question archive Companies A, B, and C supply components to three plants (F, G, and H) via two crossdocking facilities (D and E)
Companies A, B, and C supply components to three plants (F, G, and H) via two crossdocking facilities (D and E)
Subject:Operations ManagementPrice:2.87 Bought7
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? Which constraint allows for movement of product, but allows some of that product to remain at locations F, G, H, without having to be moved on to one of the final locations, F, G, or H.
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Answer:
Let XAD be the variable indicating quantity to be moved from Supplier A to Cross Docking Facility D. Similar notation is used for other decision variables.
Therefore, the required constraint allowing movement of product but allowing some of the product to remain at cross dock locations without having to be moved to one of the final locations F,G or H are following
XAD + XBD + XCD - (XDF + XDG + XDH) = K1 , where K1 is the inventory remaining at cross dock location D
XAE + XBE + XCE - (XEF + XEG + XEH) = K2 , where K2 is the inventory remaining at cross dock location E
