Project and Production Management

1. module 7: Facility Location and Layout Back to main indexexitcontinue Project and Production Management Module 7 Facility Location and Layout Prof Arun Kanda & Prof S.G. Deshmukh, Department of Mechanical Engineering, Indian Institute of Technology, Delhi

2. module 7: Facility Location and Layout MODULE 7: Facility Location and Layout • 1.Issues in Location of Facilities • 2. Mathematical Models for Facility Location • 3. Layout Planning • 4. Computerised Layout Planning 5. Product Layouts 6. Illustrative Examples 7. Self Evaluation Quiz 8. Problems for Practice 9. Further exploration Back to main indexexit

3. module 7: Facility Location and Layout Back to main indexexitBack to module contents 1. Issues in location of Facilities

4. module 7: Facility Location and Layout Back to main indexexitBack to module contents A Case StudyA Decision Model for a Multiple Objective Plant Location ProblemPrem Vrat And Arun KandaINTEGRATED MANAGEMENT, July 1976, Page 27-33

5. module 7: Facility Location and Layout Back to main indexexitBack to module contents OBJECTIVE OF LOCATION • To set up a straw board plant (Packaging material) from industrial waste Plant Sources of Industrial waste Industries needing packaging material

6. module 7: Facility Location and Layout Back to main indexexitBack to module contents RELEVANT FACTORS FOR PLANT LOCATION

7. module 7: Facility Location and Layout Back to main indexexitBack to module contents

8. module 7: Facility Location and Layout Back to main indexexitBack to module contents TRIANGULAR MATRIX

9. module 7: Facility Location and Layout Back to main indexexitBack to module contents APPLYING PARETO PRINCIPLE

10. module 7: Facility Location and Layout Back to main indexexitBack to module contents SUMMARY

11. module 7: Facility Location and Layout Back to main indexexitBack to module contents DECISION MATRIX FOR ALTERNATIVE LOCATIONS

12. module 7: Facility Location and Layout Back to main indexexitBack to module contents 80 P Points 20 L C H Capital Cost NORMAILZATION I

13. module 7: Facility Location and Layout Back to main indexexitBack to module contents D A 80 C1 Points C2 20 B L L’ H Capital Cost NORMALIZATION II

14. module 7: Facility Location and Layout Back to main indexexitBack to module contents NORMALIZATION III 80 60 Points 20 | Restive | Satisfactory Cooperative | Labour Attitudes

15. module 7: Facility Location and Layout Back to main indexexitBack to module contents NORMALIZATION IV On . . . Points O2 O1 X1 X2 - - - - - - Xn

16. module 7: Facility Location and Layout Back to main indexexitBack to module contents 2. Mathematical Models for Facility Location

17. New lathe in a job shop Tool crib in a factory New warehouse Hospital, fire station, police station New classroom building on a college campus New airfield for a number of bases Component in an electrical network New appliance in a kitchen Copying machine in a library New component on a control panel module 7: Facility Location and Layout Back to main indexexitBack to module contents SINGLE FACILITY LOCATION

18. module 7: Facility Location and Layout Back to main indexexitBack to module contents PROBLEM STATEMENT • m existing facilities at locations • P1(a1,b1), P2(a2,b2) … Pm(am,bm) • New facility is to be located at point X (x,y) • d(X,Pi) = appropriately defined distance between X and Pi • Euclidean, Rectilinear, Squared Euclidean • Generalized distance, Network • The objective is to determine the location X so as to minimize transportation related costs Sum (i=1,n) wi d(X,Pi), where wi is the weight associated with the ith existing facility (product of Cost/distance & the expected number of annual trips between X and Pi)

19. module 7: Facility Location and Layout Back to main indexexitBack to module contents SINGLE FACILITY LOCATION P3 (w3) Pn-1 (wn-1) d(X,P3) P2 (w2) d(X,P2) d(X,P n-1) X d(X,Pn) d(X,P1) P1 (w1) Pn (wn)

20. module 7: Facility Location and Layout Back to main indexexitBack to module contents COMMONLY USED DISTANCES Pi (ai,bi) Rectilinear: | (x-ai) | +| (y-bi)| Euclidean : [ (x-ai)2 + (y-bi)2]1/2 Squared Euclidean: [(x-ai)2 +(y-ai)2 ] Other , Network X (x,y) Pi (ai,bi) Pi(ai,bi) X (x,y) X (x,y)

