Companies A, B, and C supply components to three plants (F, G, and H) via two crossdocking facilities (D and E). It costs $4 to ship from D regardless of final destination and $3 to ship to E regardless of supplier. Shipping to D from A, B, and C costs $3, $4, and $5, respectively, and shipping from E to F, G, and H costs $10, $9, and $8, respectively. Suppliers A, B, and C can provide 200, 300 and 500 units respectively and plants F, G, and H need 350, 450, and 200 units respectively. Crossdock facilities D and E can handle 600 and 700 units, respectively. Logistics Manager, Aretha Franklin, had previously used "Chain of Fools" as her supply chain consulting company, but now turns to you for some solid advice.
-Which of these constraints allows for some inventory to be held at one of the crossdock facilities?
A) AD + BD + CD - DF - DG - DH ≥ 0
B) AD + BD + CD - DF - DG - DH = 600
C) AD + BD + CD = DF - DG - DH = 600
D) AD + BD + CD + DF + DG + DH = 600

Question

Quizplus · Accepted Answer

Constraint A represents the inventory balance equation, where the sum of the shipments from suppliers to the cross-dock facilities minus the sum of the shipments from the cross-dock facilities to the plants needs to be greater than or equal to zero for all components. This means that some inventory can be held at the cross-dock facilities to ensure that all plants are adequately supplied. Options B, C, and D do not allow for inventory to be held at the cross-dock facilities.

Companies A, B, and C Supply Components to Three Plants