Group-9
(Assignment- SUPPLY CHAIN NETWORK DESIGN )
Tarun Yadav (PGP30291); Shubra (PGP30283); Saurav (PGP30340); Arjun (PGP30186); Abhishek (PGP29368)
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Q9: How would you model a new objective (in addition to cost minimization) that the all-India average inventory turnover ratio for the Plant-to-Depot pipeline is above a minimum target value? Suggest a suitable extension/ modification of the MILP model proposed in the class. a= subscript which represents SKU’s b= subscript representing factory c = subscript representing technology/line d= subscript representing depot
M= subscript representing markets

Variables
Depotdepot {1, the , ℎe 0}
FactoryLine,factoryline {0, 1,2,…, }

FlowOfUnitsFactoryToMarketa,b,c,M Number of units which are transferred from the factory to market
FlowOfUnitsFactoryToDepota,b,c,d Number of units which are transferred from the factory to depot
FlowOfUnitsDepotToMarketa,d,M Number of units which are transferred from the depot to market

NumberOfTripsabd Number of trips of the product p from the factory f to depot d

Constants_____________________________________________________________
FixedCapitalOfLine costbc = Fixed cost of setting up the line l in factory f
FixedCapitalOfDepot costd = Fixed cost of setting up the depot d
TransportToDepot costbd = Quantity based transport cost from the factory f to depot d
TransportFromFactory costbM = Quantity based transport cost from the factory f to market m
TransportFromDepot costdM = Quantity based transport cost from the depot d to market m
TripBased costabd =Trip based transport cost for transporting product p from factory f to depot d
CapacityOfLineca = Capacity of line l in producing product p
CapacityOfDepotd = Capacity of depot d

Objective Function_____________________________________________________
Minimize,
Σ(FixedCapitalOfLine costbc *FactoryLine,factoryline)+Σ(FixedCapitalOfDepot costd * Depotdepot)d+Σ(TransortFromFactory costbM * FlowOfUnitsFactoryToMarketa,b,c,M)
+Σ(TransportToDepot costbd * FlowOfUnitsFactoryToDepota,b,c,d)+Σ(Trans.costd,m* FlowOfUnitsDepotToMarketa,d,M) + Σ(TripBased costabd ∗ NumberOfTripsabd)

Additional Constraints___________________________________________________
The inventory turnover ratio of the factory-depot pipeline is directly proportional to (TransportToDepot costbd + TransportFromFactory costbM + TransportFromDepot costdM)/(Total Inventory).
Thus we can set a limit on this ratio instead of inventory turnover ratio = (Limit which is given * cost of the product/(cost of the product + transportation cost))
1. Inventorydb = 12Σ FlowOfUnitsFactoryToDepota,b,c,d * NumberOfTripsabd --- (Inventory is half of the quantity/trip)
2. Σ FlowOfUnitsFactoryToMarketa,b,c,M +Σ FlowOfUnitsDepotToMarketa,d,M =aM ∀a,b,c ---- product flow management constraint
3. Σ FlowOfUnitsFactoryToDepota,b,c,d = FlowOfUnitsDepotToMarketa,d,M ∀a,b,c ---- product flow management at depots
4. ΣΣ FlowOfUnitsFactoryToMarketa,b,c,M +Σ FlowOfUnitsFactoryToDepota,b,c,d * CapacityOfLineca ≤ FactoryLine,factoryline --- Constraint for line capacity
5. Σ FlowOfUnitsFactoryToDepota,b,c,d * CapacityOfDepotd ≤ Depotdepot --- Constraint for depot capacity
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