Download - 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
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
∑ 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 (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
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