Process Analysis III The McGraw-Hill Companies, Inc., Outline Set-up times Lot sizes Effects on capacity Effects on process choice Operations -- Prof. Juran 2 The McGraw-Hill Companies, Inc., Set-up Times Many processes can be described (at least approximately) in terms of a fixed set-up time and a variable time per unit (a.k.a. cycle time) Capacity of a single activity is a function of lot size, set-up time, and cycle time Overall capacity of a system depends on these factors and the resulting bottlenecks across multiple activities Operations -- Prof. Juran

3 The McGraw-Hill Companies, Inc., Example: Kristen In general, a formula for the number of minutes to produce n one-dozen batches is given by this expression: 16 10n Set-up time Cycle time per 1-dozen batch This views the cookie operation as a single activity. We arrived at these numbers through analysis of individual sub-activities at a more detailed level. Operations -- Prof. Juran 4 The McGraw-Hill Companies, Inc., Example: Kristen Note that Kristens effective cycle time is 10 minutes per 12 cookies, or 0.8333 minutes per cookie, assuming a lot size of 12 cookies. We can determine the capacity of the system in a specific period of time T by solving for n: 16 10n T

Operations -- Prof. Juran 5 The McGraw-Hill Companies, Inc., Example 1 We can determine the capacity of the system in a specific period of time T by solving for n. How many 1-dozen batches could Kristen produce in 4 hours? 16 10n 16 10n 10n n T 240 224 22 one-dozen orders In this situation, the capacity of the system is a linear function of the time available. Operations -- Prof. Juran 6 The McGraw-Hill Companies, Inc.,

Capacity = f (Time) 60 50 Capacity (Lots) 40 30 20 10 0 0 50 100 150 200 250 300 350 400

450 500 -10 Time (Minutes) Operations -- Prof. Juran 7 The McGraw-Hill Companies, Inc., 1 2 3 4 5 6 7 8 9 10 A B C D E F

Available Time Capacity (Lots) Capacity (Cookies) Set-up Time Cycle Time Lot Size 0 -1.60 -19.20 16 0.833 12 5 -1.10 -13.20 10 -0.60 -7.20 15 -0.10 -1.20 =(A6-$D$2)/($E$2*$F$2) 20 0.40 4.80 25 0.90 10.80 30 1.40 16.80 =B9*$F$2 35 1.90

22.80 40 2.40 28.80 Operations -- Prof. Juran 8 The McGraw-Hill Companies, Inc., Example 2 This assumes that the set-up only needs to be done once. What if there were a 16-minute set-up for every lot? This effectively makes the set-up time zero, and the cycle time 26 minutes per 12-cookie lot. (16 10)n 26n n T 240 9.23 one-dozen orders Capacity is still a linear function of the time available. Operations -- Prof. Juran 9 The McGraw-Hill Companies, Inc.,

Capacity = f (Time) 60 Capacity (Lots) 50 40 30 20 10 0 0 50 100 150 200 250

300 350 400 450 500 Time (Minutes) Operations -- Prof. Juran 10 The McGraw-Hill Companies, Inc., Lets make some assumptions; a system similar (but not identical) to the Kristen system: Produce individual units (cookies) The cycle time is 0.8333 minutes per cookie The set-up time is s minutes, and needs to be performed again for every lot of 12 cookies The capacity of this system (in lots) over 240 minutes is: 240/(s + 0.8333 * 12) The capacity of this system (in lots) with a 16-minute set-up is: 240/(s + 0.8333 * 12) = 9.23 (or 9.23 * 12 = 110.77 cookies)

Operations -- Prof. Juran 11 The McGraw-Hill Companies, Inc., 1 2 3 4 5 6 7 8 9 A B C D E F Available Time Capacity (Lots) Capacity (Cookies) Set-up Time Cycle Time Lot Size 0 0.00 0.00 16 0.833 12 5

0.19 2.31 10 0.38 4.62 =A5/($D$2+$E$2*$F$2) 15 0.58 6.92 20 0.77 9.23 25 0.96 11.54 =B8*$F$2 30 1.15 13.85 35 1.35 16.15 Operations -- Prof. Juran 12 The McGraw-Hill Companies, Inc., Example 3

Now lets assume the time available is fixed at 240 minutes, and study the effect on capacity that results from changing the set-up time. The capacity of this system (in lots) with an s-minute set-up is: 240/(s + 0.8333 * 12) (a nonlinear function of the set-up time) Operations -- Prof. Juran 13 The McGraw-Hill Companies, Inc., Capacity = f (Set-up Time) 30 Capacity (Lots) 25 20 15 10 5 0

0 20 40 60 80 100 120 140 160 180 200 220 240 s = Set-up Time (Minutes) Operations -- Prof. Juran

