Space Requirements

1
Space Requirements

• Determination of the Production Rate
• Determination of Batch Production Quantities
• Economic Order Quantity Models
• Reject Allowance Problem
• Determination of Equipment Requirements
• Determination of Employee Requirements
• Manual Assembly Operators
• Machine Operators
• Determination of Space Requirements
• Tables for Aisle Allowance, Food Services and
  Restrooms
• Other Methods to Determine Space Requirements
• Parking Space

2
Determination of the Production Rate

• The production rate of a department is a major
  determinant of the amount of space required. The
  production rate of a processing station is the
  number of units produced per time unit. The
  production rate can be determined from a
  marketing forecast of the finished product.
• Notation
• a arrival rate of raw material.
• d demand rate of a product.
• p production rate of a processing station.
• s scrap probability of an inspection
  station.
• r rework probability of an inspection
  station.

3
Example 1

• Consider the operation process chart shown in
  the Figure. The percentage of rejected parts at
  inspection stations 1, 2 and 3 are 5, 4 and 6,
  respectively. The annual operating time is 2,500
  hours, and the annual demand forecast for the
  product is 490,000 units. Due to possible
  forecasting errors, 10,000 additional units per
  year are required. Find the production rate at
  each station.

4
Example 1 Solution
(good units)
5
Example 2

• Consider a product that requires a single
  operation. After the operation is performed,
  each unit is inspected. A unit passes inspection
  with probability 0.92, is scrapped with
  probability 0.05, or has to be reworked with
  probability 0.03. If the demand for this product
  is 82,000 units per year and the annual operating
  time is 2,500 hours, determine the production
  rate at the processing station.

(good units)
6
Determination of Batch Production Quantities

• In process layout, a given machine can be used to
  process different products. In certain product
  layouts, the same production (or assembly) line
  can be used to produce (or assemble) similar
  products with the same process plan. In both of
  these cases, jobs are produced in batches.
  Optimal batch production quantities can be
  computed using an inventory control model.
• Process layouts are also used in job shops where
  one-shot jobs are received and processed.
  Rather than producing for inventory, the order is
  processed and shipped to the customer. The
  reject allowance problem determines the optimal
  production lot size for a given order when a
  portion of the lot may be defective.

7
Economic Order Quantity (EOQ) Model

• Assumptions
• Items are withdrawn from stock continuously at a
  constant demand rate a (units/time unit).
• Items are produced or ordered Q units at a time,
  and all Q units arrive instantaneously, i.e.,
  there is no lead time.
• This is a continuous review process, i.e., we
  look at the inventory continuously and when it
  reaches zero, we order.
• Notation
• K setup cost (/order).
• c unit purchasing or production cost
  (/unit).
• h unit holding cost (/unit/time unit).
• X(t) inventory on hand at time t.
• T cycle time (time between consecutive
  orders).

8
Economic Order Quantity (EOQ) Model (cont.)

• Total cost per cycle (TCC) ordering cost
  holding cost

• Total cost per unit time (TC)

X(t)
-a
Q
t
T
9
Economic Order Quantity (EOQ) Model (cont.)

• Minimization of TC with respect to Q

• Solution

EOQ Formula
10
EOQ Model with Quantity Discounts

• Consider the EOQ model with the following unit
  cost structure with discount for larger amounts
• For 0 ? Q lt M1 the unit cost is c0
• M1 ? Q lt M2 c1
• . .
• Mn-1 ? Q lt Mn cn-1
• Mn ? Q cn
• Mi, i 1,, n, represent the price break
  points, such that
• M1 lt M2 lt . lt Mn.
• Assumption unit costs are such that c0 gt c1 gt
  . gt cn.

