12/25/20151 Case study organisation Automotive battery manufacturer Existing distribution network of plant, warehouses, franchisees and retailers

12/25/20152

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INTEGRATED NETWORK PLANT WAREHOUSE FRANCHISEE SMELTER Forward Flow Reverse flow MARKET

12/25/20155 AND REVERSE SUPPLY CHAIN Bi-directional open-loop supply chain network Coimbatore smelter

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

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

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

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

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.

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

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

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

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

The Objective function- Transportation cost w w f f w w s ∑ C Fj D Fj + ∑ ∑ Gji S ji + ∑ ∑ A ij U ij + ∑ ∑ B ik V ik j=1 j=1 i=1 i=1 j=1 j=1 k=1

Holding cost w w f f w w s h w ∑ D Fj /2 + h f ( ∑ ∑ S ji /2 + ∑ ∑ U ij /2) + h w ∑ ∑ V ik /2 j=1 j=1 i=1 i=1 j=1 j=1 k=1

Facility cost w f ∑ X j W j +∑YiFi J=1 i=1

Where, A ij - transportation cost per unit from franchisee ‘i’ to warehouse ‘j’. B jk - transportation cost per unit from warehouse ‘j’ to smelter ‘k’ X j - fixed cost with warehouse ‘j’ Yi – fixed cost with franchisee ‘i’ H j - maximum storage capacity of warehouse ‘j’ R k - maximum processing capacity of treatment facility ‘k’ in terms of number of units Li - maximum handling capacity of franchisee ‘i’ f - Maximum number of potential franchisee w - Maximum number of potential warehouses s - Maximum number of potential smelting plant location W j – 1, if warehouse ‘j’ is open, otherwise ‘0’ S k - 1, if smelter ‘k’ is open, otherwise ‘0’ Fi - 1, if franchisee ‘i’ is open, otherwise ‘0’

C Fj - transportation cost from factory to Warehouse ‘j’ D Fj - number of batteries shipped from factory to warehouse ‘j’ Gji - transportation cost from warehouse ‘j’ to franchisee ‘i’ S ji - number of batteries shipped from warehouse ‘j’ to franchisee ‘i’ V ik - number of old batteries shipped from warehouse ‘j’ to smelter ‘k’ M jm - demand of new batteries for each franchisee from each market zone U ij – number of batteries returned from franchisee ‘i’ to warehouse ‘j’ h w - holding cost at warehouse per unit per month h f - holding cost at franchisee per unit per mon

1. FORWARD FLOW CONSTRAINT f 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

2. REVERSE FLOW CONSTRAINT s 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 warehouse Vik - Amount of old batteries shipped from warehouse ‘i’ to smelter ‘k’ FLOW CONSTRAINTS

w w ∑ Uij + ∑ Dfj ≤ ∑ HjWj j=1 j=1 (Warehouse Storage capacity constraint) Uij – Amount of batteries returned from franchisee to warehouse DFj - 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

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 warehouse Fi - 1 if franchisee ‘i’ is open, otherwise ‘0’ Li - Maximum handling capacity of franchisee CAPACITY CONSTRAINTS (Cont.)

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 units Sk - 1 if smelter ‘k’ is open, otherwise ‘0’ CAPACITY CONSTRAINTS (Cont.)

f f ∑ Sij = ∑ Mjm i=1 i=1 where 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

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 warehouse Rk -Maximum processing capacity of treatment facility ‘k’ in terms of number of units CONSTRAINT (Cont.)

Objective function formulation MIN 7.6A A W W2 + B11+B12+6.1B B B B B17+6.1B21+6.1B22+B B24+12B25+12B26+6.6B27+0.5C11+0.5C C C C C C17+6.1C21+6.1C22+0.5C C24+12C25+ 12C26+6.6C27+6.1E E12+0E21+16E F1+2100F2+1600F3+1600F4+1600F F6+1600F7+1600F8+1600F9+2100F F F X X W W Y Y Y Y Y Y48 + 9Y49 + 0Y Y Y U U U U U U48 + 9U49 + 0U U U V V V43 + 0V A A X X E E E E V V V V B B B B B B B B B B B B B B C C C C C C C C C C C C C C Y Y Y Y Y Y Y Y Y Y U U U U U U U U U U412

