IE 419 1

IE 419 Work Design:

Productivity and Safety

Dr. Andris FreivaldsClass #5

IE 419 2

IE 419 Work Design:

Productivity and Safety

Dr. Andris FreivaldsClass #5

IE 419 3

Worker-Machine Relationships(Ch. 2, pp. 50-55)

• Worker-machine relationships– Synchronous servicing – regular cycles

– Random (asynchronous) servicing – random– Combination – real life

N ≤ (l + m) (l + w)

IE 419 4

Ex. #1 l = 1.0, m = 2.0, w = 0.1 Oper=$10/hr, Mach=$20/hr

3 machines ($1.28) 2 machines ($1.25)

IE 419 5

Ex. 3 – No Loadl = 0, m = 1.2, w = 2.0, oper = $10/hr, mach = $15/hr

Time Oper Mach

IE 419 6

Ex. 3 – No Loadl = 0, m = 1.2, w = 2.0, oper = $10/hr, mach = $15/hr

Time Oper1 Oper2 Mach

IE 419 7

Random Servicing

• Machine servicing is not regular• Most likely it is random (don’t know when)• Use probability theory to estimate % idle

time (binomial expansion) • Probability of m (out of n) machines down =

n! pm q(n-m) m! (n-m)!

p = prob of down time

q = prob of up time = 1-p

IE 419 8

Ex #1: n=3, p=0.1, q=0.9, % idle time?

Mach down (m)

Probability

n! pm q(n-m) / m! (n-m)!

Mach hrs lost (1 op)

Mach hrs lost (2 op)

Mach hrs lost (3 op)

0

1

2

3

Total

IE 419 9

Ex #1 con’t: oper = $10/hr, mach = $500/hr, prod = 120 units/hr

1 oper 2 oper 3 operidle

Prod(8 hr)Cost(8 hr)Unit cost

IE 419 10

Ex #2: n=3, p=0.4, q=0.6

m Probability Hrs lost(1 oper)

Hrs lost(2 oper)

IE 419 11

Ex #2 con’t: oper = $10/hr, mach = $60/hr, prod = 60/hr

1 oper 2 oper 3 operidle

Prod(8 hr)Cost(8 hr)Unit cost

IE 419 12

Complex Relationships (n↑)

• n > 6• Use Wright’s formula

• i = interference, % of l• n = # machines• x = m/l

n ≤ 6

i = 50{[(1+x-n)2+2n]½ - (1+x-n)}

IE 419 13

Ex #3: m = 7, l =1, n = 6

• n > 6• Use Wright’s formula

• i = interference, % of l• n = # machines• x = m/l

n ≤ 6

i = 50{[(1+x-n)2+2n]½ - (1+x-n)}

IE 419 14

(Assembly) Line Balancing (Ch. 2, pp. 56-64)

• Worker-machine relationship determining ideal number of workers/workstations in production line

• Simple straight line (Ex #1): 1 2 3 4 5

Oper ST/op Delay time

ST ReqST

#Oper New ST/op

New Delay

1 0.522 0.483 0.654 0.415 0.55

IE 419 15

Straight Line Balancing (Ex #1 con’t)

Oper ST/op Delay time

ST ReqST

#Oper New ST/op

New Delay

1 0.52 0.132 0.48 0.173 0.65 0.004 0.41 0.245 0.55 0.10

• % efficiency (E) = 100x∑ST/∑AT• % idle = 100x∑DT/∑AT• Req. production (R) = 3,200/day → required

standard (cycle) time• # oper = Rx∑ST = ∑ST/ CT=

IE 419 16

Complex Line Balancing (Ex #2)• Time set by slowest station (cycle time)• Assign operators to a workstation:

– Until cycle time is about to be exceeded– In order of decreasing positional weight – PW = ∑ST for all with “1” relationship– As allowed by precedence (i.e. immediate

predecessors (IP) need to be assigned)

2 5

1 4 7 9

3 6 8

IE 419 17

Positional Weight (PW) Matrix

Op ST DT 1 2 3 4 5 6 7 8 9 PW IP

1 .05

2 .03

3 .04

4 .05

5 .01

6 .04

7 .05

8 .04

9 .06

2 5

1 4 7 9

3 6 8

IE 419 18

Fill Workstations (Ex #2 con’t)# workstations = Rx∑ST = ∑ST/ CT=

Oper IP PW ST Station T Delay T