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Production Planning and Control

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Title: Production Planning and Control


1
Production Planning and Control
Chapter 4 Production Planning
Professor JIANG Zhibin Department of Industrial
Engineering Management Shanghai Jiao Tong
University
2
Chapter 4 Production Planning
  • Contents
  • Introduction
  • Aggregate Planning
  • Master Production Planning (MRP)
  • Material Requirement Planning (MPS)
  • Capacity Planning
  • Improvement in MRP

3
Overview of Production Planning Activities
  • Production Planning Given specific process
    planning, process technologies, and production
    conditions, production planning predetermine
    varieties, quantities, quality, and schedules of
    products to be produced according to market
    demand of products

Figure 4.1 Framework of Production Planning
Activities
4
Overview of Production Planning Activities
  • Time Dimensions
  • Long-range planning is done annually and focus on
    a planning horizon greater than one year
  • Medium-range planning usually covers a period
    from 6 months to 18 months, with monthly or
    sometimes quarterly time increments
  • Short-range planning covers a period from one day
    or less to six months, with weekly time increment
    usually.

Figure 4.1 Framework of Production Planning
Activities
5
Overview of Production Planning Activities
  • Process Planning determines the specific
    technologies and procedures required to produce a
    product a service.
  • Strategic capacity planning determines long-term
    capabilities (e. g. size and scope)
  • Aggregate planning concerns with setting up
    production rate by product family or other
    categories for intermediate term (6-18 months).

Figure 4.1 Framework of Production Planning
Activities
6
Overview of Production Planning Activities
  • Master production scheduling generates the
    amounts and dates of specific items required by
    orders.
  • The inputs into MPS are arrived orders and AP
    results.
  • Rough-cut capacity planning is used to verify
    that the production and warehouse facilities,
    equipment, and labor are available , and the key
    suppliers have allocated sufficient capacity to
    provide materials when needed.

Figure 4.1 Framework of Production Planning
Activities
7
Overview of Production Planning Activities
  • Material requirement planning takes the end
    product requirements from MPS and breaks them
    down into their components and subassemblies to
    create a material plan (production orders and
    purchase order).
  • Capacity requirement planning (CAP) allocate
    production resources to each production order.
  • Operations scheduling allocates jobs to specific
    machines, production lines or work centers.

Figure 4.1 Framework of Production Planning
Activities
8
Overview of Production Planning Activities
  • Operation scheduling

Figure 4.1 Framework of Production Planning
Activities
9
Chapter 4 Production Planning
  • Contents
  • Introduction
  • Aggregate Planning
  • Master Production Planning (MRP)
  • Material Requirement Planning (MPS)
  • Capacity Planning
  • Improvement in MRP

10
Aggregate planning-Introduction
  • Aggregate planning (AP), also called macro
    planning, addresses problem of deciding how many
    employees the firm should retain and, for a
    manufacturing firm, the quantity and the mix of
    products to be produced.
  • The aggregate planning methodology here assume
    that demand is deterministic, or known in
    advance.
  • Aggregate planning methodology is designed to
    translate demand forecast into blueprint for
    planning staffing and production level for a firm
    over a predetermined planning horizon

11
AP-Introduction (2)
  • Aggregate planning (AP) involves competing
    objectives.
  • Make frequent and large changes in size of labor
    force-a chase strategy to react quickly to
    anticipated changes in demand-cost effective, but
    a poor long-term strategy
  • Retain a stable workforce-results in larger
    buildups of inventory during period of low demand
  • Develop a production plan for a firm to maximize
    profit over the planning horizon subject to
    constraints on capacity.

12
AP- Aggregate Units of Production (1)
  • AP describes aggregate units in the following
    situations
  • In terms of average item-when the items
    produced are similar
  • In terms of weights (tons of steel), volume
    (gallons of gasoline), amount of work required
    (worker-years of programming time, and dollar
    value (value of inventory in dollars)-when many
    kinds of items are produced
  • Appropriate aggregating schema are determined by
    context of the particular planning problem and
    the level of the aggregation require.

13
AP- Aggregate Units of Production (2)
Example 3.1 Decide on aggregating schema for
the manager of a plant that produces six models
of washing machines to determine the workforce
and production levels.
14
AP- Aggregate Units of Production (3)
  • One possibility is to define aggregate unit as
    one dollar of output-Unfortunately, it is
    impossible since the selling prices of the
    various models are not consistent with the
    number of worker-hours required to produce them.
  • Since the percentages of the total number of
    sales for these six models have been fairly
    constant (32 ,21, 17, 14, 10 and 6 for six
    models respectively), he decide to define the
    aggregate unit of production as a fictitious
    washing machine requiring .32?4.2.21 ?4.9.17
    ?5.1.14 ?5.2.10 ?5.4.06 ?5.84.856 hrs of
    labor time.

15
AP- Aggregate Units of Production (4)
  • Defining an aggregate unit of production at
    higher level of the firm is more difficult
  • In cases where the firm produces a large of
    products, a natural aggregate unit is sales
    dollars
  • Aggregate planning is closely related to
    hierarchical production planning (HPP). HPP
    considers workforce sizes and production rates at
    variety of levels of the firm. The recommended
    hierarchy is as follows
  • Items-correspond to individual models of washing
    machines
  • Families-a group of items, e.g. all washing
    machines
  • Types-groups of families, e.g. large house
    appliances

16
AP-Costs in Aggregate Planning (1)
  • (1) Smoothing cost-Occurs as result of changing
    the production level from one period to the next.
  • Cost for changing size of workforce-advertise
    positions interview prospective employees, and
    training new hires
  • Assumed to be linear

17
AP-Costs in Aggregate Planning (2)
  • (2) Holding costs-Occurs as a result of having
    capital tied up in inventory.
  • Always assumed to be linear in the number of
    units being held at a particular point in time
  • For aggregate planning, it is expressed in terms
    of dollars per unit held per planning period
  • It is charged against the inventory remaining on
    hand at the end of the planning period
  • (3) Shortage costs-
  • Shortage occurs when demands are higher than
    anticipated
  • For aggregate planning, it is assumed that excess
    demand is backlogged and filled in a future
    period
  • In a highly competitive situation, the excess
    demand may be lost---lost sales
  • It is generally considered to be linear.