Constraints ST A11+C11+C12+C13+C14+C15+C16+C W1<=0 A12+C21+C22+C23+C24+C25+C26+C W2<=0 A11-B11-B12-B13-B14-B15-B16-B17=0 A12-B21-B22-B23-B24-B25-B26-B27=0 B11+B21+C11+C F1<=0 B12+B22+C12+C F2<=0 B13+B23+C13+C23-700F3<=0 B14+B24+C14+C24-700F4<=0 B15+B25+C15+C F5<=0 B16+B26+C16+C F6<=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

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+E R1<=0 E12+E R2<=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

Constraints (Cont.) X13 - Y38 - Y39 - Y310 - Y311 - Y312 = 0 X14 - Y48 - Y49 - Y410 - Y411 - Y412 = 0 X13+U38 + U39 + U310 + U311 + U W3 <=0 X14+U48 + U49 + U410 + U411 + U W4 <=0 Y38 + Y48+U38 + U F8<=0 Y310 + Y410+U310 + U F10<=0 Y39 + Y49+U39 + U F9<=0 Y311 + Y411+U311 + U F11<=0 Y312 + Y412+U312 + U F12<=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 + V R3<=0 V34 + V R4<=0 R3+R4=1

Constraints (Cont.) W3+W4 =1 F8+F9+F10+F11+F12=3 F10=1 U38 + U L81>=0 U39 + U L91>=0 U310 + U L102>=0 U311 + U L113>=0 U312 + U L123>=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

Demand data for two regions RegionMarket ZonesDemand per Month (Number of Batteries) Region IM1625 M2620 M3496 M4375 M5375 Region 2M6500 M7514 M8570

Warehouse and Franchisee Opening cost Type of Facility RegionRent cost (Rs) in Indian Rupees Electricity cost(Rs) in Indian Rupees Manpower cost(Rs) in Indian Rupees Total(Rs) in Indian Rupees Warehous e Metro* Warehous e Non- metro # Franchise e Metro Franchise e Non-metro * Metro-Chennai and Coimbatore #Non-Metro-All other towns

Storage and processing capacity of Potential facility Facility Capacity (Number of batteries per month) Warehouse Warehouse Warehouse Warehouse 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 R11800 Recycling plant R21800 Recycling plant R31200 Recycling plant R41200

Operation costs: 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

Results of the model with actual inputs-Case 1-with warehouse (Considers warehouses in the reverse chain also) REGIONWAREHOUSE SELECTED FRANCHISEES SELECTED RECYCLE PLANT SELECTED TOTAL COST in Indian Rupees Facility open cost in Indian Rupees Region 1W 2 -Vellore F 1 -NorthChennai F 2 -SouthChennai F 3 -Vellore F 5 -Trichy F 7 -Pondy R 1 -VelloreRs Rs.12,811 Region 2W 3 (Erode- Madurai) F 9 -Erode F 10 -Coimbatore F 12 -Madurai R 4 -CoimbatoreRs.57,476Rs.9,111 Total Rs.110,214Rs.21,922

Results of the model with actual inputs-Case 2-without warehouse (Do not consider warehouses in the reverse chain) REGIONWAREHOUSE SELECTED FRANCHISEES SELECTED RECYCLE PLANT SELECTED TOTAL COST in Indian Rupees Facility open cost in Indian Rupees Region 1W 2 -Vellore F 1 -NorthChennai F 2 -SouthChennai F 3 -Vellore F 5 -Trichy F 7 -Pondy R 1 -Vellore R 2 -Karaikudi Rs Rs.12,811 Region 2W 3 (Erode- Madurai ) F 9 -Erode F 10 -Coimbatore F 12 -Madurai R 3 -Karaikudi R 4 -Coimbatore Rs.51,028Rs.9,111 Total Rs.1,01,117Rs.21,922

Tirupathi Vellore Dharapuram Chennai north Chennai south Trichy Vellore Pondy Madura i Erode Trichy Vellore Coimbatore n n PLANT WAREHOUSE FRANCHISEE DEALER FORWARD OPTIMAL NETWORK

Chennai north Chennai south Vellore Trichy Pondy n n Vellore Coimbatore SMELTER WAREHOUSE FRANCHISEE DEALER REVERSE OPTIMAL NETWORK Madura i Erode Coimbatore Without Warehouse Karaikudi

Vellore Chennai north Chennai south Trichy Vellore Trichy Pondy n n Dharapuram Vellore Coimbatore SMELTER WAREHOUSE FRANCHISEE DEALER REVERSE OPTIMAL NETWORK Madura i Erode Coimbatore With Warehouse

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