1 utdallas.edu/~metin SC Design Facility Location under Uncertainty Chapter 6

2 utdallas.edu/~metin A tree representation of uncertainty u One way to represent Uncertainty is a binomial tree u Up by 1 down by -1 move with equal probability T steps

3 utdallas.edu/~metin Decision tree –One column of nodes for each time period –Each node corresponds to a future state »What is in a state? u 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 utdallas.edu/~metin 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 utdallas.edu/~metin AM Tires How many states in period 2? Consider US demand 4 or 3 states Consider the rest also 4x4x4 or 3x3x3

6 utdallas.edu/~metin 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. PlantsMarkets U.S. Mexico U.S. Mexico

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

8 utdallas.edu/~metin AM Tires: Demand Allocation for DU = 144; DM = 72, E = 14.06; Cheap Peso Plants Markets U.S. Mexico U.S. Mexico 100K; $15 44K; $21.2 6K; $9.2 Profit =Revenue-Cost US Production’s contribution=100,000*15-1,100,000=$400,000 Mex Production’s contribution=44,000* *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 utdallas.edu/~metin AM Tires: Demand Allocation for DU = 144; DM = 72, E = 8.44; Expensive Peso Plants Markets U.S. Mexico U.S. Mexico 100K; $15 44K; $16 6K; $15.4 US Production’s contribution=100,000*15-1,100,000=$400,000 Mex Production’s contribution=44,000* *15.4-4,400,000/8.44 = =$275,073 Profit(DU = 144; DM = 72, E = 8.44; Period 2; Both flexible)=$675,073

10 utdallas.edu/~metin AM Tires: Demand Allocation for DU = 144; DM = 72, E = 5.06; Very Expensive Peso Plants Markets U.S. Mexico U.S. Mexico 78K; $15 22K; $ K; $25.7 US Production’s contribution=78000* *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 utdallas.edu/~metin 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 utdallas.edu/~metin Capacity Investment Strategies u Single sourcing is risky u Hedging Strategy –Risk management? »Too much capacity or too little capacity »E.g. 200 leading financial services companies are examined from Every other company struck at least once by a risky event. u Source: Running with Risk. The McKinsey Quarterly. No »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 u Flexible Strategy –Excess total capacity in multiple plants –Flexible technologies u More will be said in aggregate planning chapter

13 utdallas.edu/~metin Summary u Decisions under uncertainty –Location –Flexibility u Decision trees