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Case study organisation

Case study organisation. Automotive battery manufacturer Existing distribution network of plant, warehouses, franchisees and retailers. INTEGRATED NETWORK. MARKET. FRANCHISEE. WAREHOUSE. PLANT. FRANCHISEE. WAREHOUSE. FRANCHISEE. WAREHOUSE. SMELTER. Forward Flow. Reverse flow.

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Case study organisation

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  1. Case study organisation • Automotive battery manufacturer • Existing distribution network of plant, warehouses, franchisees and retailers

  2. INTEGRATED NETWORK MARKET FRANCHISEE WAREHOUSE PLANT FRANCHISEE WAREHOUSE FRANCHISEE WAREHOUSE SMELTER Forward Flow Reverse flow

  3. Bi-directional open-loop supply chain network Coimbatore smelter AND REVERSE SUPPLY CHAIN

  4. Config-3 with warehouse MARKET FRANCHISEE WAREHOUSE PLANT FRANCHISEE WAREHOUSE FRANCHISEE WAREHOUSE SMELTER Forward Flow Reverse flow

  5. Config-4 without warehouse MARKET FRANCHISEE WAREHOUSE PLANT FRANCHISEE WAREHOUSE FRANCHISEE WAREHOUSE SMELTER Forward Flow Reverse flow

  6. Integrated network for region 1. SMELTERS WAREHOUSES FRANCHISEES CUSTOMER ZONES F1 C1 C2 W1 F2 P F3 C3 W2* S1 F4* F5 C4 S2 F6* C5 F7 FORWARD FLOW REVERSE FLOW

  7. Integrated network for region 2. SMELTERS WAREHOUSES FRANCHISEES CUSTOMER ZONES F8 C1 W3 F9 Plant MFG. F10 C2 W4 S3(KK) Smelter F11 C3 F12 S4(CBE) Smelter FORWARD FLOW REVERSE FLOW

  8. MATHEMATICAL MODEL Assumptions: • Factory location and Customer zones are fixed • Recovery rate of 70% is assumed • Warehouse is located at the proximity of the franchisee and also an optimal distance from the smelter. • All the batteries are routed to the smelter through the warehouse • Under normal circumstances, batteries are routed from the retail outlet to the franchisee and franchisee to warehouse, but if the customer or retailer is located closer to the franchisee, there could be direct shipment to the warehouse.

  9. MATHEMATICAL MODEL (Cont.) Assumptions (Cont.): • The model examines minimization of the in-bound and outbound costs with respect to the warehouse. Incase of direct shipment to the smelter, the cost associated with it could not be included in this model. • The distance between the franchisee to warehouse if located in the same city has been assumed suitably as well as from warehouse to smelter if located in same city has also been assumed suitably. • The smelter fixed costs are not included in this model • Identical warehouse cost for new and old batteries • Revenues based on sale of scrap batteries are not considered for this model • Recycling costs are not included for this model

  10. MATHEMATICAL MODEL (Cont.) • The primary objective of the model is to determine which of the potential facilities to be operated • The binary variables with respect to warehouses, franchisees and smelters are defined. • The variables with respect to quantity transported between different facilities are also defined

  11. MATHEMATICAL MODEL (Cont.) Parameters: • The following parameters are used in this model: • Transport cost per unit per Km. • Distance between facilities • Warehouse rent • Capacity of the warehouse • Demand per period • Percentage of returns (Percentage of sales) • Capacity of smelters

  12. The objective function is given as: Minimize (Transportation costs + Holding costs + Facility costs )

  13. The Objective function-Transportation cost w w f f w w s ∑ CFj DFj + ∑ ∑ Gji Sji+ ∑ ∑ AijUij + ∑ ∑ BikVik j=1 j=1 i=1 i=1 j=1 j=1 k=1

  14. Holding cost w w f f w w s hw∑ DFj/2 + hf( ∑ ∑ Sji/2 + ∑ ∑ Uij /2) + hw∑ ∑ Vik /2 j=1 j=1 i=1 i=1 j=1 j=1 k=1

  15. Facility cost w f ∑ XjWj +∑YiFi J=1 i=1

  16. Where,Aij - transportation cost per unit from franchisee ‘i’ to warehouse ‘j’.Bjk - transportation cost per unit from warehouse ‘j’ to smelter ‘k’Xj - fixed cost with warehouse ‘j’Yi – fixed cost with franchisee ‘i’Hj - maximum storage capacity of warehouse ‘j’Rk - maximum processing capacity of treatment facility ‘k’ in terms of number of unitsLi - maximum handling capacity of franchisee ‘i’ f - Maximum number of potential franchisee w - Maximum number of potential warehousess - Maximum number of potential smelting plant location Wj – 1, if warehouse ‘j’ is open, otherwise ‘0’Sk - 1, if smelter ‘k’ is open, otherwise ‘0’Fi - 1, if franchisee ‘i’ is open, otherwise ‘0’

