fundamentals of engineering supplied-reference handbook - Ventech!

People Requirements
n PijTij
Aj
= ∑ , where
= 1 C
i ij
Aj = number of crews required for assembly operation j,
Pij = desired production rate for product i and assembly
operation j (pieces per day),
Tij = standard time to perform operation j on product i
(minutes per piece),
Cij = number of minutes available per day for assembly
operation j on product i, and
n = number of products.
Standard Time Determination
ST = NT × AF
where
NT = normal time, and
AF = allowance factor.
Case 1: Allowances are based on the job time.
AFjob = 1 + Ajob
Ajob = allowance fraction (percentage) based on job time.
Case 2: Allowances are based on workday.
AFtime = 1/(1 – Aday)
Aday = allowance fraction (percentage) based on workday.
Plant Location
The following is one formulation of a discrete plant location
problem.
Minimize
= ∑∑+ ∑
m n
n
z c y f x
subject to
m
i=
1
n
j=
1
ij ij
i=
1 j=
1
j=
1
∑ y ≤ mx , j = 1, …,
n
ij
ij
j
∑ y = 1, i = 1, …,
m
j
m =
yij ≥ 0, for all i, j
xj = (0, 1), for all j, where
number of customers,
n = number of possible plant sites,
yij = fraction or portion of the demand of customer i
which is satisfied by a plant located at site j; i = 1,
…, m; j = 1, …, n,
xj = 1, if a plant is located at site j,
xj = 0, otherwise,
cij = cost of supplying the entire demand of customer i
from a plant located at site j, and
fj = fixed cost resulting from locating a plant at site j.
j
195
INDUSTRIAL ENGINEERING (continued)
Material Handling
Distances between two points (x1, y1) and (x1, y1) under
different metrics:
Euclidean:
( ) ( ) 2
2
x − x + y y
D =
−
1
2
1
Rectilinear (or Manhattan):
D = ⏐x1 – x2⏐ + ⏐y1 – y2⏐
Chebyshev (simultaneous x and y movement):
D = max(⏐x1 – x2⏐ , ⏐y1 – y2⏐)
Line Balancing
⎛
⎞
Nmin = ⎜OR
× ∑ti
OT ⎟
⎝ i ⎠
= Theoretical minimum number of stations
Idle Time/Station = CT – ST
Idle Time/Cycle = Σ (CT – ST)
Idle Time Cycle
Percent Idle Time = × 100 , where
N × CT
actual
CT = cycle time (time between units),
OT = operating time/period,
OR = output rate/period,
ST = station time (time to complete task at each station),
ti = individual task times, and
N = number of stations.
Job Sequencing
Two Work Centers—Johnson's Rule
1. Select the job with the shortest time, from the list of
jobs, and its time at each work center.
2. If the shortest job time is the time at the first work
center, schedule it first, otherwise schedule it last. Break
ties arbitrarily.
3. Eliminate that job from consideration.
4. Repeat 1, 2, and 3 until all jobs have been scheduled.
CRITICAL PATH METHOD (CPM)
dij = duration of activity (i, j),
CP = critical path (longest path),
T = duration of project, and
( ) ∑ = T
dij
i,
j ∈CP
2