Edison's Equipment

$($This problem is based upon $2019$ MBA graduate Sam E$.$ consulting problem. All names and contexts have been changed to protect those covered under US Code Title $27$ legislation.$)$

Due to the plethora of companies involved in the medical equipment area, Edison's Equipment needs to consolidate its warehouses to stay profitable. Warehouses S$23,$ S$27$ and S$15$ are to be closed, and their $2$ main SKU groups of products redistributed to the other $7$ active warehouses $\backslash ((\backslash$mathrm$\{$S$\}2\backslash$mathrm$\{$~S$\}4,\backslash$mathrm$\{$~S$\}6,\backslash$mathrm$\{$~S$\}8,\backslash$mathrm$\{$~S$\}10,\backslash$mathrm$\{$~S$\}12,\backslash$mathrm$\{$~S$\}14)\backslash ).$

The two main SKU groups $-$ PACKA and PACKB. Each SKU Group uses up a certain amount of warehouse space $-$ PACKA uses $5$ space units per unit of product and PACKB uses $9$ space unit per unit of product.

Our goal is to find the least cost way of sending PACKA and PACKB inventory from the three closing warehouses to the remaining $7.$ Cost is defined below per unit of product $($all products cost the same$)$ between the corresponding warehouses.

The number of product units that needs to be redistributed is shown below $-$ by warehouse by SKU group.

The following table depicts attributes about the remaining active warehouses $-$ specifically the space available to house existing SKU Group units from the $3$ closing warehouses and a measure of inventory turnover $($INV TURN$)$ for each SKU Group at each warehouse. The higher the inventory turnover measure, the quicker the products sell $($and that is 'good'$).$ Weighted averages of INV TURN will impact the model solution $($see later$).$

Create an LP model that will determine how to send the two kinds of SKU units from S$23,$ S$27$ and S$15$ to the remaining $7$ active warehouses. Cost should be minimized. Your model must be very explicit in its specifications.

Other aspects of your model:

$-$ All SKU units must be sent. No more, no less.

$-$ The space of arriving units at an active warehouse is constrained by the space available. Refer back to $\backslash (\backslash$underline$\{\backslash$underline$\{\backslash$text $\{$ rd $\}\}\}\backslash )$ paragraph for how much space each SKU group requires.

$-$ Also, at least $\backslash (60\backslash \%\backslash )$ of the space requirements at each active warehouse must be used by SKU Group arrivals. This is a de facto 'balancing' constraint.

$-$ To make sure products are sent to where they are more likely to be sold, the INV TURN of arriving units at each warehouse must average at least $22\mathrm{.}1$ per unit.

$-$ Using warehouse space as the relevant units, limit the combined warehouse space units of $($PACKA and PACKB$)$ equipment units sent from any one closing warehouse to any one active warehouse to no more than $4000.$ Again, this is in units of warehouse space.

$-$ At the end, make sure integer units are sent. But not until the end.

Note: Incorrect decision variable specification will limit available checkpoint 'points' to no more than $\backslash (40\backslash \%\backslash )$ of the possible total points that can be earned.

Version $1-$ I reserve the right to modify the problem description as necessary up until the due date.