DEPARTMENT OF MANAGEMENT SCIENCE
MScs in Management Science 2007-08
MRPII - Manufacturing Resource Planning
Introduction
Statistical inventory control, which is concerned with economic lot sizes and probability of
stockout, is inappropriate in situations such as the control of components used in the
manufacture of a finished product. At least three demonstrations of this can be presented.
First, consider a product, which costs £30, whose demand in the next ten weeks is 60.
Assume also that the set-up cost for production of this product is £25 and that the
inventory carrying cost is 20% per annum. A straightforward application of the formula
for the Economic Batch Quantity (EBQ), assuming a 50 week year, gives a production
quantity of 50. One assumption behind the EBQ is that the demand is constant, in this
case 6 per week. If, however, the demand pattern over the next 10 weeks is 20-0-20-0-00-0-0-0-20, production of 50 units will lead to a 'remnant' of 10 units being carried for 7
weeks without any purpose, as production will be required in the 10th. week. Similarly, a
demand pattern of 20-0-40-0-0-0-0-0-0-0 would imply that the EBQ will fail to cover the
third week's requirements. Therefore, in situations of 'lumpy' demand it would seem that
alternatives to the fixed lot size produced by the EBQ would be more appropriate.
Second, to demonstrate how 'lumpy' demand may arise, consider the production of four
tools from two forgings, which are both made from a particular steel. Tool 1, with a
smooth demand of one per week, and Tool 2, with a smooth demand of six per week, are
both made from Forging A. Tools 3 and 4, with smooth demands of three and seven per
week respectively, are each produced from Forging B. If we suppose that the EBQ for the
four tools are 5, 15, 10 and 25 respectively, then Tool 1 will be produced in weeks 1, 6, 11
etc., Tool 2 will be produced in weeks 1, 3, 6, 8, 11 etc., Tool 3 will be produced in weeks
1, 4, 7, 11 etc. and Tool 4 will be produced in weeks 1, 4, 8, 11 etc. The implication for the
production of the forgings, assuming lot sizes of 25 and 50 for Forgings A and B
respectively, is that Forging A will be produced in weeks 1, 3, 6 etc. and Forging B in
weeks 1, 4 etc. The demand for the steel will therfore be 75-0-25-50-0-25 in the first six
weeks, and the smooth constant demand of the four final products has produced 'lumpy'
demand for the raw material.
Third, if the probability of having one item in stock when required (the service level) is
90%, then two components, required simultaneously for the same end item, will both be in
stock with a service level of 81%. If ten components are required, the odds against all of
them being available has risen to 2:1 (34.8%). Even if the service level is set at 95%, the
probability of simultaneous availability of ten components is 60%, and for 14 components
it drops below 50% (48.8%). Thus, when components are ordered, independently of each
other, their inventories will tend not to match assembly requirements, and the cumulative
service level will be significantly lower than the service levels of the parts taken
individually.
An alternative to statistical stock control, therefore needs to be used when item demand is
dependent. The alternative is Material Requirements Planning (MRP). The principle of
MRP is that a time phased schedule of requirements over the, pre-determined, planning
horizon, is generated for each component/sub-assembly/raw material on the basis of
independent forecasts of demand for the end products. In a full requirements planning
system, such schedules of item demand will take account of consolidated demand for
common components existing physical stock levels, production/purchasing lead times and
production batching policy. MRP takes no account of available capacity, a defect which
MRPII seeks to rectify.
Inputs to an MRP System
1.
The Master Production Schedule
The overall plan of production during the planning horizon is detailed in the master
production schedule. The planning horizon normally equals or exceeds the cumulative
purchasing and production lead time for components of the items in question. It will
therefore include time to assemble the product, time to manufacture the components, time
to purchase raw materials, and, often, time to allow the purchasing department to
consolidate orders to take advantage of opportunities for bulk purchasing.
In practice this frequently will require an horizon of a year to eighteen months. It is not
possible to allow no changes to be made over this period of time, but it is important that
changes in the immediate future of the schedule are kept to a minimum. For this reason,
the planning horizon is often split into time zones, with different constraints on the
changes that can be made. In the immediate future, in which finished products are
currently being assembled, the schedule should only be changed in emergency, since the
component parts will have already been manufactured to schedule. Moving forward in
time, to the period in which parts are currently being manufactured, it may be possible to
make some changes, for example to the sequence of manufacture. In the part of the
horizon in which orders for materials have been placed on suppliers, it may be possible to
alter production quantities, if the consequent changes to orders can be made. Finally, in
the last time zone it will normally be possible to make changes without to much difficulty.
In addition to the sales of finished products, a company may also have demand for spare
parts; demand which is independent. Such demand can be incorporated into an MRP
system by adding them to the dependent demands in the appropriate time period.
