Case study organisation

04/20/23 1

Case study organisation

• Automotive battery manufacturer

• Existing distribution network of plant, warehouses, franchisees and retailers

04/20/23 2

Tirupathi

Chennai

Coimbatore

Chennai north

Chennai south

Trichy

Vellore

Coimbatorenorth

Pondy

Madurai

Erode

Salem

Trichy

Vellore

Tirunelv eli

Coimbatoresouth

1

2

3

n

1

2

3

n

PLANT

WAREHOUSE

FRANCHISEE

DEALER

FORWARD SUPPLY CHAIN NETWORK

04/20/23 3

Chennai

Chennai north

Chennai south

Trichy

Vellore

Vellore

Trichy

Pondy

1

2

3

n

1

2

3

n

Coimbatorenorth

Madurai

Erode

Salem

Tirunelv eli

Coimbatoresouth

Coimbatore

SMELTER

WAREHOUSE

FRANCHISEE

DEALER

REVERSE SUPPLY CHAIN NETWORK

Coimbatore

INTEGRATED NETWORK

PLANT WAREHOUSE

WAREHOUSE

WAREHOUSE

FRANCHISEE

FRANCHISEE

FRANCHISEE

SMELTER

Forward Flow

Reverse flow

MARKET

04/20/23 5

Tirupathi

Chennai

Coimbatore

Chennai north

Chennai south

Trichy

Vellore

Coimbatorenorth

Pondy

Madurai

Erode

Salem

Trichy

Vellore

Tirunelv eli

Coimbatoresouth

1

2

3

n

1

2

3

n

PLANT

WAREHOUSE

FRANCHISEE

DEALER

FORWARD SUPPLY CHAIN NETWORK AND REVERSE

SUPPLY CHAIN

Bi-directional open-loop supply chain network

Coimbatore smelter

Config-3 with warehouse

PLANT WAREHOUSE

WAREHOUSE

WAREHOUSE

FRANCHISEE

FRANCHISEE

FRANCHISEE

SMELTER

Forward Flow

Reverse flow

MARKET

Config-4 without warehouse

PLANT WAREHOUSE

WAREHOUSE

WAREHOUSE

FRANCHISEE

FRANCHISEE

FRANCHISEE

SMELTER

Forward Flow

Reverse flow

MARKET

P

W1

W2*

F1

F2

F3

F4*

F5

C1

C3

C4S2

S1

SMELTERS WAREHOUSES FRANCHISEES CUSTOMER ZONES

FORWARD FLOW

REVERSE FLOW

F6*

F7

C2

C5

Integrated network for region 1.

Integrated network for region 2.

PlantMFG.

W3

W4

F8

F9

F10

F11

F12

C1

C2

C3

S4(CBE)Smelter

S3(KK)Smelter

SMELTERS WAREHOUSES FRANCHISEES CUSTOMER 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


• 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


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

∑ CFj DFj + ∑ ∑ Gji Sji+ ∑ ∑ AijUij + ∑ ∑ BikVik

j=1 j=1 i=1 i=1 j=1 j=1 k=1

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

Facility cost

w f

∑ XjWj +∑YiFi

J=1 i=1

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’

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 from warehouse ‘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 month

hf - 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 warehouseVik - 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 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

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.)

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.)

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 warehouseRk -Maximum processing capacity of treatment facility ‘k’ in terms of number of units

CONSTRAINT (Cont.)

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

ConstraintsSTA11+C11+C12+C13+C14+C15+C16+C17-4250W1<=0A12+C21+C22+C23+C24+C25+C26+C27-4250W2<=0A11-B11-B12-B13-B14-B15-B16-B17=0A12-B21-B22-B23-B24-B25-B26-B27=0B11+B21+C11+C21-1200F1<=0B12+B22+C12+C22-1200F2<=0B13+B23+C13+C23-700F3<=0B14+B24+C14+C24-700F4<=0B15+B25+C15+C25-1000F5<=0B16+B26+C16+C26-1000F6<=0B17+B27+C17+C27-700F7<=0B11+B21-D11>=0B12+B22-D22>=0B13+B23-D33>=0B14+B24-D43>=0B15+B25-D54>=0B16+B26-D64>=0B17+B27-D75>=0D11=625D22=625

Constraints (Cont.)

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

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

Constraints (Cont.)W3+W4 =1F8+F9+F10+F11+F12=3F10=1U38 + U48 - 0.7L81>=0U39 + U49 - 0.7L91>=0U310 + U410 - 0.7L102>=0U311 + U411 - 0.7L113>=0U312 + U412 - 0.7L123>=0ENDINT W3INT W4INT F8INT F9INT F10INT F11INT F12INT R3INT R4INT W1INT W2INT F1INT F2INT F3INT F4INT F5INT F6INT F7INT R1INT R2

Demand data for two regions

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

Warehouse and Franchisee Opening cost

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

*Metro-Chennai and Coimbatore#Non-Metro-All other towns

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 (F3) 700

Franchisee (F4) 700



Franchisee (F7) 700

Franchisee (F8) 850

Franchisee (F9) 900




Recycling Plant R1 1800

Recycling plant R2 1800



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)

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 2-without warehouse(Do not consider warehouses in the reverse chain)

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

Tirupathi

Vellore

Dharapuram

Chennai north

Chennai south

Trichy

Vellore

Pondy

Madurai

Erode

Trichy

Vellore

Coimbatore

1

2

3

n

1

2

3

n

PLANT

WAREHOUSE

FRANCHISEE

DEALER

FORWARD OPTIMAL NETWORK

Chennai north

Chennai south

Vellore

Vellore

Trichy

Pondy

1

2

3

n

1

2

3

n

Vellore

Coimbatore

SMELTER

WAREHOUSE

FRANCHISEE

DEALER

REVERSE OPTIMAL NETWORK

Madurai

Erode

Coimbatore

Without Warehouse

Karaikudi

Vellore

Chennai north

Chennai south

Trichy

Vellore

Vellore

Trichy

Pondy

1

2

3

n

1

2

3

n

Dharapuram

Vellore

Coimbatore

SMELTER

WAREHOUSE

FRANCHISEE

DEALER

REVERSE OPTIMAL NETWORK

Madurai

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

Case study organisation

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