submitted by:
Arjyajyoti Goswami
Rachna Chawla

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Outsourcing and Capacity planning in an uncertain global environment
DECISION : to select between a domestic supplier and an offshore supplier to fulfill a certain demand and also to determine the optimum capacity sizes
DECISION MAKER : a firm , which is single expected utility maximiser
DECISION MAKING STAGES:
Stage 1 – determining the capacity sizes to be reserved with the two firms
Stage 2 – determining the production quantities with the 2 firms
Need for the decision
The domestic supplier has much higher production cost than the offshore supplier, but it does not involve any risk of fluctuating exchange rates
The overseas supplier has much less production cost than the domestic supplier but involves risks of fluctuating exchange rates
Also it has been proved that if a firm secures order from two suppliers rather than one in a global environment, then the profit incurred is higher than securing the order from a single supplier
ASSUMPTIONS WHILE MODELLING THE PROBLEM
Supplier capacity is not an issue, and both the suppliers are capable of supplying the desired quantity of items to the firm
The capacity reservation cost is in direct proportion to the quantity of the goods reserved i.e capacity size
The unit capacity reservation cost for both the suppliers, is same in domestic currency
In the solution of the model capacity investment expansion is not considered, and focus is only in fulfilling the current demand rather than thinking of long term strategies
MODEL FOR STAGE 1:
Max U (K) = E [ π ( K;x,y)] – γ/2 Var [π ( K;x,y)],
π ( K;x,y) = πT (K;x,y) – (cK 1) T K
The objective function is a mean variance utility function of π i.e the net profit over two stages.
The second equation indicates that the net profit over 2 stages is equal to the sales profit in stage 2 minus the capacity reservation cost in stage 1, and it
If γ = 0 , the firm is risk neutral
If γ > 0 , the firm is risk averse
MODEL FOR STAGE 2
In the second stage when the exchange rate and demand are realized as (x,y) the firm makes production decisions of q1(<= K1) and q2(<= K1), respectively with the two suppliers
Max πT = qT ( p1 – c.[1,x]T)
Subject to, 0<= q<= K
1Tq<= y
Objective function is to maximize the profit, which is selling price minus the production cost
The first constraint signifies that the production quantity should be less than the reserved capacities and the second constraint signifies that the total production must not exceed the realized demand
Also, p – c1 > cK , so that the domestic supplier is not ruled out of consideration
Risk-neutral newsvendors
Deterministic Demand
Uncertain Demand
DETERMINISTIC DEMAND
We divide the capacity space in 5 regions, because if K is located in different regions, the corresponding shadow prices will be different
λ1, λ2 are the shadow prices associated with K1 and K2.
Whenever the λ1 >= λ2 the off shore supplier is preferred
Whenever λ2 >=λ1 the domestic supplier is preferred.