Slide 1ObjectivesWhich products should we make?More Product InfoDecision AnalysisUsing the “Throughput Perspective”Step 2: Exploit the constraintStep 2: Exploit the constraint (cont’d)Going on with the process…An alternative approachUsing the “Cost World” approach1BA 341 – Lean OperationsDr. Bogdan BichescuApplications of the Theory of ConstraintsThe P & Q ExerciseObjectives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 QDCCABCBBAD$5 $20 $20 $20 $25101015 51051025105QP1P2P3Q1Q2ProcessTimeComponentCostComponentPMore Product InfoCost and demand info:ProductABC D TotalP 15 10 15 10 50Q 10 35 5 5 55P & Q require processing on four machines; processing times (minutes) per product are:ProductSelling Price ($/unit)Raw Material ($/unit)RevenueMargin($/unit)Weekly DemandP $90 $45 $45 110Q $100 $45 $55 60Machines run 2400 mins/week, fixed costs $4000/weekDecision 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: MachineLoad on P (@ 110 units)Load on Q(@ 60 units)Total time requiredAvailable timeA 1,650 600 2,250 2,400B 1,100 2,100 3,2002,400C 1,650 300 1,9502,400D1,100 300 1,400 2,400Step 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 machineStep 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?What is the maximum acceptable cost for this elevation?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 unitUsing 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 $45/unit – 4,000=$4,650-$4,000=$650This is $2,335 less than the TOC