Optimal Procurement Strategy for Electricity: Fixed Commitment vs. Option Contract

To determine the optimal procurement strategy, we need to calculate the expected profit for each option.

Option 1: Fixed commitment contract with Company 1 The cost of electricity is fixed at $10 per unit. The expected profit can be calculated as follows:

Expected demand = (0.1 x 100) + (0.2 x 200) + (0.4 x 300) + (0.2 x 400) + (0.1 x 500) = 310 units Total cost of electricity = 310 x $10 = $3,100 Total revenue = 310 x $20 = $6,200 Expected profit = Total revenue - Total cost of electricity = $3,100

Option 2: Option contract with Company 2 The reservation price is $6 per unit, and the cost for each unit delivered is also $6. Let x be the number of units ordered in advance, and y be the number of units ordered for delivery. The expected profit can be calculated as follows:

Expected demand = (0.1 x 100) + (0.2 x 200) + (0.4 x 300) + (0.2 x 400) + (0.1 x 500) = 310 units Total cost of electricity = (x + y) x $6 + (310 - x - y) x $6 = $1,860 + 6y - 6x Total revenue = 310 x $20 = $6,200 Expected profit = Total revenue - Total cost of electricity = $4,340 + 6x - 6y

To determine the optimal values of x and y, we need to solve for the maximum expected profit. Taking the partial derivative of the expected profit with respect to x and y and setting them equal to zero, we get:

∂(Expected profit)/∂x = 6 = 0 ∂(Expected profit)/∂y = -6 = 0

These equations have no solutions, which means that there is no optimal combination of x and y that maximizes the expected profit. Therefore, the manufacturer should choose the fixed commitment contract with Company 1, as it guarantees a higher expected profit of $3,100.