Facility Layout. Emma Ross. September 2, Emma Ross () Facility Layout September 2, / 21

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1 Facility Layout Emma Ross September 2, 2010 Emma Ross () Facility Layout September 2, / 21

2 The Problem Q: Where do we put machines on the production floor? Emma Ross () Facility Layout September 2, / 21

3 The Problem Q: Where do we put machines on the production floor? What makes a good layout? Companies want to run their factories as cheaply as possible to maximise profits But how do we calculate this cost? Emma Ross () Facility Layout September 2, / 21

4 How do we find the cost? (1) Emma Ross () Facility Layout September 2, / 21

5 How do we find the cost? (1) Cost (per unit) for transporting materials between places in the factory. c ij =cost per unit flow from place i to place j. Do not want machines far apart, transportation will be complicated and hence costly. Emma Ross () Facility Layout September 2, / 21

6 How do we find the cost? (1) Cost (per unit) for transporting materials between places in the factory. c ij =cost per unit flow from place i to place j. Do not want machines far apart, transportation will be complicated and hence costly. c12 = c 21 =10 c 13 = c 31 =30 c 23 = c 32 =20 Emma Ross () Facility Layout September 2, / 21

7 How do we find the cost? (2) Total cost of the layout: n n c ij f ij i=1 j=1 where f ij = flow between machine i and j, and n=number of machines. Emma Ross () Facility Layout September 2, / 21

8 How do we find the cost? (2) Total cost of the layout: n n c ij f ij i=1 j=1 where f ij = flow between machine i and j, and n=number of machines. Example Total Cost = (f 21 c 21 ) + (f 23 c 23 ) = (6 10)+(2 20) = 100 Emma Ross () Facility Layout September 2, / 21

9 The Model Objective Function: Min N N N i M j K i=1 j=1 n i =1 m j =1 k=1 l=1 K f ni m j c kl x ni k x mj l (1) Where { 1 if nth machine of type i is assigned to location k x ni k = 0 otherwise Emma Ross () Facility Layout September 2, / 21

10 Constraints: N N i=0 n i =1 K x ni k = 1, (2) k=1 N i i=1 n i =1 N i N i n i =1 m j =1 N x ni k = 1, (3) f ni m j t mj p c mj, (4) N j N i i=0 n i =1 f ni m j = f ij, (5) f ni m j = N N q q=0 r q=1 f mj r q. (6) Each machine is only at one location... Each loaction has only 1 machine... Use of machine doesn t exceed its capacity... Total flow for machine type = sum over copies... Input flow = Output flow, nothing lost inside. Emma Ross () Facility Layout September 2, / 21

11 But there s so much more to consider! This problem in the real world is VERY complicated. Our model is extremely simple - there are many other variables and factors which can be (and are) encorporated into other models; Emma Ross () Facility Layout September 2, / 21

12 But there s so much more to consider! This problem in the real world is VERY complicated. Our model is extremely simple - there are many other variables and factors which can be (and are) encorporated into other models; Different sized machines Emma Ross () Facility Layout September 2, / 21

13 But there s so much more to consider! This problem in the real world is VERY complicated. Our model is extremely simple - there are many other variables and factors which can be (and are) encorporated into other models; Different sized machines Different layout of positions Emma Ross () Facility Layout September 2, / 21

14 But there s so much more to consider! This problem in the real world is VERY complicated. Our model is extremely simple - there are many other variables and factors which can be (and are) encorporated into other models; Different sized machines Different layout of positions Range of products (not just the one) Emma Ross () Facility Layout September 2, / 21

15 But there s so much more to consider! This problem in the real world is VERY complicated. Our model is extremely simple - there are many other variables and factors which can be (and are) encorporated into other models; Different sized machines Different layout of positions Range of products (not just the one) Preparing for changing demand - Robustness Emma Ross () Facility Layout September 2, / 21

16 But there s so much more to consider! This problem in the real world is VERY complicated. Our model is extremely simple - there are many other variables and factors which can be (and are) encorporated into other models; Different sized machines Different layout of positions Range of products (not just the one) Preparing for changing demand - Robustness Machine copies worked equally... etc. Emma Ross () Facility Layout September 2, / 21

17 Approaches Traditional: simple e.g. Functional Layout Emma Ross () Facility Layout September 2, / 21

18 Approaches Traditional: simple e.g. Functional Layout More modern: algorithmic. Increasingly complicated, including many influencing factors Traditional is too simple but the more complex methods are so complicated that they can only solve small problems. Emma Ross () Facility Layout September 2, / 21