18
AP-Costs in Aggregate Planning (3)
19
AP-Costs in Aggregate Planning (6)
  • (4) Regular time costs-Involve the cost of
    producing one unit of output during regular
    working hours
  • Actual payroll cost of regular employees working
    on regular time
  • Direct and indirect costs of materials
  • Other manufacturing expense
  • (5) Overtime and subcontracting costs-costs of
    production units not produced on regular time
  • Overtime-production by regular-time employees
    beyond work day
  • Subtracting-the production of items by an outside
    supplier
  • Assumed to be linear
  • (6) Idle time costs-underutilization of
    workforce
  • In most contexts, the idle time cost is zero
  • Idle time may have other consequences for the
    firm, e.g. if the aggregate units are input to
    another process, idle time on the line could
    result in higher costs to subsequent processes.

20
AP-A Prototype Problem (1)
  • Example 3.2
  • Densepack is to plan workforce and production
    level for six-month period Jan. to June.
  • The firm produces a line of disk drives for
    mainframe computers.
  • Forecast demand over the next six months for a
    particular line of drives in a plant are 1,280,
    640, 900, 1,200, 2,000 and 1,400.
  • There are currently (end of Dec.) 300 workers
    employed in the plant.
  • Ending inventory in Dec. is expected to be 500
    units, and the firm would like to have 600 units
    on hand at the end of June.

21
AP-A Prototype Problem (2)
  • How to incorporate the starting and ending
    inventory constraints into formulation?-the
    simplest way is to modify the values of the
    predicated demand
  • Define the net predicated demand in period 1
    the predicated demand-initial inventory
  • If there is ending inventory constraint, this
    amount should be added to the demand in final
    period

30-1020
8020100
22
AP-A Prototype Problem (3)
  • How to handle minimum buffer inventories?-By
    modifying the predicted demand.
  • If there is a minimum buffer inventory in every
    period, this amount should be added to the first
    periods demand
  • If there is a minimum buffer inventory in only
    one period, this amount should be added to the
    that periods demand, and subtracted from the
    next periods demand
  • However, actual ending inventories should be
    computed using the original demand pattern.

23
AP-A Prototype Problem (4)
Month Predicated Demand Net Predicated Demand Net Cumulative Demand
Jan. 1,280 780(1280-500) 780
Feb. 640 640 1,420
March 900 900 2,320
April 1,200 1,200 3,520
May 2,000 2,000 5,520
June 1,400 2,000(1400600) 7,520
24
AP-A Prototype Problem (5)
If the shortage is not permitted, the cumulative
production must be at least as great as
cumulative net demand each period.
25
AP-A Prototype Problem (6)
  • How to make cost trade-offs of various production
    plans?
  • Only consider three costs
  • CHCost of hiring one worker500
  • CFCost of firing one worker1,000
  • CICost of holding one unit of inventory for one
    month80
  • Translate aggregate production in units to
    workforce levels
  • Use a day as an indivisible unit of measure
    (since not all month have equal number of working
    days) and define
  • KNumber of aggregate units produced by one
    worker in one day.
  • A known fact over 22 working days, with the
    workforce constant at 76 workers, the firm
    produced 245 disk drives.
  • Average production rate245/2211.1364 disk
    drives per day
  • One worker produces an average of
    11.1364/760.14653 drive in one day. K0.14653.

26
AP-A Prototype Problem (7)
  • Two alternative plans for managing workforce
  • Plan 1 is to change workforce each month in order
    to produce enough units to most closely match the
    demand pattern-zero inventory plan
  • Plan 2 is to maintain the minimum constant
    workforce necessary to satisfy the net
    demand-constant workforce plan

P1 Zero Inventory Plan (Chase Strategy)
minimize inv. level.
Table 3-1 Initial Calculation for Zero Inv. Plan
for Denspack
A B C D E
Month No. of Working Days No. of Units Produced per Worker (B?K) Forecast Net Demand Minimum No. of Worker required (D/C rounded up)
Jan. 20 2.931 780 267
Feb. 24 3.517 640 182
March 18 2.638 900 342
April 26 3.810 1,200 315
May 22 3.224 2,000 621
June 15 2.198 2,000 910
27
AP-A Prototype Problem (8)
  • The number of workers employed at the end of Dec.
    is 300
  • Hiring and firing workers each month to match
    forecast demand.