The essential purpose of an MRP system is to translate the schedule into individual
component requirements for specific time periods. In order to take into account the
different time zones, it is possible to have variable length time periods. In the first time
zone the time period (or time bucket) may be a day, in the second time zone a week may
be more appropriate, in the third time zone a month might be used, and, finally, in the
fourth time zone, a quarter may be used.
2.
The Inventory Record File
The individual item stock records are kept in a file which is kept up-to-date by the posting
of transactions (e.g. stock receipt, disbursement, scrap, etc) which change the status of the
respective items. An important aspect of an inventory record for an MRP system is that it
is time-phased, e.g. information on either specific dates or planning periods with which the
respective quantities are associated is recorded and stored. In many stock recording
systems the status of a given item is normally shown as consisting of only the quantity on
hand and the quantity on order.
In addition to status data, the inventory records also contain "planning factors", used
principally for determination of the size and timing of planning orders, such as lead time
and scrap allowance.
3.
Bill of Material file
The B-O-M file, as it is known, contains information on the relationships of components
and assemblies. Its conventional representation is shown in Figure 1 where the product in
question (the parent item) is assembled from four different parts. It uses only one of each
of three of the components, but uses two of the fourth.
End Product
|
Part A
Quantity 1
Part B
Quantity 1
Part C
Quantity 2
Part D
Quantity 1
Figure 1: Bill of Material
When the individual bills defining a product are linked together they form a hierarchical
pyramid-like structure, and the levels emerge into view. The items on the highest level in
a B-O-M file are the end products.
Calculation of Requirements
1.
Gross requirements
The gross requirements for an item equals the quantity of demand for that item. It is the
quantity of the item that will have to be disbursed to support a parent order, rather than the
total quantity that will be consumed by the end product. These two quantities may or not
be identical.
Assume that 50 lorries are to be produced and in stock there are
2
transmissions
5
gearboxes
7
gears
20
forging blanks
The simple product structure (B-O-M) is illustrated in Figure 2
Lorry
|
Transmission
|
Gearbox
|
Gears
|
Forging blanks
Figure 2 Product structure
The gross requirements of the forging blank are calculated as follows:
No. of lorries to be produced
Quantity of forging blanks needed
Stocks of gears containing forging blanks
Stocks of gearboxes containing gears
Stocks of transmissions containing gearboxes
50
50
7
5
2
14
36
Gross requirement for forging blanks.
If there are multiple sources of demand, and therefore of gross requirements, they are
combined and summarised, by planning period, in the gross requirements schedule which
is represented by a row of time-buckets as in Figure 3.
Period
Gross requirements
1
2
15
3
10
4
5
22
6
7
13
8
12
Total
72
Figure 3 Gross requirements schedule
2.
Net requirements
The net requirements of an item are simply found by allocating the available inventory on
hand and on order to the gross requirement. So, in the lorry example, the net requirement
of forging blanks is 16 (Gross requirement - stock). In the example given in Figure 4
there are 18 units of this item on hand and 24 on order, due in period 4. This information
can be displayed in time bucket format as in Figure 4 and the net requirements calculated.
Period
Gross requirements
Scheduled receipts
On hand
18
Net requirements
1
2
15
3
10
4
5
22
6
7
13
8
12
Total
72
24
11
12
30
24
7
Figure 4 Net requirements schedule
3.
Explosion of requirements
The 'explosion' of requirements from the master production schedule down into the
various component-material levels, is guided by the logical linkage of inventory records.
Net requirements for the high-level items are covered by planned orders. The quantity
and timing of these planned orders determine, in turn, the quantity and timing of
component gross requirements. This procedure is carried out for items on successively
lower levels until a purchased item is reached.
The computation of requirements is complicated by six factors:
1.
The structure of the product, containing several manufacturing levels of materials,
component parts and subassemblies.
2.
Lot sizing, i.e. ordering inventory items in quantities exceeding net requirements,
for reasons of economy or convenience.
3.
The different individual lead times of inventory items that make up the product.
4.
The timing of end-item requirements during a planning horizon of, typically, a
year's span or longer, and the recurrence of these requirements within such a time.
5.
Multiple requirements for an inventory item due to its 'commonality' i.e. usage in
the manufacture of a number of other items.
6.
Multiple requirements for an inventory item due to its recurrence on several levels
of a given end product.
Lot sizing
Much of the Operational Research literature related to MRP systems is devoted to discretedemand, time-series lot sizing. Some of the new techniques which have been developed
are described and evaluated in this section, along with the more traditional approaches to
lot sizing. Given a particular net requirements schedule the question arises as to what
ordering schedule should be followed.
1.
