SC Design Facility Location under Uncertainty Chapter 6

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SC Design Facility Location under
UncertaintyChapter 6
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A tree representation of uncertainty

• One way to represent Uncertainty is a binomial
  tree
• Up by 1 down by -1 move with equal probability

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T steps
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Decision tree

• One column of nodes for each time period
• Each node corresponds to a future state
• What is in a state?
• Price, demand, inflation, exchange rate, your
  OPRE 6366 grade
• Each path corresponds to an evolution of the
  states into the future
• Transition from one node to another determined by
  probabilities
• Evaluate the cost of a path starting from period
  T and work backwards in time to period 0.

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Evaluating Facility Investments AM Tires.
Section 6.5 of Chopra.
Now U.S. Demand 100,000 Mexico demand
50,000. Demand is not to be met always. But
selling more increases profit. 1US 9
pesos. Sale price 30 in US and 240 pesos in
Mexico.
Future Demand goes up or down by 20 percent with
probability 0.5 and Exchange rate goes up or
down by 25 per cent with probability 0.5.
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AM Tires
How many states in period 2? Consider US
demand 4 or 3 states Consider the rest
also 4x4x4 or 3x3x3
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AM Tires

• Four possible capacity configurations
• Both dedicated
• Both flexible
• U.S. flexible, Mexico dedicated
• U.S. dedicated, Mexico flexible
• Consider the both flexible configuration
• For each node solve the demand allocation model.

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AM Tires in period 2 Demand Allocation for DUS
144 DMex 72, E 14.06
1.1240/14.06-15-1 21.230-110/14.06-1 9.2(240-11
0)/14.06
Compare this formulation to the Transportation
problem. We maximize the profit now.
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AM Tires Demand Allocation for DU 144 DM
72, E 14.06 Cheap Peso
Plants Markets
100K 15
U.S.
U.S.
Profit Revenue-Cost
44K 21.2
Mexico
Mexico
6K 9.2
US Productions contribution100,00015-1,100,000
400,000 Mex Productions contribution44,00021.2
60009.2-4,400,000/14.06675,055 Profit(DU
144 DM 72, E 14.06 Period 2 Both
flexible)1,075,055
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AM Tires Demand Allocation for DU 144 DM
72, E 8.44 Expensive Peso
Plants Markets
100K 15
U.S.
U.S.
44K 16
Mexico
Mexico
6K 15.4
US Productions contribution100,00015-1,100,000
400,000 Mex Productions contribution44,000166
00015.4-4,400,000/8.44
70400092400-521327275,0
73 Profit(DU 144 DM 72, E 8.44 Period 2
Both flexible)675,073
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AM Tires Demand Allocation for DU 144 DM
72, E 5.06 Very Expensive Peso
Plants Markets
78K 15
U.S.
U.S.
22K 31.4
Mexico
Mexico
50K 25.7
US Productions contribution78000152200031.4-1
,100,000760,800 Mex Productions
contribution5000025.7-4,400,000/5.06415,435 Pr
ofit(DU 144 DM 72, E 8.44 Period 2 Both
flexible)1,176,235 Cheap Peso profit1,075K
Expensive Peso profit675K Very Expensive Peso
profit1,176K
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Facility Decision at AM Tires
Make profit computations for the first year nodes
one by one Compute the profit for a node and
add to that (0.9)(1/8)(Sum of the profits of all
8 nodes connected to the current one)
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Capacity Investment Strategies

• Single sourcing is risky
• Hedging Strategy
• Risk management?
• Too much capacity or too little capacity
• E.g. 200 leading financial services companies are
  examined from 1997-2002. Every other company
  struck at least once by a risky event.
• Source Running with Risk. The McKinsey
  Quarterly. No.4. 2003.
• Managers unfamiliar with risk often focus on
  relatively simple accounting metrics as net
  income, earnings per share, return on investment,
  etc.
• Match revenue and cost exposure
• Flexible Strategy
• Excess total capacity in multiple plants
• Flexible technologies
• More will be said in aggregate planning chapter

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Summary

• Decisions under uncertainty
• Location
• Flexibility
• Decision trees