  17. CFj - transportation cost from factory to Warehouse ‘j’DFj - number of batteries shipped from factory to warehouse ‘j’Gji - transportation cost from warehouse ‘j’ to franchisee ‘i’ Sji - number of batteries shipped from warehouse ‘j’ to franchisee ‘i’Vik - number of old batteries shipped fromwarehouse ‘j’ to smelter ‘k’Mjm - demand of new batteries for each franchisee from each market zoneUij – number of batteries returned from franchisee ‘i’ to warehouse ‘j’hw - holding cost at warehouse per unit per monthhf - holding cost at franchisee per unit per mon

  18. 1. FORWARD FLOW CONSTRAINTf w∑ Sij = ∑ Dfj , for j = 1,2,3… W i=1 j=1(It ensures all the batteries shipped from factories reach franchisees)Sji -Amount of batteries shipped from warehouse ‘j’ to franchisee ‘i’DFj - Amount of batteries shipped from factory to warehouse ‘j’ FLOW CONSTRAINTS

  19. 2. REVERSE FLOW CONSTRAINTs w ∑ Vjk = ∑ Uij , j=1,2…w k=1 j=1 (It ensures all the incoming flows is reaching smelters)Uij – Amount of batteries returned from franchisee to warehouseVik - Amount of old batteries shipped from warehouse ‘i’ to smelter ‘k’ FLOW CONSTRAINTS

  20. w w∑ Uij + ∑ Dfj ≤ ∑ HjWj j=1 j=1 (Warehouse Storage capacity constraint)Uij – Amount of batteries returned from franchisee to warehouseDFj - Amount of batteries shipped from factory to warehouse ‘j’Hj -Maximum storage capacity of warehouse ‘j’Wj - 1 if warehouse ‘j’ is open, otherwise ‘0’ CAPACITY CONSTRAINTS

  21. w w ∑ Sji+ ∑ Uij ≤ ∑ Fj Li for i=1,2,3…f j=1 j=1 (Franchisee handling capacity) Uij – Amount of batteries returned from franchisee to warehouseFi - 1 if franchisee ‘i’ is open, otherwise ‘0’Li - Maximum handling capacity of franchisee CAPACITY CONSTRAINTS (Cont.)

  22. s∑ Vjk ≤ ∑ RkSk j=1(Smelter processing capacity constraint)Vik - Amount of old batteries shipped from warehouse ‘i’ to smelter ‘k’Rk -Maximum processing capacity of treatment facility ‘k’ in terms of number of unitsSk - 1 if smelter ‘k’ is open, otherwise ‘0’ CAPACITY CONSTRAINTS (Cont.)

  23. f f∑ Sij = ∑ Mjm i=1 i=1where j=1,2.. w and m=1,2…n (where m refers to number of Market regions) (This constraint takes care of total output from franchisee is equal to market demand)Sji -Amount of batteries shipped from warehouse ‘j’ to franchisee ‘i’Mjm - demand of new batteries for each franchisee from each market DEMAND CONSTRAINT

  24. w n ∑ Uij = ∑ Rmi where i=1,2,….f. j=1 m=1(This constraint says that all the used/ returned batteries from market should be shipped to warehouses.)Uij – Amount of batteries returned from franchisee to warehouseRk -Maximum processing capacity of treatment facility ‘k’ in terms of number of units CONSTRAINT (Cont.)