Table 3-2 Zero Inv. Aggregate Plan for Densepack
A B C D E F G H I
Month No. of Workers No. Hired No. Fired No. of Units per Worker No. of Units Produced (B?E) Cumulative Production Cumulative Demand Ending Inv. (G-H)
Jan. 267 33 2.931 783 783 780 3
Feb. 182 85 3.517 640 1,423 1,420 3
March 342 160 2.638 902 2,325 2,320 5
April 315 27 3.810 1,200 3,525 3,520 5
May 621 306 3.224 2,002 5,527 5,520 7
June 910 289 2.198 2,000 7,527 7,520 7
Total 755 145 30
28
AP-A Prototype Problem (9)
  • The total cost of this production plan is
    obtained by multiplying the totals at the bottom
    of Table 3-2 by corresponding unit cost
  • 755?500145 ?100030 ?80524,900
  • In addition, the cost of holding for the ending
    inventory of 600 units, which was considered as
    the demand for June, should be included in
    holding cost 600 ?8048,000
  • The total cost 524,90048,000572,900.
  • Note that the initial inventory of 500 units does
    not enter into the calculation because it will be
    netted out during the month January.
  • It is impossible to achieve zero inventory at the
    end of each planning period since it is
    impossible to have a fractional number of
    workers.
  • It is possible that ending inventory in one or
    more period could build up to a point where the
    size of the workforce may be reduced by one or
    more workers.

29
AP-A Prototype Problem (10)
  • P2 Evaluation of the Constant Workforce Plan-to
    eliminate completely the need for hiring and
    firing during the planning horizon.
  • In order not incur the shortage in any period,
    compute the minimum workforce required for every
    month in the planning horizon.
  • For January, the net cumulative demand is 780
    and units produced per worker is 2.931, thus the
    minimum workforce is 267(780/2.931) in Jan
  • Units produced per worker in Jan. and Feb.
    combined2.9313.5176.448, and the cumulative
    demand is 1,420, then the minimum workforce is
    221(1420/6.448) to cover both Jan. and Feb.
  • Go on computing in the same way

30
AP-A Prototype Problem (11)
Table 3-3 Computation of the Minimum Workforce
Required by Denspack
A C C D
Month Cumulative Net Demand Cumulative No. of Units Produced per Worker Ratio B/C (Rounded up)
Jan. 780 2.931 267
Feb. 1,420 6.448 221
March 2,320 9.086 256
April 3,520 12.896 273
May 5,520 16.120 343
June 7,520 18.318 411
The minimum number of workers required for entire
six-month planning horizon is 411, requiring
hiring 111 new workers at the beginning of Jan.
31
AP-A Prototype Problem (12)
Table 3-4 Inventory Level for Constant Workforce
Schedule
A B C D E
Month No. of Units Produced per Worker Monthly Production (B?411) Cumulative Production Cumulative Net Demand Ending Inventory (D-E)
Jan. 2.931 1,205 1,205 780 425
Feb. 3.517 1,445 2,650 1,420 1,230
March 2.638 1,084 3,734 2,320 1,414
April 3.810 1,566 5,300 3,520 1,780
May 3.224 1,325 6,625 5,520 1,105
June 2.198 903 7,528 7,520 8
Total 5,962600
  • The total cost is (5,962600)?80111
    ?500580,460gt569,540 for P1
  • P2 is preferred because it has no large
    difference from P1 in cost, but keeps workforce
    stable.

32
AP-A Prototype Problem (13)
Mixed Strategy and Additional Constraints
  • The zero inventory plan and the constant
    workforce strategies are to target one objective
  • Combining the two plans may results in
    dramatically lower costs
  • Figure 3-4 shows the constant workforce strategy
    (a straight line-a fixed production rate).
    Suppose that we may use two production rates (2
    straight lines)
  • Make net inventory at the end of April to be zero
    (P1) by producing enough in each of the four
    months Jan. through April to meet the cumulative
    net demand each month produce 3,520/4880 units
    in each of the first four months
  • The May and June production is then set to 2,000,
    exactly matching the net demand in these months.

33
AP-A Prototype Problem (14)
The two lines are above the cumulative net
demand, the plan is feasible
34
AP-A Prototype Problem (15)
Month Cumulative Net Demand Cumulative Production
Jan. 780 880
Feb. 1,420 1,760
March 2,320 2,460
April 3,520 3,520
May 5,520 5,520
June 7,520 7,520
  • The graphical solution method can cope with
    additional constraints. For example
  • Suppose that the production capacity of the plan
    is only 1,800 units per month-a constraint on the
    slope of the straight line.
  • One feasible solution produce 980 in each of the
    first four months and 1,800 in each of the last
    two months.

35
AP-Aggregate Planning by Linear Programming (1)
Linear Programming (LP) is used to determine
values of n nonnegative variables to maximize or
minimize a linear function of these variables
that is m linear constraints of these variables.
Cost Parameters CHCost of hiring one worker CF
Cost of firing one worker CH Cost of holding
one unit of stock for one period CR Cost of
producing one unit product on regular time CO
Incremental cost of one unit on overtime CU
Idle cost per unit of production CS Cost of
subcontract one unit of production ntNumber
production days in period t KNumber of
aggregate units produced by one worker in one
day I0Initial inventory on hand at the start of
the planning horizon W0Initial workforce at the
start of the planning horizon DtForecast of
demand in period t
36
AP-Aggregate Planning by Linear Programming (2)
Problem Variables WtWorkforce level in period
t PtProduction level in period t ItInventory
level in period t HtNumber of workers hired in
period t FtNumber of workers fired in period
t OtOvertime production in units UtWorker
idle time in units (undertime) StNumber of
units subcontracted from outside
  • If Ptgt KntWt the number of units produced on
    overtime OtPt-KntWt
  • If Ptlt KntWt the idle time is measured in units
    of production rather than in time, Ut KntWt - Pt

37
AP-Aggregate Planning by Linear Programming (3)
Constraints-Three sets of constraints to ensure
conservation of labor and that of units
  • Conservation of workforce constraints
  • WtWt-1Ht-Ft for 1?t ?T

2. Conservation of units constraints
ItIt-1PtSt-Dt for 1?t ?T
3T constraints
3. Conservation of relating production level to
workforce levels PtKnt WtOt-Ut for 1?t ?T
  • 4. Others
  • Non negative constraints
  • Given I 0, IT, and W0.

