Ron Mason's Problem

Ron Mason would like to determine how many Cushion$-$Air$-$Pro units to manufacture each month,

and how many units to ship to the distribution centers each month in order to minimize total

transportation and inventory costs.

Assignment

Construct a discrete optimization model of the problem of minimizing the total transportation

and inventory costs over the months of April and May. What is the average monthly cost in

April and May if the logistics operation at Dellmar is optimized? What should be Dellmar's

production and shipping schedule?

Note $1$: When you calculate the inventory cost of a distribution center for a particular month,

you consider the inventory level at the end of that month as the inventory level for the whole

month. For example, if the inventory level is $20000$ in the beginning of April and reduces to

$15000$ at the end of April, then the inventory cost of the distribution center in April is $15000$

$$ cost per unit.

Note $2$: You need to first write down the optimization model $($including the objective function

and constraints$)$ and then use Excel $($or other softwares$)$ to solve the problem. You are

required to submit both the optimization model and the Excel file. When I grade your

solution, I will first look at your optimization model to see whether it is correct, and then

check your Excel file. It is ok if you submit a scanned$/$photoed version of your handwriting of

the optimization model. If the objective function is too long, you need to provide explanations

for each component in the objective function. Please also explain each constraint.

Note $3$: When you run the solver but cannot get a solution, you may try $"$GRG Nonlinear"

instead of "Simplex LP$".$