The Metal Company has a plant in Chicago, IL, that ships truckloads of product to customers daily. Shipments from Metal are dependent on customer demands and follow the following distribution:
Trucks Demanded Probability
0 0.2
1 0.3
2 0.3
3 0.2
Fast is a trucking company that supplies trucks to Metal. To provide a truck to Metal in a given period, Fast has to plan for truck availability the previous period. It costs Fast $200 per truck that it plans to make available to Metal. Metal pays Fast $400 per truck used. If Metal needs a truck that Fast does not have, Fast pays Metal a penalty per truck of $200. Metal then rents a truck and driver for a period at a cost of $800 per truck.
a. Provide the planned trucks at Fast that will maximize Fast's profits. Also provide the associated service level that Metal will observe, given this number of planned trucks by Fast.
b. Given Fast's planned trucks, provide Metal's expected costs.
c. An executive at Metal offers Fast the following deal: Metal will guarantee Fast usage of one truck every period, i. e., Metal will pay Fast for one truck whether they need it or not, but in return Fast should provide 100% service level. What would be the impact of this deal on Metal's expected costs and Fast's expected profits? Should Fast accept this offer?