11
EOQ Model with Quantity Discounts (cont.)

• Algorithm to find Q

Step 1 Determine
Step 2 Find the interval (Mi, Mi1), where Q
falls in.
Step 3 Compare the total cost for the amount Q,
with the total cost for the
amounts Mi1, Mi2, , Mn,
Step 4 Select the amount corresponding to the
minimum total cost per time unit
TC min TC, TC(Mi1), TC(Mi2), , TC(Mn).
12
Example 3 EOQ Model

• The publisher of a newspaper periodically
  replenishes paper for stock. Paper comes in
  large rolls. The demand is 32 rolls/ week. The
  cost of ordering is 25 and the cost per roll is
  40. The cost of keeping paper is 1/roll/week.
  Determine the EOQ and the optimal cycle time.
• a 32 rolls/week,
• K 25/order,
• h 1/roll/week.

13
Example 4 EOQ Model with Quantity Discounts

• In the newspaper example, find Q given the
  following quantity discounts
• 1 - 9 rolls 12/roll,
• 10 - 49 rolls 10/roll,
• 50 - 99 rolls 9.50/roll,
• 100 rolls or more 9/roll.

40 ? (10, 49)
Min 360, 345, 346345 ? Q
50 rolls
14
Reject Allowance Problem

• In job shops, one time jobs are received and
  processed. There is no production to inventory.
  Each batch is only produced once. If there is a
  defective rate, how many units must be produced?
  The following expected profit model is formulated
  to determine the optimal batch size

where Q lot size, x number of good
parts, pQ(x) PXx lot size is Q,
x0,1,,Q, R(Q,x) revenue for producing Q
parts with exactly x good ones, C(Q,x) cost
for producing Q parts with exactly x good
ones, P(Q,x) R(Q,x) - C(Q,x) profit for
producing Q parts with x good ones, E?
expected value.
15
Example 5

• A company receives an order for 10 machined
  parts. The unit sale price is 1,000. Only one
  production can be made due to the long setup time
  required and short due date of the order. If 8
  or fewer parts are acceptable, the customer will
  cancel the order. If 9 or 10 parts are
  acceptable, the customer will purchase all of
  them. If more than 10 parts are acceptable, the
  customer will only buy 10. The remaining parts,
  good or bad, can be sold for 25 each. The cost
  of producing a part is estimated to be 600.
  Find the optimal lot size.
• Probability mass function pQ(x)

16
Example 5 Solution
C(Q,x) C(Q) 600?Q
17
Example 5 Solution (cont.)

• EP(10) 975(9?0.310?0.2) 9750?0 - 575?10
  -1167.50
• EP(11) 975(9?0.310?0.3) 9750?0.2 - 575?11
  1182.50
• EP(12) 975(9?0.210?0.3) 9750(0.20.2) -
  575?12 1680.00
• EP(13) 975(9?0.210?0.2) 9750(0.30.20.1)
  - 575?13 2080.00
• EP(14) 975(10?0.2) 9750(0.20.30.20.1) -
  575?14 1700.00
• ? Optimal lot size Q 13 units
• Expected profit EP(Q) 2,080.00

18
Determination of Equipment Requirements

• Given the desired production rate at each
  processing stage, we can determine the number of
  required machines

where Pij production rate for product i on
machine j (units/period), Tij processing time
for product i on machine j (hrs./unit), Hij
time units available per period for the
processing of product i on machine j
(hrs.), Mj number of machines of type j
required, n number of products.
19
Example 5

• CIN-A1 Workcenters are used to produce three
  types of parts, 1, 2, 3. Production rates and
  unit processing times for the different items are
  given in the following table

The facility operates one shift per day (8
hrs./day 480 min./day). Determine the number
of workcenters required to meet production
requirements. Hi min. available to process
item i per day (Hi 480 min.), MA number of
workcenters.
20
Employee Requirements - Manual Assembly

• In the case of manual assembly operations, the
  number of employees required is determined in
  the same way machine requirements are calculated

where Pij production rate for assembly
operation j of product i (units/period), Tij
standard time for assembly operation j of product
i (hrs./unit), Hij time units available per
period for assembly operation j of product i
(hrs.), Aj number of operators required for
assembly operation j, n number of products.
21
Multiple Activity Chart Analysis of Multi-Machine
Assignment
O-1
M-1
O-1
M-1
M-2
O-1
M-1
M-2
M-3
0
R
L-1
L
L
L-1
L-1
L
2
I
R
LEGEND O Operator M Machine L Load U
Unload I Inspection T Travel R Automatic
run
IT
IT
IT
R
4
U-2
U
U-2
U
6
L-2
L
R
R
R
L-2
L
IT
8
IT
U-3
U
10
L-3
L
Idle time
R
12
U-1
U
U
U-1
IT
R
14
U-1
U
L-1
L
L
L-1
R
16
I
IT
L-1
L
R
R
18
IT
R
U-2
U
U-2
U
20
22
Employee Requirements - Machine Operators