38
AP-Aggregate Planning by Linear Programming (5)
Objective function-to choose valuables Wt, Pt,
It, Ht, Ft,Ot, Ut and St (total 8T) to
  • Subject to
  • the above 3T constraints,
  • nonnegative constraint Wt, Pt, It, Ht, Ft,Ot, Ut
    and St ?0, and
  • I0, IT, and W0.

39
AP-Aggregate Planning by Linear Programming (6)
  • Rounding the Variables
  • Some variables such as It, W, Ft, Ht should be
    integers
  • May calculate by integer linear programming,
    however, may be too complex
  • Results of LP should be rounded up- by
    Conservative approach
  • Round Wt to the next larger integer, and then
    calculate Ht, Ft, and Pt
  • Always feasible solution, but rarely optimized
  • Additional constraints
  • OtUt0-either one is zero in case that there are
    both overtime an idle production in the same
    period
  • HtFt0- either in case of hiring and firing
    workers in the same period
  • Both the two constraints are linear

40
AP-Aggregate Planning by Linear Programming (7)
  • Extensions
  • Account for uncertainty in demand by minimum
    buffer inventory Bt It?Bt, for 1?t?T, where Bt
    should be specified in advance
  • Capacity constraints on amount of production
    Pt?Ct
  • In some cases, it may be desirable to allow
    demand exceed the capacity. To treat the
    backlogging of excess demand, the inventory needs
    to be expressed in terms of two different
    non-negative variables It and It-, such that It
    It - It-, and holding cost is charged against
    It, while the penalty cost for back orders
    against It-.
  • Convex piece-linear functions-composed of
    straight-lines segments Figure 3-5

41
AP-Aggregate Planning by Linear Programming (8)
Cost of hiring workers, the marginal cost of
hiring one additional worker increases with
number of workers that have been already hired.
42
AP-Aggregate Planning by Linear Programming (9)
Example 4.2 Since no subcontracting, overtime,
or idle time allowed, and the cost coefficients
are constant with respect to time, the objective
function is simplified as
W1-W0-H1F10 W2-W1-H2F20 W3-W2-H3F30 W4-W3
-H4F40 W5-W4-H5F50 W6-W5-H6F60
P1-I1I01,280 P2-I2I1640 P3-I3I2900 P4-I4
I31,200 P5-I5I32,000 P6-I6I51,400
P1-2.931W10 P2-3.517W2 0 P3-2.638W30 P4-3.81
0W40 P5-3.224W50 P6-2.198W60
Wi, Pi, Ii, Fi, Hi (i1-6) ?0 W0300, I0500,
I6600
43
AP-Aggregate Planning by Linear Programming (10)
  • Solved by LNGO system
  • The value of objective function is 379,320.90,
    considerably less than that obtained by either P1
    and P2, since this value is obtained by
    fractional values of variables .
  • Rounded up result the total cost465 ?
    5001,000??27900 ?80379,500

A B C D E F G H I
Month No. of Workers No. Hired No. Fired No. of Units per Worker No. of Units Produced (B?E) Cumulative Production Cumulative Demand Ending Inv. (G-H)
Jan. 273 27 2.931 800 800 780 20
Feb. 273 3.517 960 1,760 1,420 340
March 273 2.638 720 2,480 2,320 160
April 273 3.810 1,040 3,520 3,520 0
May 738 465 3.224 2,379 5,899 5,520 379
June 738 2.198 1,622 7,521 7,520 1
Total 465 27 900
44
Chapter 4 Production Planning
  • Contents
  • Introduction
  • Aggregate Planning
  • Master Production Planning (MRP)
  • Material Requirement Planning (MPS)
  • Capacity Planning
  • Improvement in MRP

45
Mater Production Scheduling (1)
Aggregate production plan for mattress
Month 1 2
Mattress production 900 950
Week 1 2 3 4 5 6 7 8
Model 327 200 400 200 100
Model 538 100 100 150 100
Model 749 100 200 200
MPS for mattress models
  • Aggregate production plan for mattress specifies
    the total number of mattress planned per month,
    without regard of mattress types
  • MPS specifies the exact types of mattress and
    quantities planned for production by week

46
Mater Production Scheduling (2)
  • Aggregate planning specifies product groups,
    rather than exact items
  • As the next level down in the planning process,
    MPS is time phased plan that specifies how many
    and when a firm to build each end item.
  • In the case of the furniture company
  • Its AP may specify the total volume of mattress
    it plan to produce over next month, e. g. 900
    for the next 1 month
  • Its MPS identifies period by period ( usually
    weekly)
  • which mattress styles and how many of these
    mattress styles are needed, 200 Model 200 for Wk
    1, 100 Model 538 for both Wks 2 and 3
    respectively, and 100 Model 749 for Wk 3.

47
Mater Production Scheduling (3)
  • Could a MPS be changed?-Flexibility of MPS
  • The flexibility with a MPS depends on the
    following factors
  • Production lead time
  • Commitment of parts and components to a specified
    end items
  • Relationship between the customer and vender,
  • Amount of access capacity and
  • Reluctance and willing of management to make
    changes
  • Time Fences are defined as periods of time having
    some specified level of opportunity for customer
    to make change
  • Time fences are introduced to maintain a
    reasonable controlled flow through the production
    system.

48
Mater Production Scheduling (4)
  • Each company may have its own time fences and
    operating rules
  • Frozen absolutely no change could be made in a
    firm, or the most minor changes may be allowed in
    another.
  • Moderately firm some changes to specific
    products within a products group so long as parts
    are available
  • Flexible almost an variations in products are
    allowable, providing that capacity remains about
    the same and that there are no long lead time
    items involved.

