Baykasoglu and Gindy (2001) – Simulated Annealing (SA)

4. Balakrishnan et al. (2003) – Genetic Algorithm with Dynamic Programming (GADP)

5. Baykasoglu et al. (2006) – Ant colony

6. McKendall et al. (2006) – Modified SA-I and SA-II

•For the robust approach, the solution values show (for 8 sets of data in each size of problem) 0.32–1% deviation among periods of planning horizon and 2.1–9.89% deviation for the entire planning horizon from the best results of adaptive approach

•Table 10:Robust approach results for the data of Balakrishnan and Cheng using proposed method

•Table 11:Comparison of adaptive and robust approach results for the 8-data set of 6 Department and 5 Period problems

Total penalty cost (TPC)•The Total Penalty Cost (TPC) suggested by Braglia et al. (2003) is used to test the suitability of the suggested layout to be a robust layout for the given data set

•The TPC is defined as the minimum re-layout cost acceptable to support an agile strategy

Where, is the material handling cost when robust layout is applied to period p, is Material handling cost of optimum layout of the period p

Total penalty cost (cont.…)•They established that the maximum acceptable limit of TPC for a layout to be robust is 15%

•Eg. For 6-departments 5-periods ,data1 problemMHC for robust with SA=106419

MHC for agile with zero relocation cost =98229

TPC=

•TPC is calculated for all the data set and, it is within the specified limit and hence we can infer that the robust layout strategy is suitable for the given data set

•A poor TPC (high value) of a layout may be interpreted as the need for an agile plant suitable for frequent relocation of the facility

CONCLUSIONSSA based meta-heuristic is developed for solving layout formation problemsA robust layout procedure is developed for dynamic environment, which generate a layout for an expected demand scenarioEven though, this layout may not be optimal for any period in the planning horizon, the performance of this layout over the entire period of the planning horizon is betterThe robust approach has been applied to the problems from Chan et al. (2004). The results show that the developed robust method provides better performance compared to sameFor standard DPLP problems from Balakrishnan and Cheng, the MHC for the layouts from the robust method are not significantly different from the best results for the adaptive approach

CONCLUSIONS

The robust approach has the advantage of no relocation of facilities in the periods of planning horizon and hence no disruptions of the operations. Also it is computationally efficient compared to the adaptive model

The robustness of the layouts is measured with the Total Penalty Cost (TPC) as suggested in Braglia et al. (2003). TPC is calculated for 48-data set from Balakrishnan and Cheng and it is within the percentage mentioned in Braglia et al. (2003)

The suggested robust layout procedure provides good robust layout for the given problem situations

Future scope•The present algorithms for DPLP consider only single objectives. Multiple objective cases of DPLP can also be modeled and solved

•Unequal department areas and multiple floors cases of DPLP can be modeled and solved

•A rolling horizon type planning horizon can be considered for DPLP and based on a trade off, changes in layout may be considered under this type of planning horizon.

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