19 Where our model comes in Intent: Emma Ross () Facility Layout September 2, / 21

20 Where our model comes in Intent: Apply this basic optimisation model to numerically small problems which can be easily solved. Experiment by changing variables such as Demand Volume, Job type, Machine capacities. Try to spot emerging patterns in the optimal layouts. Emma Ross () Facility Layout September 2, / 21

21 Where our model comes in Intent: Apply this basic optimisation model to numerically small problems which can be easily solved. Experiment by changing variables such as Demand Volume, Job type, Machine capacities. Try to spot emerging patterns in the optimal layouts. Find a way to characterise an optimal layout by words. Apply results to larger more realistic problems. Emma Ross () Facility Layout September 2, / 21

22 Experimentation Emma Ross () Facility Layout September 2, / 21

23 Experimentation MPL Optimisation Software Emma Ross () Facility Layout September 2, / 21

24 Experimentation MPL Optimisation Software Input Model (objective, constraints and a demand volume) Datafile for costs Datafile for the machines capacities Emma Ross () Facility Layout September 2, / 21

25 Experimentation MPL Optimisation Software Input Model (objective, constraints and a demand volume) Datafile for costs Datafile for the machines capacities Output A table indicating where machines should go (the layout design) A table describing the flow Emma Ross () Facility Layout September 2, / 21

26 Unhelpful output format Machine Place Activity Reduced Cost 0 po p p p pt m1 po m1 p m1 p m1 p m1 pt (n + 2) 2 rows in the design table - so 3 machines: 21 rows of numbers, 10 machines: 144 rows. Emma Ross () Facility Layout September 2, / 21

27 I get by with a little help from R R Program: Layout Emma Ross () Facility Layout September 2, / 21

28 I get by with a little help from R R Program: Layout Input Design table from MPL Flow Table from MPL Character string for how many copies of each machine there are: e.g. 2-3 = 2 type 1 machines and 3 type 3 machines Emma Ross () Facility Layout September 2, / 21

29 I get by with a little help from R R Program: Layout Input Output Design table from MPL Flow Table from MPL Character string for how many copies of each machine there are: e.g. 2-3 = 2 type 1 machines and 3 type 3 machines Flow diagram with machine layout and flow Emma Ross () Facility Layout September 2, / 21

30 Layout s Output Example Emma Ross () Facility Layout September 2, / 21

31 Results (1) Parameters which were varied; Machine capacities Demand volume Tasks required - e.g. type 1 type 2 Collection of machines - how many of each type Emma Ross () Facility Layout September 2, / 21

32 Results (1) Parameters which were varied; Machine capacities Demand volume Tasks required - e.g. type 1 type 2 Collection of machines - how many of each type Recall... Aim was to characterise patterns in the layout by words. Emma Ross () Facility Layout September 2, / 21

33 Results (1) Parameters which were varied; Machine capacities Demand volume Tasks required - e.g. type 1 type 2 Collection of machines - how many of each type Recall... Aim was to characterise patterns in the layout by words. Observations; Emma Ross () Facility Layout September 2, / 21

34 Results (1) Parameters which were varied; Machine capacities Demand volume Tasks required - e.g. type 1 type 2 Collection of machines - how many of each type Recall... Aim was to characterise patterns in the layout by words. Observations; Varying demand voume has little effect on layout Emma Ross () Facility Layout September 2, / 21

35 Results (1) Parameters which were varied; Machine capacities Demand volume Tasks required - e.g. type 1 type 2 Collection of machines - how many of each type Recall... Aim was to characterise patterns in the layout by words. Observations; Varying demand voume has little effect on layout Copies of a machine type most often distanced from their dupliacte(s) Emma Ross () Facility Layout September 2, / 21

36 Results (1) Parameters which were varied; Machine capacities Demand volume Tasks required - e.g. type 1 type 2 Collection of machines - how many of each type Recall... Aim was to characterise patterns in the layout by words. Observations; Varying demand voume has little effect on layout Copies of a machine type most often distanced from their dupliacte(s) Varying the capacity does have an effect; Largest capacity copies of a machine placed in prime positions. Smaller copies sit more on outside positions - only used for overspill. Emma Ross () Facility Layout September 2, / 21

37 A more useful model? Useful starting point but a better model will represent The ability to make multiple products in one factory and, The stochasticity of demand. Emma Ross () Facility Layout September 2, / 21