Figure 4.2 MPS Time Fences
49
Chapter 4 Production Planning
  • Contents
  • Introduction
  • Aggregate Planning
  • Master Production Planning (MRP)
  • Material Requirement Planning (MPS)
  • Capacity Planning
  • Improvement in MRP

50
MRP-Overview
  • MRP create schedules identifying
  • the specific parts and materials required to
    produce end items planned by MPS
  • The exact numbers needed and
  • The date when orders for these materials should
    be released and be received or completed within
    the production cycle.
  • The main purpose of MRP are to control inventory
    levels, assign operating priorities for items,
    and plan capacity to load the production system.
  • Inventory-Order the right part in right quantity
    at the right time
  • Priorities-Order with right due date keep the
    due date valid
  • Capacity-Plan for a complete load, an accurate
    load, or for an adequate time to view future load.

51
MRP-Overview
  • Philosophy MRP Materials should be expedited
    (hurried) when their lack would delay the overall
    production schedule.
  • The main advantages of MRP
  • Ability to price more competitively
  • Reduced inventory
  • Reduced price
  • Better customer service
  • Better response to market demand
  • Ability to change master schedule
  • Reduced setup and tear-down costs
  • Reduced idle time

52
MRP-Principle
  • Master production specifies the number of items
    (end products or subassemblies or parts as
    independent requirements, usually as repair
    parts) to be produced during specific time
    periods
  • BOM identifies the specific materials used to
    make each item and correct quantities of each
  • The inventory records file supplies data such as
    the number of units on hand and on order
  • MRP explosion calculus implements the calculation
    of MRP

53
MRP-Inputs (BOM)
  • BOM contains complete description, listing not
    only the materials, parts, and components but
    also the sequence in which the product is
    created
  • BOM, along with MPS and inventory record are the
    three inputs
  • BOM is often called product structure file or
    product tree because it show how all the
    materials, parts, components, and subassemblies
    are put together to form a product.

54
MRP-Inputs (BOM)
  • Deferent representations of BOM
  • Indented part list
  • Single level part list

Indented Part Lists Single-Level Part Lists
End Item A(2) C(1) D(2) B(1) C(2) E(3) End Item A(2), B(1) A C(1) D(2) B C(2) E(3)
55
MRP-Inputs (BOM)
  • Low-level Coding

Although Cs appear at both Level 1 and 2, they
should be listed at the lowest level they appear,
so that computation may become easier.
56
MRP-the Explosion Calculus
  • Example 7.1 the Harmon Music Company, model 85C
    trumpet
  • Minimize the amount of money tired with
    inventory, and production level should be set to
    match the predicted demand as closed as possible.

57
MRP-the Explosion Calculus
Indented BOM
Level 0 Level 1 Level 2
1 Trumpet 1 Bell assembly 1 Valve assembly 3 Slide assemblies 3 Valves
58
MRP-the Explosion Calculus
  • The lead time for producing a trumpet is 7
    weeks-the company should begin the production now
    on trumpet to be shipped in 7 weeks.
  • Only consider forecasts for demand that are at
    least 7 weeks into the future. (if the current
    week is labeled as week 1, then requires
    forecasts for the sales for week 8 and later)

The predicated demand for week 8 through 17
Week 8 9 10 11 12 13 14 15 16 17
Demand 77 42 38 21 26 112 45 14 76 38
59
MRP-the Explosion Calculus
  • Harmon periodically receive returned trumpet
    which are defective for some reason or damaged in
    shipping. After necessary repair, they are
    returned into pool of those ready for shipping.
    The receipts are 12, 6, 9 in weeks 8, 10 and 11
    respectively.
  • These are scheduled receipts which are not on
    hand, but could be used to fill the order in due
    periods.

Week 8 9 10 11 12 13 14 15 16 17
Scheduled Receipts 12 0 6 9
60
MRP-the Explosion Calculus
  • The on-hand inventory at the end of week 7 is 23
  • Netting out on-hand inventory and scheduled
    receipts obtain MPS for trumpet

The predicated demand for week 8 through 17
Week 8 9 10 11 12 13 14 15 16 17
Demand 77 42 38 21 26 112 45 14 76 38
The net predicated demand
Week 8 9 10 11 12 13 14 15 16 17
Net predicated Demand
42
42
32
12
26 112 45 14 76 38
61
MRP-the Explosion Calculus
  • Translates MRP for the end product into a
    production schedule for the components at the
    next level of the product structure (bell
    assembly and valve casting assembly).
  • Gross requirement-on hand inventory-scheduled
    receipts
  • Net requirement
  • Net requirement is shifted by LTTime-phased
    requirement
  • Time-phased requirement is treated by lot-sizing
    algorithm planned order release

MRP for the bell assembly (LT2 weeks)
Week 6 7 8 9 10 11 12 13 14 15 16 17 Gross requirement (GR) 42 42 32 12 26 112 45 14 76 38 Net requirement (NR) 42 42 32 12 26 112 45 14 76 38 Timed-phased NR 42 42 32 12 26 112 45 14 76 38 Planned order release (LFL) 42 42 32 12 26 112 45 14 76 38
LFT-Order as actually required.
62
MRP-the Explosion Calculus
MRP for the valve casting assembly (LT4 weeks)
Week 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Gross requirement (GR) 42 42 32 12 26 112 45 14 76 38 Net requirement (NR) 42 42 32 12 26 112 45 14 76 38 Timed-phased NR 42 42 32 12 26 112 45 14 76 38 Planned order release (LFL) 42 42 32 12 26 112 45 14 76 38
  • MRP for the valves
  • On-hand inventory at the end of week 3186
  • Receive 96 at the end of week 4 from outside
    supplier
  • LT3 weeks