• The number of machine operators required depends
  on the number of machines tended by one or more
  operators. The determination of the number of
  machines to be assigned to one operator can take
  two approaches
• deterministic,
• probabilistic.
• A deterministic approach is to employ the
  multiple activity chart. This chart shows the
  multiple activity relationships graphically
  against a time scale. The chart is useful in
  analyzing multiple activity relationships,
  specially, when non-identical machines are
  supervised by a single operator.
• Let a concurrent activity time (loading,
  unloading, etc.),
• b independent operator activity time
  (inspecting, packing, etc.),
• t independent machine activity time
  (automatic run),
• n maximum number of machines that can be
  assigned to an operator.

23
Employee Req. - Machine Operators (cont.)

• Note that n may be non-integer.
• Let m (integer) number of machines assigned to
  an operator,
• Tc repeating cycle time,
• I0 idle operator time during a repeating
  cycle,
• Im idle time per machine during a repeating
  cycle.

(1)
24
Employee Req. - Machine Operators (cont.)

• Let c1 cost per operator - hr.,
• c2 cost per machine - hr.,
• TC(m) cost per unit produced, based on the
  assignment of m machines per operator.

(2)

• Substituting (1) into (2),

25
Employee Req. - Machine Operators (cont.)

• We want to find the value of m that minimizes
  TC(m).
• Note that for m ? n, m (?) ? TC(m) (?),
• and for m gt n, m (?) ? TC(m) (?).
• If n is integer, n is the optimal number of
  machines per operator.
• Otherwise, let n lt n lt n1. In this case,
  TC(n) and TC(n1) have to be compared

where

• If ? lt1, assign n machines per operator.
• If ? gt1, assign n1 machines per operator.

26
Example 6

• Semiautomatic machines are used to produce a
  particular product. It takes 4 minutes to load
  and 3 minutes to unload a machine. A machine
  runs automatically for 25 minutes in producing
  one unit of the product. Travel time between
  machines is 20 seconds. While machines are
  automatically running, the operator inspects the
  unit previously produced 75 seconds are required
  to inspect one unit. An operator costs 15 per
  hour, and a machine costs 40 per hour.
• a) Determine the number of machines assigned to
  an operator to minimize the cost per unit
  produced.
• a 4 3 7 min., b 20 75 95 sec.
  1.58 min., t 25 min.,
• c1 15/hr. 0.25/min., c2 40/hr.
  0.67/min.

? m 3 machines/operator.
27
Example 6 (cont.)

• b) For what range of values of machine cost per
  hour will the optimal assignment determined in
  part (a) be economic.
• TC(3) ? TC(4),

• (0.25 3?c2) 1.24 ? (0.25 4?c2),
• 0.0607 ? 0.27?c2 ? c2 ? 0.225,
• c2 ? 0.225/min. 13.48/hr.

28
Space Reqs. Workstation Specification

• A workstation consists of the fixed assets needed
  to perform a specific operation(s).
• The equipment space consists of space for
• - The equipment - Machine maintenance
• - Machine travel - Plant services
• Equipment space requirements are available from
  machinery data sheets (provided by the supplier).
  If this data is not available, the following
  information must be obtained for each machine
• - Machine manufacturer and type - Maximum
  travel to the left
• - Machine model and serial number - Maximum
  travel to the right
• - Location of machine safety stops - Static
  depth at maximum point
• - Floor loading requirement - Maximum
  travel towards the operator
• - Static height at maximum point - Maximum
  travel away from the operator
• - Maximum vertical travel - Maintenance
  requirements and areas
• - Static width at maximum point - Plant
  service requirements and areas

