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Optimizing Production for Products P and Q: A Constraint Management Approach

This analysis addresses the manufacturing constraints faced by a system producing products P and Q. Each product has distinct time and resource requirements, with defined market demands and contribution margins. The objective is to maximize profits by identifying bottlenecks, particularly focusing on Resource B. By exploiting this constraint and considering market variations, we calculate optimal production strategies and profits. The analysis includes sensitivity tests for production adjustments and explores the feasibility of investments to enhance capacity, notably in the context of expanding into the Japanese market.

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Optimizing Production for Products P and Q: A Constraint Management Approach

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  1. Practice: A Production System Manufacturing Two Products, P and Q $90 / unit $100 / unit Q: P: 60 units / week 110 units / week D D Purchased Part 10 min. 5 min. $5 / unit C B C 10 min. 5 min. 25 min. B A A 15 min. 10 min. 10 min. RM1 RM2 RM3 $20 per $20 per $25 per unit unit unit Time available at each work center: 2,400 minutes per week. Operating expenses per week: $6,000. All the resources cost the same.

  2. 1. Identify The Constraint(s) Contribution Margin: P($45), Q($55) Market Demand: P(110), Q(60) Can we satisfy the demand? Resource requirements for 110 P’s and 60 Q’s: • Resource A: 110 (15) + 60 (10) = 2250 minutes • Resource B: 110(10) + 60(35) = 3200 minutes • Resource C: 110(15) + 60(5) = 1950minutes • Resource D: 110(10) + 60(5) = 1400 minutes

  3. 2. Exploit the Constraint : Find the Throughput World’s Best Solution Resource B is Constrained - Bottleneck Product P Q Profit $ 45 55 Resource B needed (min) 10 35 Profit per min of Bottleneck 45/10 =4.555/35 =1.6 Per unit of bottleneck Product P creates more profit than Product Q Produce as much as P, then Q

  4. 2. Exploit the Constraint : Find the World’s Best Solution to Throughput For 110 units of P, need 110 (10) = 1100 min. on B, leaving 1300 min. on B, for product Q. Each unit of Q requires 35 minutes on B. So, we can produce 1300/35 = 37.14 units of Q. We get 110(45) +37.14(55) = 6993 per week. After factoring in operating expense ($6,000), we make $993 profit.

  5. 2. Exploit the Constraint : Find the World’s Best Solution to Throughput • How much additional profit can we make if market for P increases from 110 to 111; by 1 unit. • We need 1(10) = 10 more minutes of resource B. • We need to subtract 10 min of the time allocated to Q and allocate it to P. • For each unit of Q we need 35 min of resource B. • Our Q production is reduced by 10/35 = 0.29 unit. • One unit increase in P generates $45. But $55 is lost for each unit reduction in Q. Therefore if market for P is 111 our profit will increase by 45(1)-55(0.29) = $29.

  6. Practice: LP Formulation Decision Variables x1 : Volume of Product P x2 : Volume of Product Q Resource A 15 x1 + 10 x2  2400 Resource B 10 x1 + 35 x2  2400 Resource C 15 x1 + 5 x2  2400 Resource D 10 x1 + 5 x2  2400 Market for P x1 110 Market for Q x2 60 Objective Function Maximize Z = 45 x1 +55 x2 -6000 Nonnegativity x1  0, x2 0

  7. Practice: Optimal Solution Continue solving the problem, by assuming the same assumptions of 20% discount for the Japanese market.

  8. A Practice on Sensitivity Analysis • What is the value of the objective function? Z= 45(?) + 55(37.14)-6000! • 2400(0)+ 2400(1.571)+2400(0) +2400(0)+110(29.286)+ 60(0) =6993 • Is the objective function Z = 6993? • 6993-6000 = 993

  9. A Practice on Sensitivity Analysis • How many units of product P? • What is the value of the objective function? • Z= 45(???) + 55(37.14)-6000 = 993. • 45X1= 4950 • X1 = 110

  10. Step 4 : Elevate the Constraint(s). Do We Try To Sell In Japan? Even without increasing capacity of B, we can increase our profit. $/Constraint Minute 4.5 1.57 2.7 1

  11. 2. Exploit the Constraint : Find the World’s Best Solution to Throughput For 110 units of P, need 110 (10) = 1100 min. on B, leaving 1300 min. on B, for product P in Japan. Each unit of PJ requires 10 minutes on B. So, we can produce 1300/10 = 130 units of PJ. We get 110(45) +130(27) = $8460 - $6000 = $2460 profit. Check if there is another constraint that would not allow us to collect that much profit. Let’s see.

  12. 1. Identify The Constraint(s) Contribution Margin: P($45), PJ($27) Market Demand: P(110), PJ(infinity) Can we satisfy the demand? Resource requirements for 110 P’s and 130 PJ’s: • Resource A: 110 (15) + 130 (15) =3600 minutes • Resource B: 110(10) + 130(10) = 2400 minutes • Resource C: 110(15) + 130(15) = 3600minutes • Resource D: 110(10) + 130(10) = 2400 minutes • We need to use LP to find the optimal Solution.

  13. Step 4 : Exploit the Constraint(s). Not $2460 profit, but $1345. The $6000 is included. Let’s buy another machine B at investment cost of $100,000, and operating cost of $400 per week. Weekly operating expense $6400. How soon do we recover investment?

  14. Step 4 : Elevate the Constraint(s). New Constraint Original Profit: $993 No Machine but going to Japan: $1345 profit. Buy a machine B: $2829 profit. The $6400 is included. Going to Japan has no additional cost. Buying additional machine has initial investment and weekly operating costs. $2829-$1345 = $1484  $100,000/$1484 = 67.4 weeks

  15. Buying a machine A at the same cost Also add one machine A. Initial investment 100,000. Operating cost $400/week. From $2829 to $3533 = $3533 - $2829 = $704. The $6800 included.. $100,000/$704 = 142 weeks Now B & C are a bottleneck

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