Week 2 3 4 5 6 7 8 9 10 11 12 13 Gross requirement (GR) 126 126 96 36 78 336 135 42 228 114 Scheduled receipts 96 On-hand inventory 186 60 30 Net requirement (NR) 0 0 66 36 78 336 135 42 228 114 Timed-phased NR 66 36 78 336 135 42 228 114 Planned order release (LFL) 66 36 78 336 135 42 228 114
63
MRP- Alternative Lot-sizing Schemes
  • Lot for lot LFL the number of units scheduled
    for production each period is the same as the net
    requirement.
  • LFL is only for convenience and ease of use,
    rather than optimal
  • The problem of finding the best or near optimal
    production plan is described as
  • Having known the time-varying demand and costs of
    setup and holding, what production quantities
    will minimize the total holding and setup cost
    over planning horizon?
  • Neither the methods of Chapter 4 nor those of
    Chapter 5 may be appropriate.
  • EOQ Lot Sizing
  • Three parameters are required the average demand
    ?, the holding cost h, and setup cost K
  • Consider the valve casting assembly K132 the
    holding cost is 0.6 per unit per week

64
MRP- Alternative Lot-sizing Schemes
  • EOQ Lot Sizing (Cont.)
  • The planned order release resulting from a LFL
    policies requires production in each week
  • If the holding cost is charged against the
    inventory each week, the total holding cost
    incurred from week 6 through 15 is 0
  • Since there is one setup each week, the total
    setup cost incurred over 10 weeks planning
    horizon is 10?1321,320
  • The cost can be reduced largely by producing
    larger amounts less often
  • As the first cut, EOQ formula is used to
    determine an alternative production policy
  • The total of the time-phased requirements over
    week 8 through 17 is 439, the average is
    43.9/week
  • Using ?43.9, h0.6, and K132,

65
MRP- Alternative Lot-sizing Schemes
  • If we schedule the production in lot size 139,
    while ensuring that the net requirements are
    satisfied, then resulting MRP is as follows

Week 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Net requirement (NR) 42 42 32 12 26 112 45 14 76 38 Planned deliveries 139 0 0 0 139 0 139 0 0 139 Planned order release(EOQ) Ending Inventory 97 55 23 11 124 12 106 92 16 117
139 0 0 0 139 0 139 0
0 139
Ending Inv.Beginning Inv.(Ending Inv. In the
last period)Planned deliveries-Net requirement
  • Cost of Using Sizing
  • During week 8-17, there are 4 setups, the total
    setup cost is 528
  • The cumulative ending inventories are
    9755653, the total holding cost is
    653?0.6391.80
  • The total cost is 391.80653919.80lt1,320 for
    LFL.

66
MRP- Alternative Lot-sizing Schemes
  • The Silver-Meal Heuristic (Named for Harlan Meal
    and Edward Meal)
  • A forward method that requires determining the
    average cost per period as a function of the
    number of periods the current order to span, and
    stopping the computation when this function first
    increase.
  • Define C(T) as the average holding cost and setup
    cost per period if the current order spans the
    next T periods

67
MRP- Alternative Lot-sizing Schemes
  • Let (r1, r2, , rn) be the requirements over the
    n-period horizon
  • Consider period 1.
  • If we produce just enough in period 1 to meet the
    demand in period 1, then only the order cost K is
    incurred. Hence,
  • C(1)K/1
  • If we produce just enough in period 1 to meet the
    demand in both periods 1 and 2, then r2 is held
    for one period. Hence, C(2)(Khr2)/2
  • Similarly, C(3)(Khr22hr3)/3
  • In general, C(j)((Khr22hr3(j-1) hrj)/j
  • Once C(j)gtC(j-1), stop and set y1r1r2rj-1
    and start the process at period j.

68
MRP- Alternative Lot-sizing Schemes
  • Let (r1, r2, , rn) be the requirements over the
    n-period horizon
  • Consider period 1.
  • If we produce just enough in period 1 to meet the
    demand in period 1, then only the order cost K is
    incurred. Hence,
  • C(1)K/1
  • If we produce just enough in period 1 to meet the
    demand in both periods 1 and 2, then r2 is held
    for one period. Hence, C(2)(Khr2)/2
  • Similarly, C(3)(Khr22hr3)/3
  • In general, C(j)((Khr22hr3(j-1) hrj)/j
  • Once C(j)gtC(j-1), stop and set y1r1r2rj-1
    and start the process at period j.

69
MRP- Alternative Lot-sizing Schemes
  • Example 7.2

r(18, 30, 42, 5, 20 ) h2 K80
  • Starting in period1

C(1)K/180
C(2) (Khr2)/2 (80(2)(30))/270
C(3)(Khr22hr3)/3(80(2)(30)(2)(2)(42))/3102.
67
Stop at period 2, y1r1r2183048
  • Starting in period 3

C(1)K/180
C(2) (Khr4)/2 (80(2)(5))/245
C(3)(Khr42hr5)/3(80(2)(5)(2)(2)(20))/356.67

Stop at period 4, y3r3r442547
70
MRP- Alternative Lot-sizing Schemes
  • Example 7.2 (Cont.)

