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SC Design Facility Location under Uncertainty Chapter 6

SC Design Facility Location under Uncertainty Chapter 6. A tree representation of uncertainty. One way to represent Uncertainty is a binomial tree Up by 1 down by -1 move with equal probability. <Show Applet balldrop.htm>. T steps. Decision tree. One column of nodes for each time period

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SC Design Facility Location under Uncertainty Chapter 6

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  1. SC DesignFacility Locationunder UncertaintyChapter 6

  2. A tree representation of uncertainty • One way to represent Uncertainty is a binomial tree • Up by 1 down by -1 move with equal probability <Show Applet balldrop.htm> T steps

  3. 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.

  4. 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.

  5. AM Tires How many states in period 2? Consider US demand 4 or 3 states Consider the rest also 4x4x4 or 3x3x3

  6. PlantsMarkets U.S. U.S. Mexico Mexico 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.

  7. AM Tires in period 2: Demand Allocation for DUS = 144; DMex = 72, E = 14.06 1.1=240/14.06-15-1 21.2=30-110/14.06-1 9.2=(240-110)/14.06 Compare this formulation to the Transportation problem. We maximize the profit now.

  8. AM Tires: Demand Allocation for DU = 144; DM = 72, E = 14.06; Cheap Peso PlantsMarkets 100K; $15 U.S. U.S. Profit =Revenue-Cost 44K; $21.2 Mexico Mexico 6K; $9.2 US Production’s contribution=100,000*15-1,100,000=$400,000 Mex Production’s contribution=44,000*21.2+6000*9.2-4,400,000/14.06=$675,055 Profit(DU = 144; DM = 72, E = 14.06; Period 2; Both flexible)=$1,075,055

  9. AM Tires: Demand Allocation for DU = 144; DM = 72, E = 8.44; Expensive Peso PlantsMarkets 100K; $15 U.S. U.S. 44K; $16 Mexico Mexico 6K; $15.4 US Production’s contribution=100,000*15-1,100,000=$400,000 Mex Production’s contribution=44,000*16+6000*15.4-4,400,000/8.44 =704000+92400-521327=$275,073 Profit(DU = 144; DM = 72, E = 8.44; Period 2; Both flexible)=$675,073

  10. AM Tires: Demand Allocation for DU = 144; DM = 72, E = 5.06; Very Expensive Peso PlantsMarkets 78K; $15 U.S. U.S. 22K; $31.4 Mexico Mexico 50K; $25.7 US Production’s contribution=78000*15+22000*31.4-1,100,000=$760,800 Mex Production’s contribution=50000*25.7-4,400,000/5.06=$415,435 Profit(DU = 144; DM = 72, E = 8.44; Period 2; Both flexible)=$1,176,235 Cheap Peso profit=$1,075K; Expensive Peso profit=$675K; Very Expensive Peso profit=$1,176K

  11. 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)

  12. 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

  13. Summary • Decisions under uncertainty • Location • Flexibility • Decision trees

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