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Recycling Operations in Country A

Recycling is an important and complex activity in Country A. To enable timely operations, the country is divided into 10 sectors and recycling operations are commenced simultaneously in each sector. The recyclable garbage is collected from public bins, loaded into trucks, and transported to recycling sites. Each site can accommodate different amounts of recyclable garbage because of its available land size at the facility. The annual capacities for five recycling sites are given in the table below (in megatonnes): Recycling Site 1 2 3 4 5 Capacity 10 7 15 12 6 Each recycling site is installed with facilities that have different recycling efficiencies which are summarised in the table below (in percentages): Recycling Site 1 2 3 4 5 Efficiency 35% 45% 25% 75% 55% The cost of collecting and transporting recyclable garbage primarily depends on the distance between the sectors and the recycling sites.

The following table summarises the distances between each sector and each recycling site (in kilometres): Recycling Site Sector 1 2 3 4 5 1 24 10 34 52 65 2 17 15 58 64 62 3 10 20 26 66 60 4 18 25 32 57 62 5 11 22 15 55 62 6 29 34 46 54 43 7 34 43 69 43 40 8 38 42 36 53 34 9 22 29 46 53 50 10 22 46 50 42 58 Using historical data, the country estimates the annual volume of the recyclable garbage for each sector in the coming year shown in the table below (in megatonnes): Estimated Recyclable Garbage 1 2 3 4 5 6 7 8 9 10 4.6 4.6 4.7 4.2 3.8 3.9 3.4 3.3 3.9 4.1

It will cost approximately $109,603 to move one megatonne of recycling garbage for one kilometre. The management would like to maximise the amount of recycled garbage and minimise the transportation cost.

a. Formulate an multiple-objective linear programming (MOLP) model for this problem in a Word file with a brief description of an equation, and implement the MOLP model in an Excel spreadsheet.

b. Determine the optimal value for each objective in the problem.

c. Suppose the management considers maximising the amount of recycled garbage to be three times as important as minimising the transportation cost. Formulate a GP model to optimise both objectives simultaneously with a brief description of an equation in a Word file, and implement the MOLP model in an Excel spreadsheet.

Company B's Warehouse Optimization

Company B has twenty petrol stations across Melbourne. It is creating strategies to consolidate warehouse operations so that there will be three warehouses that supply the stations. The company plans to sell all its extant warehouses and build new, state-of-the-art warehouses. Each warehouse can supply multiple stations; however, each station will be supplied by a single warehouse. The location of each station is summarised in the table below: Suburb X Y Suburb X Y Ascot Vale 25 13.8 Laverton North 13.5 7.2 Avondale Heights 19.7 14.2 Melbourne 28.6 8.9 Brooklyn 18.2 9.4 Seabrook 10.9 2.3 Burnside 10.7 16.2 Southbank 29.8 8.1 Caroline Springs 9.7 16.8 St Kilda 30.4 3.4 Derrimut 10.7 10.2 Sunshine West 16.6 10.2 Flemington 24.3 11.8 Tarneit 5.2 8.1 Footscray 22.4 11 Tarneit 5.1 6.6 Footscray 23.7 11.1 Werribee 0.5 0 Hoppers Crossing 6.3 4.7 Wyndham Vale 0 2 The company wants to build its warehouses in locations that minimise the distances to each of the stations it serves. Formulate a non-linear programming (NLP) model for this problem in a Word file with a brief description of an equation, and implement the NLP model in an Excel spreadsheet. What do the results suggest? (20 marks)

Case 3 David Jones is planning to buy a new van for his work as a trady. After narrowing his choices down to three models (A, B, and C) within his budget, he is having difficulty in deciding which one to purchase. David has compared each model against one another on the basis of four criteria: price, safety, economy, and comfort. His comparisons are summarised below: Price Safety X Y Z X Y Z X 1 1/3 4 X 1 1/3 2 Y 3 1 7 Y 3 1 8 Z 1/4 1/7 1 Z 1/2 1/8 1 Economy Comfort X Y Z X Y Z X 1 1/6 1/3 X 1 1/8 1/4 Y 6 1 1/3 Y 8 1 1/3 Z 3 3 1 Z 4 3 1 David wants to incorporate all of the four criteria into his final decision. However, the criteria are not equally important. The following matrix summarises his comparisons of the importance of the criteria: Criteria Price Safety Economy Comfort Price 1 1/6 1/3 1/5 Safety 6 1 4 2 Economy 3 1/4 1 1/3 Comfort 5 1/2 3 1 Use analytic hierarchy process to compute the overall score for each van. What do the results suggest? (15 marks)

Case 4 The distributor is interested in selecting the best location for a new warehouse. After a detailed study of 10 sites, the three location finalists are Smithfield, New South Wales; Eagle Farm, Quensland; and Derrimut, Victoria. The management provides the following data on the location criteria, criteria importance, and location ratings. Conduct TOPSIS in an Excel spreadsheet to determine the best location for the new plant. What do the results suggest? Criteria Weight Ratings Objective Smithfield, NSW Eagle Farm, QLD Derrimut, VIC Land cost 4 5 7 6 Min Labour cost 6 7 6 6 Min Labour availability 8 6 7 5 Max Construction cost 5 5 6 7 Min Transportation 5 6 6 7 Max Access to customers 9 8 7 7 Max Long-range goals 7 5 7 6 Max