14 The McGraw-Hill Companies, Inc., apacity could also be measured in cookies instead of 12-cookie lots: Capacity = f (Set-up Time) 350 Capacity (Cookies) 300 250 200 150 100 50 0 0 20 40 60 80 100

120 140 160 180 200 220 240 s = Set-up Time (Minutes) Operations -- Prof. Juran 15 The McGraw-Hill Companies, Inc., Extreme Case 1: If the set-up time is zero, then the capacity of this system (in lots) over 240 minutes is: 240/(0 + 0.8333 * 12) = 24 lots Extreme Case 2: If the set-up time is 240, then the capacity of this system (in lots) over 240 minutes is zero (because all of the time

is consumed by setting up) Operations -- Prof. Juran 16 The McGraw-Hill Companies, Inc., 1 2 3 4 5 6 7 8 A B C D E F Set-up Time Capacity (Lots) Capacity (Cookies) Available Time Cycle Time Lot Size 0 24.00 288.00 240 0.833 12

1 21.82 261.82 2 20.00 240.00 =$D$2/(A5+$E$2*$F$2) 3 18.46 221.54 4 17.14 205.71 =B7*$F$2 5 16.00 192.00 6 15.00 180.00 Operations -- Prof. Juran 17 The McGraw-Hill Companies, Inc., Example 4 Now lets assume the time available is fixed at 240 minutes, AND fix the set-up time at 16 minutes, to study

the effect on capacity that results from changing the lot size. The capacity of this system (in cookies) with an s-minute set-up is: 240/(16 + 0.8333 * Q) (another nonlinear function) Operations -- Prof. Juran 18 The McGraw-Hill Companies, Inc., Extreme Case 1: 240/16 = 15 gives an upper bound to the number of lots; in that case we would use up all of our time setting up, and never make any cookies. Extreme Case 2: If we assume only one set-up, then the capacity is 240 - 16/0.8333 = 268.8 cookies The largest lot that can be completed in 240 minutes is 268. Extreme Case 3: If we assume no set-up, then the capacity is 240/0.8333 = 288 cookies The largest lot that can be completed in 240 minutes is 288. Operations -- Prof. Juran 19

The McGraw-Hill Companies, Inc., Capacity = f (Lot Size) 300 Capacity (Cookies) 250 200 150 100 50 0 0 20 40 60 80 100

120 140 160 180 200 220 240 Q = Lot Size (Cookies) Operations -- Prof. Juran 20 The McGraw-Hill Companies, Inc., 1 2 3 4 5 6 7

8 A Lot Size 0 1 2 3 4 5 6 B C D E F Capacity (Lots) Capacity (Cookies) Available Time Cycle Time Set-up Time 15.00 0.00 240 0.833 16 14.26 14.26 13.58 27.17 =$D$2/($F$2+$E$2*A5) 12.97

38.92 12.41 49.66 =B7*A7 11.90 59.50 11.43 68.57 Operations -- Prof. Juran 21 The McGraw-Hill Companies, Inc., Example 5 What if the lot size AND the set-up time are variables? We can determine the capacity of the system in a specific period of time using this complicated function of lot size, cycle time, set-up time, and the time available for production: Capacity in lots Capacity in units Operations -- Prof. Juran time available set - up time cycle time * lot size

lot size * time available set - up time cycle time * lot size 22 The McGraw-Hill Companies, Inc., Assume 240 minutes available, and 0.8333 minute cycle time: Operations -- Prof. Juran 23 The McGraw-Hill Companies, Inc., A B 240 0.8333 1 2 3 4 5 6 7 Set-up Time 8 9 10

11 12 13 14 0 2 4 6 8 10 12 14 16 18 20 C D 1 288.0 84.7 49.7 35.1 27.2 22.2 18.7

16.2 14.3 12.7 11.5 12 288.0 240.0 205.7 180.0 160.0 144.0 130.9 120.0 110.8 102.9 96.0 Operations -- Prof. Juran E F G H I Lot Size 24 36 48

60 288.0 288.0 288.0 288.0 261.8 270.0 274.3 276.9 240.0 254.1 261.8 266.7 221.5 240.0 250.4 257.1 205.7 227.4 240.0 248.3 192.0 216.0 230.4 240.0 180.0 205.7 221.5 232.3 169.4 196.4 213.3 225.0 =E$2*$A$1/($B11+$B$1*E$2) 160.0 187.8 205.7 218.2 151.6 180.0 198.6 211.8 144.0 172.8 192.0 205.7 J 24 The McGraw-Hill Companies, Inc., Why Do We Care? It might be on the quiz Needed for cases like Kristen Drives major decisions regarding operations strategy, technology choice, process design, and capital investment Operations -- Prof. Juran

