You manage a group of 40 pilots. Based on experience and skill level, 10 of the 40 are Ă˘â‚¬Ĺ“Class AĂ˘â‚¬Âť pilots, 22 of the 40 are Ă˘â‚¬Ĺ“Class BĂ˘â‚¬Âť fliers, and the remaining 8 are Ă˘â‚¬Ĺ“Class CĂ˘â‚¬Âť pilots. (Class A pilots have a quality of Ă˘â‚¬Ëś10Ă˘â‚¬â„˘, Class Ă˘â‚¬Ĺ“B: a quality of Ă˘â‚¬Ëś9Ă˘â‚¬â„˘, and Class C pilots a quality of Ă˘â‚¬Ëś8′)
Over the next 10 weeks, you must have each of them attend some military professional development program classes (referred to as MPD). During that time, they are not available to perform normal work duties. Thus, you have to manage their scheduled training time to make sure the number of pilots available to perform normal work does not fall below Ă˘â‚¬ËśminimumĂ˘â‚¬â„˘ numbers. 40 pilots
You have 7 different MPD classes that span the next 10 weeks. Three week classes can have all three pilot classes enroll Ă˘â‚¬â€ś two week classes can only accommodate Class Ă˘â‚¬Ĺ“AĂ˘â‚¬Âť and Class Ă˘â‚¬Ĺ“BĂ˘â‚¬Âť (this is shown in the table below). Each MPD has a Ă˘â‚¬Ĺ“learning valueĂ˘â‚¬Âť parameter (measuring the effectiveness of that specific MPD class) and a Ă˘â‚¬Ĺ“costĂ˘â‚¬Âť (in units per person attending).
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The total cost of the staffing model must not exceed 675 units.
The table below provides all needed information.
|Starting||(per person)||(per person)||(per person)|
|Week||Min Pilots||Week||Min Pilots|
There are two additional requirements related to the number of pilots that can be assigned to each MPD. No more than 8 total pilots (Class Ă˘â‚¬Ĺ“AĂ˘â‚¬Âť plus Class Ă˘â‚¬Ĺ“BĂ˘â‚¬Âť plus Ă˘â‚¬Ĺ“Class CĂ˘â‚¬Âť) can be assigned to any one MPD. And, no more than 5 pilots from a specific pilot Ă˘â‚¬Ĺ“ClassĂ˘â‚¬Âť can be assigned to any one MPD.
Create a linear prescriptive analytic model that will determine how to maintain proper staffing levels for normal work in your squadron while scheduling all 40 of your pilots in MPD classes. Your objective should be to maximize the Ă˘â‚¬Ĺ“valueĂ˘â‚¬Âť of the scheduled pilots to classes (must be integers). A simple objective function.