29
Space Reqs. Workstation Specification (cont.)

• Area requirements for a machine
• Total width (static width) (max. travel
  to left) (max. travel to right)
• Total depth (static depth) (max. travel
  toward operator) (max. travel away from
  operator)
• Area (machine machine travel) (total
  width) (total depth)
• The materials areas consists of space for
• Receiving and storing materials
• In-process materials
• Storing and shipping materials
• Storing and shipping waste and scrap
• Tools, fixtures, jigs, dies, and maintenance
  materials
• The personnel areas consists of space for
• The operator
• Material handling
• Operator ingress and egress

30
General Guidelines for Design of Workstations

• The operator should be able to pick up and
  discharge materials without walking or making
  long or awkward reaches.
• The operator should be utilized efficiently and
  effectively.
• The time spent manually handling materials should
  be minimized.
• The safety, comfort and productivity of the
  operator must be maximized.
• Hazards, fatigue and eye strain must be
  minimized.
• A workstation sketch is required to determine
  total area requirements.

31
Space Reqs. Department Specification

• Department area requirements are not simply the
  sum of the areas of the individual workstations
  included in each department.
• Machine maintenance, plant services, incoming and
  outgoing materials, and operator ingress and
  egress areas for various workstations must be
  combined.
• Additional space is required for material
  handling within the department. Space
  requirements for aisles can be approximated since
  the relative sizes of the loads to be handled are
  known.

32
Tables for Aisle Allowance
Table 2. Recommended Aisle Widths for Various
Types of Flow
Table 1. Aisle Allowance Estimates
In Example 7,
33
Example 7

• A planning department for the ABC Company
  consists of 13 machines that perform turning
  operations. Five turret lathes, six automatic
  screw machines, and two chuckers are included in
  the planning department. Bar stock, in 8-ft
  bundles, is delivered to the machines. The
  footprints for the machines are 4?12 ft2 for the
  turret lathes, 4?14 ft2 for the screw machines,
  and 5?6 ft2 for the chuckers. Personnel space
  footprints of 4?5 ft2 are used. Materials
  storage requirements are estimatefd to be 20 ft2
  per turret lathe, 40 ft2 per screw machine, and
  50 ft2 per chucker. An aisle space allowance of
  13 is used. The space calculations are
  summarized in the table below.

34
Food Services
Table 3. Shift Timing for 30 min. Lunch Breaks
Table 5. Space Requirements for Full Kitchens
Table 4. Space Requirements for Cafeterias
35
Example 8

• Statement
• If a facility employs 600 people and they are to
  eat in three equal 30 min. shifts, how much space
  should be planned for the cafeteria with vending
  machines, serving lines, or a full kitchen?
• Solution
• If 36-in. square tables are to be utilized, Table
  4 indicates 12 ft.2 are required for each of the
  200 employees to eat per shift. Therefore, a
  2,400 ft.2 cafeteria should be planned. If a
  vending area is to be used in conjunction with
  the cafeteria, an area of 200 ft.2 should be
  allocated for vending machines. Thus, a vending
  machine food service facility would require 2,600
  ft.2
• A service line may serve 70 employees in the
  first third of the meal shift. Therefore, three
  serving lines of 300 ft.2 each should be planned.
  A total of 3,300 ft.2 would be required for a
  food service facility using serving lines.
• A full kitchen will require 3,300 ft.2 for
  serving lines plus (from Table 5) 2,100 ft.2 for
  the kitchen. Therefore, a total of 5,400 ft.2
  would be required for a full kitchen food service
  facility.

36
Restrooms
Table 7. Number of Sinks Needed for Type of
Employment and Number of Employees
Table 6. Number of Toilets Needed for Number of
Employees
37
Other Methods to Determine Space Requirements

• Converting Method
• The present space requirements are converted to
  those required for the proposed layout. It is
  important to establish valid assumptions, because
  the total space required is not a linear function
  of the production quantity.
• This method is used to determine space
  requirements for supporting service, storage
  areas, etc.
• Roughed-out Layout Method
• Templates or models are placed on the layout to
  estimate the general configuration and space
  requirements.