25 The McGraw-Hill Companies, Inc., Process Choice Sometimes we get to choose among several possible technologies One important factor is capacity: Which technology can meet demand fastest? This may depend on lot size Similar to make-vs-buy decisions Operations -- Prof. Juran 26 The McGraw-Hill Companies, Inc., Operations -- Prof. Juran The McGraw-Hill Companies, Inc., Example: Make vs. Buy Colarusso Confectioners needs to fill an order for 500 sfogliatelle (a famous Italian pastry) for one of their clients. Colarusso has the in-house capability to produce sfogliatelle, but this is an unusually large order for them and they are considering whether to outsource the job to Tumminelli Industries, Inc. (a

regional pastry supplier with equipment designed for greater volume). The customer service rep from Tumminelli quotes a rate for sfogliatelle as follows: a fixed order cost of $135 plus $0.25 per sfogliatella. Colarussos inhouse costs are $75.00 to set up production and $0.39 per unit. Operations -- Prof. Juran The McGraw-Hill Companies, Inc., What should Colarusso do with this order for 500 svogliatelle? A B C D 1 Colarusso Tumminelli 2 Set-up cost $ 75.00 $ 135.00 3 Per unit $ 0.39 $ 0.25 4 5 500 $ 270.00 $ 260.00 6 =B$2+$A5*B$3 =C$2+$A5*C$3 7

The total cost of the order will be lower if Colarusso outsources this job to Tumminelli. Operations -- Prof. Juran The McGraw-Hill Companies, Inc., Obviously Colarusso has an advantage for small lot sizes, and Tumminelli has an advantage for large lot sizes. What is the break-even point? Make vs. Buy? $500 $450 $400 Colarusso Tumminelli Total Cost $350 $300 $250 $200 $150 $100 $50 $0

100 200 300 400 500 600 700 800 900 1000 Lot Size Operations -- Prof. Juran The McGraw-Hill Companies, Inc., Finding the break-even point algebraically: sC cCQ

75 0.39Q 0.39 0.25Q 0.14Q Q sT cT Q 135 0.25Q 135 75 60 429 Operations -- Prof. Juran The McGraw-Hill Companies, Inc., Process Choice Example All-American Industries is considering which of two machines to purchase: Setup Time (min) Cycle Time (min./ unit) Yamada 5 2.2

Fukuda 60 2 1. If the typical lot size is 200 units, which machine should they buy? 2. What is the capacity of that machine in a 480-minute shift? 3. What is the break-even lot size for these two machines? Operations -- Prof. Juran The McGraw-Hill Companies, Inc., 1. If the typical lot size is 200 units, which machine should they buy? Total flow time for a 200 -unit lot: Yamada: sY cY Q 5 2.2 * 200 445 Fukuda: sF cF Q 60 2 * 200 460 Operations -- Prof. Juran The McGraw-Hill Companies, Inc.,

D E Yamada Setup Time (min) 5 Cycle Time (min./unit) 2.2 1 2 3 4 5 6 Flow Time per Lot 445 F Fukuda 60 2 460 G H Shift

480 I minutes 200 lot size =F2+F3*$H$4 Operations -- Prof. Juran The McGraw-Hill Companies, Inc., 2. What is the capacity of that machine in a 480-minute shift? Capacity of Yamada machine in 480 minutes: time available set- up time cycletime* lot size 480 5 2.2* 200 =about 1.1 Lots lot size * time available set- up time cycletime* lot size

200* 480 5 2.2* 200 =about 215.7 Units Operations -- Prof. Juran The McGraw-Hill Companies, Inc., D 1 2 3 4 5 6 7 E Yamada Setup Time (min) 5 Cycle Time (min./unit) 2.2 Capacity in Lots

Capacity in Units 1.1 215.7 F Fukuda 60 2 G H Shift 480 I minutes 200 lot size =H2/(E2+E3*H4) =E6*H4 Operations -- Prof. Juran The McGraw-Hill Companies, Inc.,

3. What is the break-even lot size for these two machines? Break-even Lot Size: sY cY Q sF cF Q 5 2.2Q 60 2 *Q 0.2Q Q 55 275 Operations -- Prof. Juran The McGraw-Hill Companies, Inc., D E Yamada Setup Time (min) 5 Cycle Time (min./unit) 2.2

1 2 3 4 5 6 Flow Time 7 8 610 0 F Fukuda 60 2 610 G H Shift 480 I minutes 275

lot size =F2+F3*$H$4 =10000000*(E6-F6) Operations -- Prof. Juran The McGraw-Hill Companies, Inc., Summary Set-up times Lot sizes Effects on capacity Effects on process choice Operations -- Prof. Juran 39 The McGraw-Hill Companies, Inc.,