38 A more useful model? Useful starting point but a better model will represent The ability to make multiple products in one factory and, The stochasticity of demand. Our simple model can be adapted to include more than one scenario and find the best layout given that any of them might occur. This gives a model which Gives a more flexible, robust design which will cope with more tasks and possible changes in demand, and Will make a compromise between optimal layouts for individual scenarios. Emma Ross () Facility Layout September 2, / 21

39 Adapting the Model Input Unchanged: 2 datafiles for capacity and cost Different: Model now has multiple scenarios each with a different task and/or demand volume. Emma Ross () Facility Layout September 2, / 21

40 Adapting the Model Input Unchanged: 2 datafiles for capacity and cost Different: Model now has multiple scenarios each with a different task and/or demand volume. New Objective: Min S N N N i M j K s=1 i=1 j=1 n i =1 m j =1 k=1 l=1 K π s f ni m j sc kl x ni kx mj l (7) Where S is the total number of scenarios and π s is the probability of scenario s occuring. Emma Ross () Facility Layout September 2, / 21

41 Adapting the Model Input Output Unchanged: 2 datafiles for capacity and cost Different: Model now has multiple scenarios each with a different task and/or demand volume. New Objective: Min S N N N i M j K s=1 i=1 j=1 n i =1 m j =1 k=1 l=1 K π s f ni m j sc kl x ni kx mj l (7) Where S is the total number of scenarios and π s is the probability of scenario s occuring. Unchanged: One table representing the optimal layout design Different: Now have multiple tables representing the flow for each scenario Emma Ross () Facility Layout September 2, / 21

42 Analysis of the Results Now have even more tabular data to make sense of, so a diagram drawing progam will save much time and potential for mistakes. Emma Ross () Facility Layout September 2, / 21

43 Analysis of the Results Now have even more tabular data to make sense of, so a diagram drawing progam will save much time and potential for mistakes. Layout is adapted to give outputs such as; Emma Ross () Facility Layout September 2, / 21

44 Results (2) Parameters which were varied; Number of scenarios Probability of each scenario Emma Ross () Facility Layout September 2, / 21

45 Results (2) Parameters which were varied; Number of scenarios Probability of each scenario Basis of Results... Results are based on comparison of Optimal layout from each scenario individually (first model), and The stochastic model s result, for very small problems only. Emma Ross () Facility Layout September 2, / 21

46 Results (2) Parameters which were varied; Number of scenarios Probability of each scenario Basis of Results... Results are based on comparison of Optimal layout from each scenario individually (first model), and The stochastic model s result, for very small problems only. Observations; Demand volume again has very little effect on the layout. Emma Ross () Facility Layout September 2, / 21

47 Results (2) Parameters which were varied; Number of scenarios Probability of each scenario Basis of Results... Results are based on comparison of Optimal layout from each scenario individually (first model), and The stochastic model s result, for very small problems only. Observations; Demand volume again has very little effect on the layout. If scnerios differ only by demand volume then no compromise made. Emma Ross () Facility Layout September 2, / 21

48 Results (2) Parameters which were varied; Number of scenarios Probability of each scenario Basis of Results... Results are based on comparison of Optimal layout from each scenario individually (first model), and The stochastic model s result, for very small problems only. Observations; Demand volume again has very little effect on the layout. If scnerios differ only by demand volume then no compromise made. Seems that compromise evident only when the scenrio s tasks are different, e.g. Scenario 1(type 1 type 2), Scenario 2(type 2 type 1). Emma Ross () Facility Layout September 2, / 21

49 Limitations and Thoughts Experimenting with just some combinations of variables is time costly. Cannot think of a quicker way to analyse without losing the details needed to understand patterns. Emma Ross () Facility Layout September 2, / 21

50 Limitations and Thoughts Experimenting with just some combinations of variables is time costly. Cannot think of a quicker way to analyse without losing the details needed to understand patterns. Too simple? Precisely the point! Awkward problem which merits this approach. Goes some way to predicting good layouts for larger problems - can always be built up in complexity over time. Emma Ross () Facility Layout September 2, / 21

51 Limitations and Thoughts Experimenting with just some combinations of variables is time costly. Cannot think of a quicker way to analyse without losing the details needed to understand patterns. Too simple? Precisely the point! Awkward problem which merits this approach. Goes some way to predicting good layouts for larger problems - can always be built up in complexity over time. Wordy results? Better than figurative results in this case More useful to manufacturers? Can only go so far in predicting demand and problem is very awkward Emma Ross () Facility Layout September 2, / 21

52 Last words Have been reminded of how useful going back to basics and understanding the fundamentals of a problem are - can go a surprisingly long way with even very complex problems. Thank you for asking easy questions. Emma Ross () Facility Layout September 2, / 21