Q1a             Total  Estimated Recycleble Garbage         
    x1 x2 x3 x4 x5                  
Objective  Decision  1.28E-07 8.93E-08 1.91E-07 1.53E-07 7.65E-08                  
  Capacity  10 7 15 12 6 7.07E-06                
                               
                               
constrains                             
  sectors                             
  1 2630472 1096030 3726502 5699356 7124195 2.56398 4.6              
  2 1863251 1644045 6356974 7014592 6795386 3.19449 4.6              
  3 1096030 2192060 2849678 7233798 6576180 2.491283 4.7              
  4 1972854 2740075 3507296 6247371 6795386 2.643668 4.2              
  5 1205633 2411266 1644045 6028165 6795386 2.126398 3.8              
  6 3178487 3726502 5041738 5918562 4712929 2.969408 3.9              
  7 3726502 4712929 7562607 4712929 4384120 3.4 3.4              
  8 4164914 4603326 3945708 5808959 3726502 2.871546 3.3              
  9 2411266 3178487 5041738 5808959 5480150 2.864556 3.9              
  10 2411266 5041738 5480150 4603326 6356974 2.997368 4.1              
                               
suburb x y Wh1 Wh2 Wh3 Distance                  
Ascot Vale 25 13.8 0 1 0 3.21 1                
Avondale 19.7 14.2 0 1 0 5.42 1                
Brooklyn 18.2 9.4 1 0 0 5.21 1                
Burnside 10.7 16.2 1 0 0 6.29 1                
Caroline 9.7 16.8 1 0 0 7.25 1                
Derrimut 10.7 10.2 1 0 0 2.4 1                
Flemington 24.3 11.8 0 1 0 1.09 1                
Footscray 22.4 11 0 1 0 1.52 1                
Footscray 23.7 11.1 0 1 0 0.38 1                
Hoppers 6.3 4.7 0 0 1 1.28 1                
Leverton 13.5 7.2 1 0 0 3.21 1                
Melbourne 28.6 8.9 0 1 0 5.06 1                
Seabrook 10.9 2.3 0 0 1 6.33 1                
Southbank 29.8 8.1 0 1 0 6.48 1                
St Kilda 30.4 3.4 0 1 0 9.83 1                
Sunshine 16.6 10.2 1 0 0 3.52 1                
Tameit 5.2 8.1 0 0 1 3.46 1                
Tameit 5.1 6.6 0 0 1 1.96 1                
Werribee 0.5 0 0 0 1 6.48 1                
Wyndham 0 2 0 0 1 5.68 1                
                               
Wh1 13.1 10.4   Total    86.06                  
Wh2 23.9 10.8                          
Wh3 5 4.6                          
                               
                               
Q3                              
                               
      price  safety  economy  comfort  GM PV   price A B C GM PV
    price 1 0.166667 0.333333 0.2 0.324668 0.061042   A 1 0.333333 4 1.100642 0.262753
    safety 6 1 4 2 2.632148 0.494876   B 3 1 7 2.758924 0.65863
    economy 3 0.25 1 0.333333 0.707107 0.132945   C 0.25 0.147619 1 0.332936 0.079481
    comfort  5 0.5 3 1 1.654875 0.311137   SUM= 4.25 1.480952 12 4.188883  
    sum = 15 1.916667 8.333333 3.533333 5.318798 1   SUM PV = 1.116701 0.975399 0.95377    
    sum PV = 0.915624 0.948513 1.107873 1.099351       LAMBA MAX =  3.032367        
    Labda max 4.071362             CI 0.016183        
    CI 0.023787             RI 0.58        
    CR 0.02643             CR 0.027902        
                               
                               
                               
                               
    price A B C GM PV     price A B C GM PV
    A 1 0.333333 2 0.87358 0.210251     A 1 0.166667 0.333333 0.381572 0.10253
    B 3 1 8 2.884499 0.694235     B 6 1 0.333333 1.259921 0.338545
    C 0.5 0.125 1 0.39685 0.095513     C 3 3 1 2.080084 0.558926
    SUM= 4.5 1.458333 11 4.15493       SUM= 10 4.166667 1.666666 3.721576  
    SUM PV = 0.946132 1.012426 1.050644         SUM PV = 1.025296 1.410604 0.931542    
    LAMBA MAX =  3.009202             LAMBA MAX =  3.367442        
    CI 0.004601             CI 0.183721        
    RI 0.58             RI 0.58        
    CR 0.007933             CR 0.31676        
                               
                               
                               
    price A B C GM PV                
    A 1 0.125 0.25 0.31498 0.07892                
    B 8 1 0.333333 1.386722 0.347451                
    C 4 3 1 2.289428 0.573629                
    SUM= 13 4.125 1.583333 3.991131                  
    SUM PV = 1.025961 1.433235 0.908246                    
    LAMBA MAX =  3.367442                        
    CI 0.183721                        
    RI 0.58                        
    CR 0.31676                        
                               
