Question

The following table shows how long does a team take to deliver projects for clients.      

	CLIENT
TEAM	RV Ltd	Roadster Ltd	Launch LLC
Tame	12	15	2
Carle	9	18	5
Mac	15	13	3

Each client requires one project to be delivered. Each team can deliver one project. The objective is to deliver each project in the least time possible.

Draw the Network Model

Come up with the Objective Function (which is the equation that needs to be solved to find the minimum time to deliver the projects)

Create the model in excel, show the constraints.

Solve using Solver - Please do the screen capture with the solver window, so that I can see the constraints. Select LP or Simplex LP (linear) in Solver.

Answer 1

Let X_ij be the binary integer such that X_ij=1 when the i-th team is assigned to the j-th customer. i=1,2,3 and j=1,2,3

Objective Function: Minimize Z = total time to deliver
Z = 12X₁₁ + 15X₁₂ + 2X₁₃ + 9X₂₁ + 18X₂₂ + 5X₂₃ + 15X₃₁ + 13X₃₂ + 3X₃₃

Subject to,

X₁₁ + X₁₂ + X₁₃ = 1
X₂₁ + X₂₂ + X₂₃ = 1
X₃₁ + X₃₂ + X₃₃ = 1

X₁₁ + X₂₁ + X₃₁ = 1
X₁₂ + X₂₂ + X₃₂ = 1
X₁₃ + X₂₃ + X₃₃ = 1

X_ij = {0,1};  i=1,2,3 and j=1,2,3

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