Question

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, Jack Beauregard, had previously used ʺChain of Foolsʺ as his supply chain consulting company, but now turns to you for some solid advice.

1. How many demand-side constraints are there? Write the demand-side constraints.

Answer 1

We prepare a network diagram for better understanding:

Let the units shipped from Company A to Cross-docking facility D be Xad, Company A to Cross-docking facility E be Xae and so on. Hence, we get decision variables as Xad, Xae, Xbd, Xbe, Xcd, Xce, Xdf, Xdg, Xdh, Xef, Xeg, Xeh

Total Capacity = 200 + 300 + 500 = 1000

Total Demand = 350 + 450 + 200 = 1000

Total Demand = Total capacity. hence, we will get "=" sign for all constraints

We get Demand Constraints at final destinations as:

Xdf + Xef = 350.................Constraint for demand at plant F

Xdg + Xeg = 450.................Constraint for demand at plant G

Xdh +Xeh = 200.................Constraint for demand at plant H

Above are the three demand constraints for PLants F, G and H

We further have 2 demand constraints for Cross docking facilities

Xae + Xbe + Xce <= 600.................Constraint for maximum demand/capacity at facility E

Xaf + Xbf + Xcf <= 700....................Constraint for maximum demand/capacity at facility F

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