  25. Objective function formulation MIN 7.6A11 + 4.25A12 + 5148W1 + 3811W2 + B11+B12+6.1B13+3.25B14+15.8B15+ 17.1B16+8.25B17+6.1B21+6.1B22+B23+3.05B24+12B25+12B26+6.6B27+0.5C11+0.5C12+ 6.1C13+3.25C14+15.8C15+17.1C16+8.25C17+6.1C21+6.1C22+0.5C23+3.05C24+12C25+ 12C26+6.6C27+6.1E11+17.5E12+0E21+16E22+2100F1+2100F2+1600F3+1600F4+1600F5+ 1600F6+1600F7+1600F8+1600F9+2100F10+1600F11+1600F12+ 20.8X13 + 26.85X14 + 3811W3 + 5148W4 + 0.8Y38 + 0.8Y39 + 5.8Y310 + 9.8Y311 + 2.3Y312 + 4.5Y48 + 9Y49 + 0Y410 + 7.4Y411 + 10Y412 + 0.8U38 + 0.8U39 + 5.8U310 + 9.8U311 + 2.3U312 + 4.5U48 + 9U49 + 0U410 + 7.4U411 + 10U412 + 10V33 + 5.8V34 + 15V43 + 0V44+0.25A11+0.25A12+0.25X13+0.25X14+0.25E11+0.25E12+ 0.25E21+0.25E22+0.25V33+0.25V34+0.25V43+0.25V44+ 0.125B11+0.125B12+0.125B13+0.125B14+0.125B15+0.125B16+0.125B17+0.125B21+0.125B22+0.125B23+0.125B24+ 0.125B25+0.125B26+0.125B27+0.125C11+0.125C12+0.125C13+0.125C14+0.125C15+0.125C16+0.125C17+0.125C21+ 0.125C22+0.125C23+0.125C24+0.125C25+0.125C26+0.125C27+0.125Y38+0.125Y39+0.125Y310+0.125Y311+0.125Y312+ 0.125Y48+0.125Y49+0.125Y410+0.125Y411+0.125Y412+0.125U38+0.125U39+0.125U310+0.125U311+0.125U312+0.125U48+ 0.125U49+0.125U410+0.125U411+0.125U412

  26. Constraints ST A11+C11+C12+C13+C14+C15+C16+C17-4250W1<=0 A12+C21+C22+C23+C24+C25+C26+C27-4250W2<=0 A11-B11-B12-B13-B14-B15-B16-B17=0 A12-B21-B22-B23-B24-B25-B26-B27=0 B11+B21+C11+C21-1200F1<=0 B12+B22+C12+C22-1200F2<=0 B13+B23+C13+C23-700F3<=0 B14+B24+C14+C24-700F4<=0 B15+B25+C15+C25-1000F5<=0 B16+B26+C16+C26-1000F6<=0 B17+B27+C17+C27-700F7<=0 B11+B21-D11>=0 B12+B22-D22>=0 B13+B23-D33>=0 B14+B24-D43>=0 B15+B25-D54>=0 B16+B26-D64>=0 B17+B27-D75>=0 D11=625 D22=625

  27. Constraints (Cont.) D33+D43=372 D54+D64=496 D75=372 C11+C12+C13+C14+C15+C16+C17+C21+C22+C23+C24+C25+C26+C27> 1250 C11+C12+C13+C14+C15+C16+C17-E11-E12=0 C21+C22+C23+C24+C25+C26+C27-E21-E22=0 E11+E21-1800R1<=0 E12+E22-1800R2<=0 W1+W2=1 R1+R2=1 F1+F2+F3+F4+F5+F6+F7=5 F1=1 F2=1 F7=1 F3+F4=1 F5+F6=1 C11+C21-0.7D11>=0 C12+C22-0.7D22>=0 C13+C23-0.7D33>=0 C14+C24-0.7D43>=0 C15+C25-0.7D54>=0 C16+C26-0.7D64>=0 C17+C27-0.7D75>=0

  28. Constraints (Cont.) X13 - Y38 - Y39 - Y310 - Y311 - Y312 = 0 X14 - Y48 - Y49 - Y410 - Y411 - Y412 = 0 X13+U38 + U39 + U310 + U311 + U312 - 2700W3 <=0 X14+U48 + U49 + U410 + U411 + U412 - 2700W4 <=0 Y38 + Y48+U38 + U48 - 850F8<=0 Y310 + Y410+U310 + U410 - 900F10<=0 Y39 + Y49+U39 + U49 - 850F9<=0 Y311 + Y411+U311 + U411 - 970F11<=0 Y312 + Y412+U312 + U412 - 970F12<=0 Y38+Y48-L81>=0 Y39+Y49-L91>=0 Y310+Y410-L102>=0 Y311+Y411-L113>=0 Y312+Y412-L123>=0 L81+L91=500 L102=514 L113+L123=570 U38 + U39 + U310 + U311 + U312 + U48 + U49 + U410 + U411 + U412 >500 U38 + U39 + U310 + U311 + U312 - V33 - V34 =0 U48 + U49 + U410 + U411 + U412 - V43 - V44 =0 V33 + V43 - 1200R3<=0 V34 + V44 - 1200R4<=0 R3+R4=1

  29. Constraints (Cont.) W3+W4 =1 F8+F9+F10+F11+F12=3 F10=1 U38 + U48 - 0.7L81>=0 U39 + U49 - 0.7L91>=0 U310 + U410 - 0.7L102>=0 U311 + U411 - 0.7L113>=0 U312 + U412 - 0.7L123>=0 END INT W3 INT W4 INT F8 INT F9 INT F10 INT F11 INT F12 INT R3 INT R4 INT W1 INT W2 INT F1 INT F2 INT F3 INT F4 INT F5 INT F6 INT F7 INT R1 INT R2