21. module 7: Facility Location and Layout Back to main indexexitBack to module contents RECTILINEAR DISTANCES • Z = Total cost • = Sum (i =1,n) [ wi | (x-ai) + (y-bi)|] • = Sum (i=1,n) [wi |(x-ai)| + wi |(y-bi)| ] • = Sum (i=1,n) wi |(x-ai)| + Sum (i=1,n) wi |(y-bi)| • = f1(x) + f2(y) • Thus to minimize Z we need to minimize f1(x) and f2(y) independently.

22. module 7: Facility Location and Layout Back to main indexexitBack to module contents EXAMPLE 1(RECTILINEAR DISTANCE CASE) • A service facility to serve five offices located at (0,0), (3,16),(18,2) (8,18) and (20,2) is to be set up. The number of cars transported per day between the new service facility and the offices equal 5, 22, 41, 60 and 34 respectively. • What location for the service facility will minimize the distance cars are transported per day?

23. module 7: Facility Location and Layout Back to main indexexitBack to module contents SOLUTION (X-COORDINATE) x* = 8

24. module 7: Facility Location and Layout Back to main indexexitBack to module contents SOLUTION (Y- COORDINATE) y* = 16

25. module 7: Facility Location and Layout Back to main indexexitBack to module contents EXAMPLE 2SQUARED EUCLIDEAN CASE CENTROID LOCATION x* = Σ wi ai /Σ wi =( 0 x5 + 3x22 + 18x41 + 8x60 + 20x34)/162 = 12.12 y* = Σ wibi/Σ wi = (0x5 + 16x22 + 2x41 + 18x60 + 2x34)/162 = 9.77 (Compare with the median location of (8,16)

26. module 7: Facility Location and Layout Back to main indexexitBack to module contents Solution to the euclidean distance location problem Rm R2 m P Mn R1 m+n 2 M2 M1 1 m+2 m+1

27. module 7: Facility Location and Layout Back to main indexexitBack to module contents MINIMAX PROBLEMS For the location of emergency facilities our objective would be to minimize the maximum distance *

28. module 7: Facility Location and Layout Back to main indexexitBack to module contents COST CONTOURS Increasing Cost Cost Contours help identify alternative feasible locations

29. module 7: Facility Location and Layout Back to main indexexitBack to module contents SUMMARY • Decision Matrix approach to handle multiple objectives in Plant Location (problem of choosing the best from options) • Single Facility Location Models • Rectilinear distance • Squared Euclidean • Euclidean distance • (to generate the best from infinite options)

30. module 7: Facility Location and Layout Back to main indexexitBack to module contents SUMAARY(CONTD) • Notion of Minisum and Minimax problem (Objective depending on the context) • Use of Cost Contours to accommodate practical constraints (Moving from ideal to a feasible solution)

31. module 7: Facility Location and Layout Back to main indexexitBack to module contents Location decisions are STRATEGIC • LIABLE TO AFFECT THE ENTIRE ORGANIZATION • OPERATIVE OVER LONG TIME SPANS • DIFFICULT TO REVERSE • CAPITAL INTENSIVE

32. module 7: Facility Location and Layout Back to main indexexitBack to module contents Location of ‘Plant’ HIERARCHY OF LOCATION PROBLEMS Plant Layout ( Location of ‘Depts’) Physical Arrangements of M/cs Work Place Layout ( Location of ‘tools’ or ‘raw materials’)

33. module 7: Facility Location and Layout Back to main indexexitBack to module contents The term ‘FACILITY LOCATION’ emphasizes the generalized approach that handles the variety of above mentioned problems.

