For an optional ungraded assignment (see it as a complex problem that won't be graded, more to test our skills and knowledge) I was given the following problem. It is not as straightforward as all the other examples we covered and I would really like to know how to solve the problem.
A hotel is estimating that in the next 7 days they will need to have available the following number of sheets:
Starting day 1 they have 0 sheets. They need to buy sheets at $20 per set and they can wash to reuse. There are 2 types of laundry services:
$6 requiring 2 days (sheets can be used on day 1 and then again on day 3)
$3 requiring 3 days (sheets can be used on day 1 and then again on day 4)
How can I formulate the linear programming model to determine the optimal laundry and purchasing policy? And how can I run this using Gurobi (Python)?
All I know up to now is that I need to minimize costs of buying, cheap and luxury laundry. Lets say buy = b_i and ranges from 1-7, luxury = x_i and ranges from 1-5 and cheap = y_ij and ranges from (1.4, 1.5, 1.6, 1.7 , 2.5, 2.6, 2.7, 3.6, 3.7 and 4.7), other than that I do not know how to go further.