Some simple approaches
A fixed batch quantity may be specified and determined arbitrarily, or, if determined
using cost factors an economic batch quantity (EBQ) can be calculated. This will be
determined by using the 'square-root' formula, but the known future demand, rather than
historical demand, can be used. In contrast to all the other approaches that will be
described these two approaches create 'remnants', i.e. quantities that could be carried in
stock for some length of time without being sufficient to cover a future period's
requirements in full. (NB. If there is a net requirement during a period that is higher than
the order quantity, the order quantity is increased to the net requirement).
All other approaches are discrete lot-sizing techniques because they generate order
quantities that equal the net requirements in an integral number of consecutive planning
periods. The simplest is lot-for-lot ordering when the planning order quantity always
equals the quantity of the net requirements being covered. Fixed period requirements is
equivalent to the primitive rule of ordering 'X months' supply except that here the supply is
determined not by forecasting but by adding up discrete future net requirements. The
period of coverage every planned order should provide is specified. Lot-for-lot ordering
is, obviously, a particular case of fixed period requirements lot sizing.
Figure 5 illustrates the effect of these different policies for a particular net requirements
schedule. For the calculation of the EBQ the set-up (A) is £100, the unit cost (C) is £50,
the carrying cost (I) is £0.24 per annum and D = 200 is obtained by annualizing the 9
month demand. It is assumed that the fixed period is 2.
Net requirements
Fixed batch quantity
Economic batch quantity
Lot-for-lot
Fixed period requirements
1
35
60
58
35
45
2
10
10
3Month4
40
60
58
40
40
5
6
20
20
25
7
5
8
10
5
58
10
40
9
30
60
30
Total
150
180
174
150
150
Figure 5 Some simple lot-sizing approaches
2.
Period order quantity (POQ)
POQ is based on the logic of the EBQ, modified for use in an environment of discrete
period demand. The EBQ is calculated, as described in the previous section and the
number of orders per year calculated. The number of planning periods during a year is
then divided by this quantity to determine the ordering interval.
So the POQ technique is identical to the fixed period requirements approach, except that
the ordering interval is computed, and is more effective than the EBQ, as set-up cost per
year is expected to be the same but the carrying cost will tend to be lower, as 'remnants' are
avoided.
However, the predetermined ordering interval might prove inoperative, if several periods
show zero requirements and force the technique to order fewer times per year than
intended.
Using the previous example with D = 200 and Q* = 58 the number of orders per year is
3.4 and the ordering interval is 3.5 months. The effect of this policy, (assuming the
interval alternates between 3 and 4 periods), is shown in Figure 6.
Net requirements
Period Order Quantity
1
35
85
2
10
3Month4
40
5
6
20
35
7
5
8
10
9
30
30
Total
150
150
Figure 6 POQ
3.
Least unit cost and least total cost approaches
These approaches, and those that follow, all share the assumption of discrete inventory
depletions at the beginning of each period, i.e. a portion of each order, equal to the net
requirements in the first period covered by the order, is consumed immediately upon
arrival in stock and thus incurs no inventory carrying charge. Inventory carrying cost,
under these lot-sizing approaches, is computed on the basis of this assumption rather than
on average inventories in each period.
In determining the order quantity, the least unit cost (LUC) technique calculates the 'unit
cost' (i.e. set-up plus inventory cost per unit) for each of the order quantities obtained by
covering the next period's requirements, the next two periods' requirements and so on.
The one with the least unit cost i chosen to be the lot size. The calculation of the first lot
in the example is as follows. (A = £100, IC = £1 per unit per month). The results of the
whole calculation are given in Figure 7, and illustrate the limitation of the approach in that
only one lot is considered at a time. Tradeoffs between consecutive lots can sometimes be
made that would reduce the total cost of two or more lots. For instance, if the
requirement in period 7 were added to the second lot, its inventory carrying cost would
increase by £15, but that of the third lot would decrease by £40.
Net requirements
LUC
1
35
45
2
10
3Month4
40
60
5
6
20
7
5
45
8
10
9
30
Total
150
150
Figure 7 LUC
The least total cost approach (LTC) attempts to overcome this flaw in LUC logic, on the
basis that the total cost for all lots within the planning horizon will be minimised if the setup cost per unit and the carrying cost per unit are as nearly equal as possible (as in the
classical EBQ approach). The approach involves calculating the 'economic part-period'
(EPP) factor, which is defined as that quantity of the item which, if carried in stock for one
period, would result in a carrying cost equal to the cost of set-up. It is computed simply by
dividing the inventory carrying charge per unit per period (IPC) into set-up cost. In our
example:
EPP = A/IPC = 100
The order quantity selected by the LTC approach is that for which the part period cost
most nearly equals the EPP. The calculation for the first lot in the example is
Month
1
2
4
Net Requirements
35
10
40
Part-periods(Cumulative)
0
10
130
So the quantity chosen for the first lot would be 85, because the 130 part-periods that it
would cost most nearly approximate the EPP of 100. The second order, 65, would cover
the requirements of months 6-9.
