1.Optimal Contract Quality

VeloScience is a company that makes technological devices for bicyclists. One of their products is the iPed, which uses GPS information and wind speed to deliver real-time feedback on how many calories a cyclist has burned on a given route. Hilly terrains and high headwinds cause cyclists to burn more calories than flat terrains and high tailwinds, and the iPed takes all of that into consideration when it does its calculations.

VeloScience has privately decided that their current model, the iPed3, has one year remaining before it is replaced by the iPed4. Still, the company needs to finalize a contract with a manufacturer in China regarding how many iPed3 units to produce for its final year. VeloScience sells the iPed3 for $100.

The manufacturer in China will produce the iPed3 at a unit cost of $50 provided they have a contract with a guaranteed order quantity (minimum 10k units). Because the lead-time is very long, VeloScience can only place and receive one order from China to use for the final year of the iPed3. In the event annual demand is less than the Chinese order, VeloScience can clear the leftover devices for $30 per unit.

You have been given the job of finalizing the contract with the Chinese manufacturer. VeloScience has forecasted next year's demand to be 20k with a standard deviation of 5k. A normal distribution can be assumed for modeling the demand.

a.Specify the order size to the nearest 1000 units that VeloScience should commit to in the Chinese contract. Assume VeloScience has no inventory from the previous year to begin the final year. Build a simulation model and use at least 10000 trials to justify your answer. (Hint: test increments of 1000, from 15,000 units up to 30,000 units.) What is the new optimal expected profit?

b.Suppose the situation is identical to part (a) except now VeloScience has access to a second manufacturer in Mexico who can rapidly satisfy any excess ("overflow") demand via emergency orders should the main order from China be exhausted before year's end. The manufacturer in Mexico charges $64 per unit (no minimum order, no contract). What is the new order size specified in the Chinese contract? Build another simulation model and use at least 10,000 trials to justify your answer. What is the new optimal expected profit?