y5r520
y(48, 0, 47, 0, 20)
Hint Streamline the computation by
C(j1)(j/(j1))(C(j)hrj1)
  • Example 7.3

r(10,40,30) h1 K50
y(50,0,30)
Notes Silver-Meal heuristic does not always
result in optimal solution.
71
MRP- Alternative Lot-sizing Schemes
  • Least Unit Cost (LUC)
  • LUC heuristics is similar to Silver-Meal
    Heuristic method except that instead of dividing
    the cost over j periods by the the periods, j,
    but by the total number of units demanded from 1
    through j period, r1r2rj
  • C(1)K/r1
  • C(2)(Khr2)/(r1r2)
  • .
  • .
  • .
  • C(j) (Khr22hr3(j-1)hrj)/(r1r2rj)

72
MRP- Alternative Lot-sizing Schemes
  • Example 7.4

r(18,30,42,5,20 ) h2 K80
  • Starting in period1

C(1) K/r1 80/184.44
C(2) (Khr2)/(r1r2) (80(2)(30))/(1830)2.92
C(3)(Khr22hr3)/(r1r2 r3)(80(2)(30)(2)(2)(4
2))/ (183042) 3.42
Stop at period 2 y1r1r2183048
  • Starting in period3

C(1) K/r3 80/421.90
C(2) (Khr4)/(r3r4) (80(2)(5))/(425)1.92
Stop at period 3 y3r342
73
MRP- Alternative Lot-sizing Schemes
  • Example 7.4

r(18, 30, 42, 5, 20 ) h2 K80
  • Starting in period4

C(1) K/r4 80/516
C(2) (Khr5)/(r4r5) (80(2)(20))/(520)4.8
y4r4r552025
y(48, 0, 42, 25, 0)
Silver-Meal (48,0,47,0,20) 340
LUC (48,0,42,25,0) 310
74
MRP- Alternative Lot-sizing Schemes
  • Part Period Balancing
  • More popular in practice
  • Set the order horizon equal to the number of
    periods that mostly matches the total holding
    cost with the setup cost over that period.
  • The exact matching is rare in an integer number.

Example 7.5
r(18,30,42,5,20 ) h2 K80
228 exceeds the setup cost of 80. 80 is closer to
60 than to 228
  • Starting in period1

Order Horizon Total holding cost

y1r1r2183048
1 0
2 60
3 228
75
MRP- Alternative Lot-sizing Schemes
Example 7.5
r(18, 30, 42, 5, 20 ) h2 K80
  • Starting in period3

90 is close to 80 than is 10
Order Horizon Total holding cost

y3r3r4 r5 4252067
1 0
2 10
3 90
Silver-Meal (48,0,47,0,20) 340
LUC (48,0,42,25,0) 310
PPB (48,0,67,0,0) 310
76
MRP- Alternative Lot-sizing Schemes
  • Given
  • Requirements ( r1, r2, , rn)
  • Capacity (c1, c2, , cn)
  • The objective is to find optimal production
    quantities (y1, y2, , yn) subject to yi?ci,
    i1n.
  • Feasibility condition

If the above feasibility cannot be satisfied, no
solution is available.
77
MRP-Lot Sizing with Capacity Constraints
  • Even feasibility is OK, however, requirements in
    some period may exceeds corresponding capacities.
  • Lot-shifting Technology for obtaining initial
    feasible solution, such that ri?ci, i1n.
  • Method
  • Back-shift demand from periods in which demand
    exceeds capacity to earlier periods in which
    there is free capacity
  • Repeat the process for the period in which demand
    exceeds capacity until ri?ci, i1n, that is,
    feasible for lot-for-lot.

78
1 2 3 4 5 6 7 8 9












120
r 100 79 230 105 3
10 99 126 40 c 120 200
200 400 300 50 120 50 30
200
109
50
50
18
30
28
Extra holding cost(2)(158) 316lt450
y 100 109 200 105 28
50 120 50 30
Extra holding cost(2)(30)(4)240lt450
Extra holding cost(2)(50)(3)300lt 450
Extra holding cost(2)(50)(1)100lt 450
Excess capacity 20 91 0 295
272 0 0 0 0
79
MRP-Lot Sizing with Capacity Constraints
y (100, 109, 200, 263, 0, 0,
120, 0, 0) r (100, 79, 230, 105,
3, 10, 99, 126, 40) Ending inv.( 0, 0, 0,
158, 155, 145, 166, 40,0)
  • The total cost5( 450)2(694)225013883638.

80
Chapter 4 Production Planning
  • Contents
  • Introduction
  • Aggregate Planning
  • Master Production Planning (MRP)
  • Material Requirement Planning (MPS)
  • Capacity Planning
  • Improvement in MRP

81
Capacity Planning -Framework
  • Long range Strategic capacity planning
  • Medium range Rough-cut capacity planning and
    capacity requirement planning
  • Short-range Finite loading and Input/output
    analysis

Finite loading
Input/output analysis
82
Capacity Planning Rough-cut planning
  • Strategic capacity planning or resources planning
  • Directly linked to aggregate production planning
  • The most highly aggregated and longest range
    capacity planning decision
  • Typically revolves converting monthly, quarterly,
    or even annual data from aggregate production
    planning into aggregate resources such as gross
    labor-hours, floor space, and machine-hours
  • Involves new capital expansion, bricks and
    mortar, machine tools, warehouse space, and so
    on, which requires a time horizon of months or
    years.

83
Capacity Planning - Framework
  • Rough-cut capacity planning
  • MPS is the primary information sources
  • Several techniques Capacity planning using
    overall planning factors (CPOF) Capacity bill
    or Resource profiles
  • Capacity requirement planning (CRP)
  • Time-phased material plan supplied by MRP are the
    basis for calculating time-phased capacity
    requirements
  • Date used by CRP techniques include WIP, routing,
    scheduled receipts, and planned order
  • Information provided by CRP can be used to
    determine capacity needs for both key machine
    centers and labor skills, typically covering a
    planning horizon of several weeks to a year .

