Applications of the Theory of Constraints The P Q Exercise BA 341 Lean Operations Dr Bogdan Bichescu 1 Objectives Understanding the role the Theory of Constraints plays in decision making Which products to make New equipment necessary How should we price our products Which products should we make Goldratt s P Q example The Haystack Syndrome Goldratt 1991 A process can produce two products P and Q P 10 10 15 Component Process Time D C A 5 10 C B Q 5 5 10 C B D 25 10 B A 5 20 20 20 25 P3 P P2 Q1 Q2 1 Component Cost More Product Info Cost and demand info Product Selling Price unit Raw Material unit Revenue Margin unit Weekly Demand P 90 45 45 110 Q 100 45 55 60 P Q require processing on four machines processing times minutes per product are Product A B C D Total P 15 10 15 10 50 Q 10 35 5 5 55 Machines run 2400 mins week fixed costs 4000 week Decision Analysis Goal maximize our profit Decision output How many units of P and Q should we make Model Inputs Costs of components of P and Q machining times for components sales price of P and Q maximum machine time available etc Using the Throughput Perspective Step 1 Machine Load on P 110 units Load on Q 60 units Total time required Available time A 1 650 600 2 250 2 400 B 1 100 2 100 3 200 2 400 C 1 650 300 1 950 2 400 D 1 100 300 1 400 2 400 Step 2 Exploit the constraint Which product generates the most throughput on the bottleneck machine Why Which product is most profitable to produce Answer P generates the highest profit per unit of time on the bottleneck machine Step 2 Exploit the constraint cont d Which is the most profitable product mix Answer 2 400mins 10 mins unit 240 units Demand 110 produce 110 units to meet demand 1 100 mins Make product Q in the remaining time i e 1 300 mins 35 mins unit 37 units The Throughput World Approach Profit is Going on with the process Now how can we Subordinate the system to our production plan Make sure that all resources work toward producing 110 units of P and 37 units of Q How about elevating the constraint Increase Capacity What changes would you make if we increased capacity of machine B to 3 300 minutes Does the constraint change An alternative approach How would the P Q problem be approached using conventional wisdom i e the cost world approach Rank the products in order of revenues margin per unit Highest to lowest Answer Q 55 P 45 Which product appears to be the one that you would like to produce the most Why Answer Q as it has the highest profit margin per unit Using the Cost World approach Which is the most profitable product mix 2 400mins 35mins unit 68 units Demand 60 produce 60 units of product Q 2 100 minutes to meet demand Use remaining time to produce product P produce 300mins 10mins unit 30units The Cost World Approach Profit is 60 units of Q x 55 unit 30 units of P x