  30. Region Market Zones Demand per Month (Number of Batteries) Region I M1 625 M2 620 M3 496 M4 375 M5 375 Region 2 M6 500 M7 514 M8 570 Demand data for two regions

  31. Type of Facility Region Rent cost (Rs) in Indian Rupees Electricity cost(Rs) in Indian Rupees Manpower cost(Rs) in Indian Rupees Total(Rs) in Indian Rupees Warehouse Metro* 1898 850 2400 5148 Warehouse Non- metro # 911 650 2250 3811 Franchisee Metro 600 300 1200 2100 Franchisee Non-metro 450 250 900 1600 Warehouse and Franchisee Opening cost *Metro-Chennai and Coimbatore #Non-Metro-All other towns

  32. Storage and processing capacity of Potential facility Facility Capacity (Number of batteries per month) Warehouse-1 4250 Warehouse-2 4250 Warehouse 3 2700 Warehouse-4 2700 Franchisee (F1) 1200 Franchisee (F2) 1200 Franchisee (F3) 700 Franchisee (F4) 700 Franchisee (F5) 1000 Franchisee (F5) 1000 Franchisee (F7) 700 Franchisee (F8) 850 Franchisee (F9) 900 Franchisee (F10) 850 Franchisee (F11) 970 Franchisee (F12) 970 Recycling Plant R1 1800 Recycling plant R2 1800 Recycling plant R3 1200 Recycling plant R4 1200

  33. Transport cost per unit per Km (Long distance) (in Indian Rupees) Rs.0.05 Transport cost per unit per Km (Within City limits-Chennai and Coimbatore)( in Indian Rupees) Rs.0.10 Warehouse Holding cost per unit (in Indian Rupees) Rs.0.50 Franchisee Holding cost per unit ( in Indian Rupees) Rs.0.25 Operation costs:

  34. REGION WAREHOUSE SELECTED FRANCHISEES SELECTED RECYCLE PLANT SELECTED TOTAL COST in Indian Rupees Facility open cost in Indian Rupees Region 1 W2-Vellore F1-NorthChennai F2-SouthChennai F3-Vellore F5-Trichy F7-Pondy R1-Vellore Rs.52738. Rs.12,811 Region 2 W3(Erode-Madurai) F9-Erode F10-Coimbatore F12-Madurai R4-Coimbatore Rs.57,476 Rs.9,111 Total Rs.110,214 Rs.21,922 Results of the model with actual inputs-Case 1-with warehouse (Considers warehouses in the reverse chain also)

  35. REGION WAREHOUSE SELECTED FRANCHISEES SELECTED RECYCLE PLANT SELECTED TOTAL COST in Indian Rupees Facility open cost in Indian Rupees Region 1 W2-Vellore F1-NorthChennai F2-SouthChennai F3-Vellore F5-Trichy F7-Pondy R1-Vellore R2-Karaikudi Rs.50089. Rs.12,811 Region 2 W3(Erode-Madurai) F9-Erode F10-Coimbatore F12-Madurai R3-Karaikudi R4-Coimbatore Rs.51,028 Rs.9,111 Total Rs.1,01,117 Rs.21,922 Results of the model with actual inputs-Case 2-without warehouse (Do not consider warehouses in the reverse chain)

  36. 1 2 PLANT Chennai south WAREHOUSE 3 FRANCHISEE Chennai north DEALER Vellore Vellore Vellore n Trichy Trichy Pondy 1 2 Coimbatore 3 Erode Tirupathi Dharapuram Madurai n FORWARD OPTIMAL NETWORK

  37. 1 2 Chennai south 3 Chennai north Vellore Vellore Pondy n Vellore Karaikudi Trichy SMELTER Madurai 1 WAREHOUSE 2 Coimbatore Coimbatore FRANCHISEE 3 DEALER Erode REVERSE OPTIMAL NETWORK n Without Warehouse

  38. 1 2 Chennai south 3 Chennai north Vellore Pondy Vellore Vellore n Trichy Trichy Vellore Coimbatore SMELTER Coimbatore 1 WAREHOUSE 2 Dharapuram Erode FRANCHISEE 3 DEALER Madurai REVERSE OPTIMAL NETWORK n With Warehouse

  39. Results • The results show clearly that there are major cost differences between the two cases of the network designs. The CONFIG-B is less costly and it is about 8.25% lower than the CONFIG-A. • The result recommends change in existing facilities. • Management may feel lesser power if flows are directed from the franchisee to smelter (Config-B) • Centralized Vs Decentralized collection network

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