Question

In the wake of the Covid-19 pandemic, Honeywell Inc. has orders for 1000 face masks from Richardson and 800 face masks from Plano. Honeywell Inc. has 1200 masks ready in a Frisco facility and 1000 masks in an Irving facility. It costs $10 to ship a mask from Frisco to Richardson, and $7 to ship it from Frisco to Plano. It costs $9 to ship a mask from Irving to Richardson and $12 to ship it from Irving to Plano. How many masks should Honeywell Inc. ship from each facility to Richardson and Plano to fulfill the orders at the minimum cost?

a)What are the decision variables?

b)Write the linear programming problem.

c)The shipping company that Honeywell is using has also been impacted due to Covid-19. It informs Honeywell that it can ship at most 400 masks from Frisco to Richardson and at most 500 masks from Irving to Plano. What is the change to your LP formulation?

Answer 1

a) Decision Variable:

Xfr = No. of unit transfer from Frisco to Richardson

Xfp = No. of unit transfer from Frisco to Plano

Xir = No. of unit transfer from Irving to Richardson

Xip = No. of unit transfer from Irving to Plano

b) Linear Programming Model:

Objective Function:

Minimize Transportation Cost (Z) = 10Xfr + 8Xfp + 9Xir + 12Xip

Constrains:

Demand Constrain:

1. Demand from Richardson: Xfr + Xir = 1000

2. Demand from Plano : Xfp + Xip = 800

Supply Constrain:

3. Supply from Frisco: Xfr+ Xfp <=1200

4. Supply from Irving: Xir + Xip <= 1000

Integer Constrains:

All Value of Decision Variables Xfr, Xfp, Xir, Xip >=0 (integers)

c) We need to add two Additional Constrains in the LP

Frisco to Richardson: Xfr <=400

Irving to Plano: Xip <=500

All other constrains remain the same.