The LTC logic has a flaw of its own because the premise that 'the least total cost is where
the inventory cost and setup cost are equal' holds true for the EBQ but not for a discrete
lot-sizing approach which assumes that inventory depletions occur at the beginning of
each period.
4.
An incremental heuristic
This heuristic simply sequentially increases the lot size by the requirements of successive
periods until the incremental cost of carrying the next period's requirements in inventory
exceeds the cost of set-up.
Month
1
2
4
Net requirements
35
10
40
Inventory cost
10
120>100 so set-up in period 4
The use of this heuristic indicates that lots be produced in periods 1,4 and 9.
5.
The Silver-Meal heuristic
The objective of this algorithm is to minimise the total relevant costs per unit time. The
approach is similar to the least unit cost calculation, but this time the total relevant costs
are divided by the number of time periods, rather than the lot size. The lot size is the sum
of the requirements in all periods up to and including that period for which the total cost
per unit time is a minimum.
The calculation of the first lot in the example is as follows:
Month
1
2
4
Net requirements
35
10
40
Inventory cost
0
10
120
Total cost
100
110
230
Total cost/No of periods
100
55
57.5
Thus the first lot will be for the demand in periods 1 and 2, and is of size 45. The use of
this heuristic indicates that lots will be produced in periods 1,4 and 8.
6.
Comparison between the various approaches
Every one of the lot-sizing approaches reviewed above suffers from some deficiency.
Furthermore any comparison based on an example, such as the one that has been
considered, is meaningless because a change in the data can produce a different order of
performance. For the example, the results given below are obtained (all inventory
carrying costs are based on discrete depletion at the beginning of the period) .
If the set-up cost were £300, however, the POQ would outperform LTC and match LUC in
effectiveness. In fact, the requirements data can be changed to produce practically any
results desired.
Therefore, there does not seem to be one 'best' lot-sizing algorithm that could be selected
for a given manufacturing environment, for a class of items, or even a single specific item.
If set-up costs are low then the lot-for-lot approach may as well be used and in cases of
significant set-up cost LUC, LTC or POQ may be chosen.
Algorithm
Silver-Meal
Incremental
LUC
LTC
Fixed period requirements
POQ
EBQ
Fixed batch quantity
Lot-for-lot
7.
Set-up cost
300
300
300
200
400
300
300
300
700
Carrying cost
95
105
120
245
45
155
206
220
-
Total cost
395
405
420
445
445
455
506
520
700
When to use the heuristics
If there is no variability of demand then it doesn't make sense to use an algorithm that
allows for such a situation. Clearly the variability should exceed some threshold value
before a heuristic is used.
Silver suggests that the Silver-Meal heuristic should be used when a Variability
Coefficient (VC) is greater than one quarter, where VC is the variance of demand per
period divided by the square of the average demand per period, ie.
N
N
VC = ((N  D 2i ) / (  D i ) 2 )  1.
i=1
i=1
N
In the example,
N
 Di  150 and
D
i=1
i=1
2
i
 4350
So VC = (9 x 4350/(150)2 )-1 = 0.74. As this is greater than one quarter, it would be
sensible to use the heuristic in this case.
System Outputs
An MRP system can provide a great number of outputs because the data base, and the
inventory status records in particular, contain a wealth of information that provides an
opportunity for extracting or further processing the data. Four examples are given here.
1.
Inventory order action
These types of output are generally self-explanatory. Outputs for inventory order action
are based primarily on planned orders becoming mature for release. The MRP system
detects such orders by examining the contents of planned-order release buckets in the
time-phased inventory records. Other types of inventory order action are increases,
reduction, and cancellations of order quantities.
2.
Replanning order priorities
When there are cases of divergence between open-order due dates and dates of actual
need, as indicated by the timing of net requirements, an MRP system has the capability to
indicate precisely by how many time periods each item affected should be rescheduled,
and in what direction.
3.
Safeguarding priority integrity
To keep priorities honest, the master production schedule must reflect the realities of
production, i.e. it must not contain end product requirements that cannot be met for lack of
capacity, material or lead time. Some companies use reports in this category to provide
guidance in accepting customer orders for guaranteed delivery. Such reports are
generated by 'trial fit' of the order into the master production schedule, and then letting the
MRP system determine component-material and lead-time availability. If the order does
not fit, the report indicates a best delivery date alternative.
4.
Capacity requirements planning
Outputs for purposes of capacity requirements planning are based on quantities and due
dates of both open and planned shop orders, which serve as input to the capacity
requirements planning (or loading) system. The MRP system makes it possible for the
load report to be complete, valid, and extending far enough into the future to allow
capacity-adjustment action to be taken in time. To keep the load projection up-to-date
and valid, it must be repeatedly recomputed as the order schedules in the MRP system
change.