38
Other Methods to Determine Space Reqs. (cont.)

• Space-Standards Method
• In certain cases industry standards can be used
  to determine space requirements.
• Standards may be established based on past
  successful applications.
• Ratio Trend and Projection Method
• One can establish a ratio of square feet to some
  other factor that can be measured and predicted
  for the proposed layout. For example,
• square feet per machine
• square feet per operator
• square feet per unit produced
• square feet per labor-hour

39
Parking Space
( angular ? one-way )
( cross aisle )
( cross aisle )
( 900 ? two-way )
40
Parking Space (cont.)

• Table 8. Parking Dimensions for a 7.5-ft.
  Compact Automobile Parking Space Width and a
  8.5-ft. Standard-Sized Automobile Parking Space
  Width

41
Parking Space (cont.)
1/2 aisle space allocated
Width parallel to aisle (9.8 ft.)
Parking space
Parking space
Depth perpendicular to aisle (19.0 ft.)
Aisle width (18.0 ft.)

• Parking space 1/2 aisle space (for 600
  standard)
• 19.0 ? 9.8 18.0 ? 9.8 / 2 186.2 88.2 ?
  274 ft.2

42
Example 9

• Problem Statement
• A new facility is to have 200 employees. A
  survey of similar facilities indicates that one
  parking space must be provided for every two
  employees and that 35 of all automobiles driven
  to work are compact automobiles. The available
  parking lot space is 180 ft. wide and 200 ft.
  deep. What is the best parking layout?
• Solution
• If the new facility were to have the same number
  of parking spaces as similar facilities, 100
  spaces would be required. Of these 100 spaces,
  35 could be for compact automobiles. However,
  not all drivers of compact cars will park in a
  compact space. Therefore, only 25 compact spaces
  will be provided. A parking layout consisting of
  one-way traffic between five rows of 900
  standard-sized automobiles and one row of 900
  compact automobiles would require a parking lot
  width of
• 5 (18.5) 3 (28) 1 (16) 192.5 ft.
• Similarly, four rows of 900 standard-sized
  automobiles, one row of 750 standard-sized
  automobiles, and one row of 750 compact
  automobiles would require a parking lot width of
• 4 (18.5) 2 (28) 1 (19.5) 1 (17.3) 1
  (25) 191.8 ft.
• which is too wide to be placed in a lot 180 ft.
  wide.

43
Example 9 (cont.)

• Replacing the 750 aisle with a 600 aisle still
  requires 184.7 ft. Four rows of 900
  standard-sized automobiles, one row of 450
  standard-sized automobiles, and one row of 450
  compact automobiles requires a parking lot width
  of
• 4 (18.5) 2 (28.0) 1 (17.5) 1 (17.0) 1
  (13.0) 177.5 ft.
• This configuration will be utilized.
• Leaving 24 ft. for two-way cross-aisle traffic
  at the front of the lot and 14 ft. for one-way
  cross-aisle traffic at the rear of the lot, the
  900 standard-sized automobile rows can each
  accommodate

The last 900 standard-sized row does not require
the 14 ft. one-way cross-aisle. Therefore, it
accommodates
The 450 standard-sized row can accommodate
44
Example 9 (cont.)

• The 450 compact automobile row is the first and
  does not require the 14.0 ft. one-way
  cross-aisle. It can accommodate

Hence, a total of 3 (19) 20 13 16 106
automobiles can be accommodated, with 15 being
allocated to compact automobiles. The following
Figure illustrates the plan for the parking
lot. If the compact automobile row is replaced
by standard-sized automobiles, the lot still fits
within the 180 ft. ? 200 ft. configuration and
104 cars may be accommodated. Therefore, a
decision must be made regarding the advantages of
providing compact automobile spaces versus not
segmenting the parking lot.
45
Parking Lot for Example 9
20 Standard-sized automobiles (900)
19 Standard-sized automobiles (900)
19 Standard-sized automobiles (900)
19 Standard-sized automobiles (900)
13 Standard-sized automobiles (450)
16 Compact automobiles (450)