Supply Chain Management $-$ Winter $2024$

Question $1$: Adding a distribution center $($DC$)$ to the problem introduces an intermediary step in the

supply chain. Now, we must account for transportation costs not only from factories to customers but

also from factories to the distribution center and then from the distribution center to the customers.

We'll assume a single distribution center for simplicity.

Now we have four factories $($F$1,$ F$2,$ F$3,$ F$4),$ one distribution center $($DC$),$ and six customers $($C$1,$ C$2,$ C$3,$

$C4,C5,C6.$ The factories send goods to the DC$,$ which in turn distributes them to the customers. We

need to decide whether to open or close each factory and minimize the total costs, including operating

factories, transporting goods to the DC$,$ and then from the DC to the customers.

Additional Assumptions:

Fixed costs of operating the distribution center $($DC$)$: $$20,000$

Variable transportation costs per unit from factories to the DC:

DC

F$1$ $$1$

F$2$ $$2$

F$3$ $$1\mathrm{.}5$

F$4$ $$2\mathrm{.}5$

Variable transportation costs per unit from the DC to customers:

Assume the DC has unlimited capacity.

$1-$ Carefully write the mathematical formulations including the constraints.

$2-$ Using Excel Solver, Minimize the total cost of operating factories, the distribution center, and

transporting goods from factories to the DC and then to customers.