84
Capacity Planning - Framework
  • Finite loading technique
  • Also relates to a firms that use time-phased
    detailed material plan
  • Can be better viewed as a shop floor scheduling
    techniques
  • Clarifies the relationship between scheduling and
    availability
  • Is a method for scheduling work center or
    resource group.
  • Input/output analysis
  • Provides a method of monitoring the actual
    consumption of capacity during execution of
    detailed material plans obtained by MRP
  • Can indicate the need to update capacity plans as
    actual shop performance deviates from the current
    plan, and the need to modify planning factors
    used in capacity planning techniques.

85
Capacity Planning Techniques (CPOF)
  • CPOF is relatively simple approach to rough-cut
    capacity planning
  • The calculation procedure is based on the
    planning factors, such as direct labor time per
    end product unit, derived from standard or
    historical data for end products
  • These factors are applied to MPS data to estimate
    overall labor or machine-hour capacity
    requirements
  • These overall estimate is then allocated to
    individual work center on basis of historical
    data on shop work loads.
  • CPOP plans are usually stated in terms of weekly
    or monthly time period and accordingly are
    revised as the firm changes the MPS.
  • .

86
Capacity Planning Techniques (CPOF)
Example Problem data
Estimated CPOF in standard direct labors
62.8(0.9533)(1.8517) using the standard from
the above table
87
Capacity Planning Techniques (Capacity Bills)
  • Capacity bill procedure is a rough-cut method
    providing more direct between individual end
    product in MPS and the capacity required for each
    work centers
  • It considers any shifts in product mix
  • It requires more data than CPOF
  • Not only BOM and routing date are required, but
    also direct labor-hour or machine-hour data must
    be available.
  • Calculation procedures
  • First calculate bill of capacity of end product,
    that is total time/unit for each end product on
    each resource, based on BOM, routing data, direct
    labor-hour or machine-hour
  • Then, apply bill of capacity to MPS to obtain
    capacity requirements of each resources in each
    period

88
Capacity Planning Techniques (Capacity Bills)
Routing and standard time data of an example
89
Capacity Planning Techniques (Capacity Bills)
Routing and standard time data of an example
90
Capacity Planning Techniques (Capacity Bills)
Routing and standard time data of an example
91
Capacity Planning Techniques (Capacity Bills)
Routing and standard time data of an example
92
Capacity Planning Techniques (Capacity Bills)
Having obtained bill of capacity for end
products, capacity requirements for each work
center in each period could be calculated by
applying capacity bills of end products to MPS
For example, capacity requirements for work
center 100 in period 1 is as follows 330.05171
.323.75
93
Capacity Planning Techniques (CPR)
  • CRP is to calculate capacity requirements placed
    on a work center or resource group by using the
    output of MRP, that is, the time-phased material
    plan information generated by MRP.
  • The information include actual lot sizes and lead
    time for both open shop orders (scheduled
    receipts) and orders planned for future release
    (planned orders).
  • By calculating capacity requirements both for
    open shop orders (scheduled receipts) and orders
    planned for future release (planned orders) in
    the MRP data base, CRP accounts for the capacity
    already stored in the form of finished and WIP
    inventories.

94
Capacity Planning Techniques (CPR)
1 2 3 4 5 6 7 8 9 10 11 12 13
33 33 33 40 40 40 30 30 30 37 37 37 37
Product A MPS
Component C Lot size40 Lead time2 On hand
inv.37
1 2 3 4 5 6 7 8 9 10 11 12 13
33 33 33 40 40 40 30 30 30 37 37 37 37
40
4 11 18 18 18 18 28 38 8 11 14 17 20
0 0 40 40 40 40 40 40 40 40 40 40
40 40 40 40 40 40 40 40 40 40
Gross Req.
Scheduled Receipts
Inventory balance
Planned deliveries
Planned order release
95
Capacity Planning Techniques (CPR)
Worker center 300 capacity requirements using CRP
1 2 3 4 5 6 7 8 9 10 11 12 13
8 8 8 8 8 8 8 0 8 8 8 8 8
Hrs of capacity
Total88
  • We have already known that the time to fabricate
    a component C in machine center 300 is 0.2 hrs
  • The 8 hrs of capacity is derived from the
    scheduled receipt and planned order quantities of
    40 units multiplied by 0.2

96
Chapter 4 Production Planning
  • Contents
  • Introduction
  • Aggregate Planning
  • Master Production Planning (MRP)
  • Material Requirement Planning (MPS)
  • Capacity Planning
  • Improvement in MRP

97
Improvement for MRPClosed-Loop MRP
  • When MRP system has information feedback from its
    module output, this is termed closed loop MRP
  • The closed-loop is realized by checking if
    sufficient capacity is available. If not, the
    schedule should be modified.
  • The modification may be made by either changing
    MPS or by regulating the planned order release.

98
Improvement for MRPMRP-II
  • Manufacturing Resource Planning (MRP-II) was
    first proposed by Ollie Wright 1977
  • As a complex planning computer system, MRP-II was
    to plan and monitor all the resources of a
    manufacturing firm through a closed-loop system.
  • The manufacturing resource include theses for
    manufacturing, marketing, finance, and
    engineering.
  • MRP-II help a firm cope with complex balancing
    problem among production, purchasing, and sales
    to shorten lead time for manufacturing and
    purchasing, and reduce production cost, enhance
    adaptability, and increase economic efficiency.

99
Improvement for MRPMRP-II
  • Additional common functions for MRP-II
  • Purchasing management
  • Production costing
  • Shop floor management
  • Inventory management
  • Accounting

100
  • The End !
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