Production Planning for three Machine Assembly shops of

Heavy Mechanical Complex Using Simplex Method

Mian Saad Razaq16-IED-M.Sc-EM/FT-06

Case Study: • The Heavy Mechanical Complex (HMC) has Three Machine and

Assembly shops with excess production capacity. The HMC has a new product ready to begin production, and all three plants have this capability, so some of the excess capacity can be used in this way.

• This product can be made in three sizes—large, medium, and small

Profit:• Unit Profit for small Size product = $300• Unit Profit for medium Size product = $360• Unit Profit for Large Size Product = $420

Area: • Area for storage per unit (small) = 12 square feet • Area for storage per unit (Medium) = 15 square feet• Area for storage per unit (Large) = 20 square feet

• Area available in each plant:

• Plant 1 = 13000 square feet• Plant 2 = 12000 square feet• Plant 3 = 5000 square feet

Solution: Variable Defined.• Production of Large Products in Plant 1 = • Production of Medium Products in Plant 1 = • Production of Small Products in Plant 1 = • • Production of Large Products in Plant 2 = • Production of Medium Products in Plant 2 = • Production of Small Products in Plant 2 = • • Production of Large Products in Plant 3 = • Production of Medium Products in Plant 3 = • Production of Small Products in Plant 3 =

Solution: Objective Function• The objective is to predict how much of small, medium and large size

products can be produce in the three plants so that we can get the maximum profit. • The objective function is to: • Maximize P = +++

Solution: Constrained• Capacity of Plant 1= +• Capacity of Plant 2= +• Capacity of Plant 3= + • Area for plant 1 = +• Area for plant 2 = +• Area for plant 3 = +

• Maximum sales for an year of large product = +• Maximum sales for an year of large product = +• Maximum sales for an year of large product = +

Solution: Equation

Results: • Production of Large Products in Plant 1 = 500 units• Production of Medium Products in Plant 1 = 0• Production of Small Products in Plant 1 = 250 units• • Production of Large Products in Plant 2 = 150 units• Production of Medium Products in Plant 2 = 200 units• Production of Small Products in Plant 2 = 500 units• • Production of Large Products in Plant 3 = 350 units• Production of Medium Products in Plant 3 = 0• Production of Small Products in Plant 3 = 0

Profit:

• Maximum Profit = P = $675000

Equations Verification:

Equation s1 s2 s3 s4 s5 s6 s7 s8 s9 Right Side1 210000 0 75000 63000 72000 150000 105000 0 0 0 0 0 0 0 0 0 0 0 6750002 500 0 250 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7503 0 0 0 150 200 500 0 0 0 0 0 0 0 0 0 0 0 0 8504 0 0 0 0 0 0 250 0 0 0 0 0 0 0 0 0 0 0 2505 10000 0 3000 0 0 0 0 0 0 0 0 0 -24 0 0 0 0 0 129766 0 0 0 3000 3000 6000 0 0 0 0 0 0 0 -24 0 0 0 0 119767 0 0 0 0 0 0 5000 0 0 0 0 0 0 0 -24 0 0 0 49768 500 0 0 150 0 0 250 0 0 0 0 0 0 0 0 -60 0 0 8409 0 0 0 0 200 0 0 0 0 0 0 0 0 0 0 0 0 0 20010 0 0 250 0 0 500 0 0 0 0 0 0 0 0 0 0 0 0 750

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•THE END?