34. module 7: Facility Location and Layout Back to main indexexitBack to module contents LOCATION DECISIONS ARE DYNAMIC Owing to changing technology, competition, change of consumer tastes, decisions like • NEW PLANTS • EXPANSION • DECENTRALIZATION • PLANT SHUTDOWN ARE CONSTANTLY UNDER REVIEW

35. module 7: Facility Location and Layout Back to main indexexitBack to module contents IMPORTANT FACTORS IN LOCATION • MARKET • RAW MATERIALS • TRANSPORTATION • POWER • CLIMATE AND FUEL • LABOUR AND WAGES • LAWS AND TAXATION • COMMUNITY SERVICES • WATER AND WASTE • GOVT. INCENTIVES

36. module 7: Facility Location and Layout Back to main indexexitBack to module contents ANNUAL OPERATION EXPENSES CONSIST OF • MATERIALS • TRANSPORTATION • REAL ESTATE TAXES • FUEL COSTS • SUNDRY STATE TAXES • ELECTRIC POWER • WATER

37. module 7: Facility Location and Layout Back to main indexexitBack to module contents Location A FIXED & VARIABLE COST Location B Annual Cost Volume of Production

38. module 7: Facility Location and Layout Back to main indexexitBack to module contents MECHANICAL ANALOGUE FOR FINDING BEST LOCATION OF A MANUFACTURING PLANT (ALSO KNOWN AS VARIGNON’S FRAME AFTER INVENTOR)

39. module 7: Facility Location and Layout Back to main indexexitBack to module contents Rm R2 m P Mn R1 m+n 2 M2 M1 1 m+2 m+1

40. module 7: Facility Location and Layout Back to main indexexitBack to module contents • Assumptions: • R1,R2, ……Rm Locations of Raw Material Sources • M1,M2 …Mn location of markets • Euclidean (Straight tine travel) • Each weight (there are m+n in all • Wi = No. of annual trips between P and that pt X (Cost per unit distance) In the absence of friction, the common knot P of (m+n) strings comes to equilibrium at least Cost location [Here we draw an analogy between Min. Potential Energy & Min. Travel Cost ]

41. module 7: Facility Location and Layout Back to main indexexitBack to module contents MULTI-OBJECTIVE CONSIDERATIONS IN LOCATION DECISIONS FACTORS AFFECTING LOCATION ARE : SUBJECTIVE / OBJECTIVE (labour attitudes) (eg. Costs) INTANGIBLE / TANGIBLE INCOMMENSURATE UNITS

42. module 7: Facility Location and Layout Back to main indexexitBack to module contents A Decision Matrix approach with proper evaluation of weights of factors, Normalization of scores can help in ranking alternative locations. (THIS IS DEMONSTRATED THROUGH A CASE STUDY)

43. module 7: Facility Location and Layout Back to main indexexitBack to module contents MULTI PLANT OPERATION - AN EXAMPLE OF PLANT ADDITION P1 A P1 Existing plant P2 Existing plant A,B,C,D,E Warehouses X,Y,Z Possible Locations for new plant P2 C B Y D X E Z

44. module 7: Facility Location and Layout Back to main indexexitBack to module contents Owing to increase of weekly demand to 72,000 there is a capacity deficit of 25,000/wk and it is felt that a plant of capacity 25000 could be set up X,Y or Z.

45. module 7: Facility Location and Layout Back to main indexexitBack to module contents Problem Data

46. module 7: Facility Location and Layout Back to main indexexitBack to module contents OPTIMUM PRODUCTION - DISTRIBUTION SOLUTIONS Product Cost = 192,500 Distn. Cost = 026,450 Total = 218,950

47. module 7: Facility Location and Layout Back to main indexexitBack to module contents OPTIMUM PRODUCTION -DISTRIBUTION SOLUTIONS (Cont.) Product Cost = 193,750 Distn. Cost = 026,960 Total = 220,710

48. module 7: Facility Location and Layout Back to main indexexitBack to module contents OPTIMUM PRODUCTION -DISTRIBUTION SOLUTIONS (Cont.) Product Cost = 192,000 Distn. Cost = 026,400 Total = 218,400* (* MINIMUM) (Demand and Capacity in thousands) hence choose plant at size Z

49. module 7: Facility Location and Layout Back to main indexexitBack to module contents LOCATIONAL DYNAMICS • Suppose third plant is set up at site Z. • After some time demand drops from, 72,000 to 56,000 per week • Which plant to shut down ? Which to run at partial capacity ? (These are again location decisions)

50. module 7: Facility Location and Layout Back to main indexexitBack to module contents Alternatives for investigation : 1. Run all plants at partial capacity 2. SHUT DOWN P1, Use Overtime in others 3. SHUT DOWN P2, Use Overtime in others 4. SHUT DOWN Z, Use Overtime in others