                               
                               
      price  economy  safety  comfort                   
    Pv of factors  0.061052 0.132945 0.494876 0.311137                  
    A 0.262753 0.10253 0.210252 0.07892 0.158276                
    B 0.65863 0.338545 0.694235 0.347451 0.536884                
    C 0.078617 0.558925 0.095513 0.573629 0.30485                
                               
                               
  Land Cost  Labor cost  Labor availability  Construction cost  Transportation  Access to customers  Long – range goals                 
Smithfield, NSW 5 7 6 5 6 8 5                
Eagle farm, QLD 7 6 7 6 6 7 7                
Derrimut, VIC 6 6 5 7 7 7 6                
weight  4 6 8 5 5 9 7                
                               
squares                               
                               
  Land Cost  Labor cost  Labor availability  Construction cost  Transportation  Access to customers  Long – range goals                 
Smithfield, NSW 25 49 36 25 36 64 25                
Eagle farm, QLD 49 36 49 36 36 49 49                
Derrimut, VIC 36 36 25 49 49 49 36                
                               
Total  110 121 110 110 121 162 110                
                               
sum square root  29.05168                            
                               
  Land Cost  Labor cost  Labor availability  Construction cost  Transportation  Access to customers  Long – range goals                 
Smithfield, NSW 0.17211 0.24095 0.20653 0.17211 0.20653 0.27537 0.17211                
Eagle farm, QLD 0.24095 0.20653 0.24095 0.20653 0.20653 0.24095 0.24095                
Derrimut, VIC 0.20653 0.20653 0.17211 0.24095 0.24095 0.24095 0.20653                
                               
                               
multiply each of the columns by the respective weights given to the criterion.                 
                               
  Land Cost  Labor cost  Labor availability  Construction cost  Transportation  Access to customers  Long – range goals                 
Smithfield, NSW 0.68843 1.4457 1.65223 0.86054 1.03264 2.47834 1.20475                
Eagle farm, QLD 0.9638 1.23917 1.9276 1.03264 1.03264 2.16855 1.68665                
Derrimut, VIC 0.82611 1.23917 1.37686 1.20475 1.20475 2.16855 1.4457                
                               
                               
                               
                               
  Ideal solution  Negative ideal solution                           
Smithfield, NSW 0.15 0.29                          
Eagle farm, QLD 0.21 0.31                          
Derrimut, VIC 0.39 0.09                          
                               
                               
                               
  Closeness                             
Smithfield, NSW 0.34                            
Eagle farm, QLD 0.41                            
Derrimut, VIC 0.81                            
                               
Q1c             Total  Estimated Recycleble Garbage         
    x1 x2 x3 x4 x5                  
Objective  Decision  0 2.68E-07 4.93E-07 8.91E-07 2.3E-07                  
  Capacity  10 7 15 12 6 2.13E-05                
                               
                               
constrains                             
  sectors                             
  1 2630472 1096030 3726502 5699356 7124195 8.8478 13.8              
  2 1863251 1644045 6356974 7014592 6795386 11.38884 13.8              
  3 1096030 2192060 2849678 7233798 6576180 9.951034 14.1              
  4 1972854 2740075 3507296 6247371 6795386 9.593112 12.6              
  5 1205633 2411266 1644045 6028165 6795386 8.390731 11.4              
  6 3178487 3726502 5041738 5918562 4712929 9.84283 11.7              
  7 3726502 4712929 7562607 4712929 4384120 10.2 10.2              
  8 4164914 4603326 3945708 5808959 3726502 9.212987 9.9              
  9 2411266 3178487 5041738 5808959 5480150 9.774482 11.7              
  10 2411266 5041738 5480150 4603326 6356974 9.616332 12.3              
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My Assignment Help. (2020). Multiple-Objective Linear Programming And Analytic Hierarchy Process For Optimization Problems. Retrieved from https://myassignmenthelp.com/free-samples/omgt2087-garbage-management/megatonne-of-recycling.html.

"Multiple-Objective Linear Programming And Analytic Hierarchy Process For Optimization Problems." My Assignment Help, 2020, https://myassignmenthelp.com/free-samples/omgt2087-garbage-management/megatonne-of-recycling.html.

My Assignment Help (2020) Multiple-Objective Linear Programming And Analytic Hierarchy Process For Optimization Problems [Online]. Available from: https://myassignmenthelp.com/free-samples/omgt2087-garbage-management/megatonne-of-recycling.html
[Accessed 30 May 2024].

My Assignment Help. 'Multiple-Objective Linear Programming And Analytic Hierarchy Process For Optimization Problems' (My Assignment Help, 2020) <https://myassignmenthelp.com/free-samples/omgt2087-garbage-management/megatonne-of-recycling.html> accessed 30 May 2024.

My Assignment Help. Multiple-Objective Linear Programming And Analytic Hierarchy Process For Optimization Problems [Internet]. My Assignment Help. 2020 [cited 30 May 2024]. Available from: https://myassignmenthelp.com/free-samples/omgt2087-garbage-management/megatonne-of-recycling.html.

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