3 - MRP Model · 2017. 5. 12. · •MRP procedure operates –in a recurrentway –according to...

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Inventory systems for dependent demand

Roberto [email protected]

Department of Management, Economics and Industrial Engineering Politecnico di Milano

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Overall view (taxonomy)

The planning of requirements consists of the determination of • What• How much and• When

to order at every stage of the production process

Planning systems

Push systems(needs based)(requirements based)

Pull systems(stock based)

Dependent demand

Independent demand

Traditional

Just in Time

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Characteristics of pull (stock based) systems • Objective:

having “always” the required product stored in the warehouse (according to the service level)

• Required information:order issuing criteria (re‐order policy), i.e. the triggering mechanism

• Implicit hypotheses: Smoothed and even stock consumption Independent demands among finished

products Reduced demand variance

• Distinctive feature:each phase of the production process only “sees” the warehouse immediately downstream and it is completely blind with reference to the remainder of the supply chain

• Saw‐tooth profile over time • Safety stocks based on variance• Service level taken from the

Gauss function

This does not protect the inventory system against the so‐called

bullwhip effect

Pull planning system

Information flow

Physical flow

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A note on the bullwhip (Forrester, 1961) effect• Even a very small change at the finished product level

(end customer) may represent a remarkable source of variance when going upstream along the supply chainand/or along the bill of materials

‐80

‐60

‐40

‐20

0

20

40

60

80

61626364656667686970717273747576777879808182838485868788899091

Deman

d Va

riance (%

)

Distribution stage

Production stage

Components stage

Example referred to the US automotive industry (see Anderson et al. 2000, Upstream volatility in the supply chain: the machine tool industry as a case study, Production & Operations Management, 9, (3), 239‐261)

A bullwhip …

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A note on the bullwhip(Forrester, 1961) effect Finished products

Inventory level

time

Re‐order point

Manufacturing lead time

Re‐order

r1 r3r2

Components

r1 r3r2

Rawmaterials

r2

Inventory level

Inventory level

time

time

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Characteristics of push (needs / requirements based) systems • Objective:

calculating which, how many and when components, sub‐assemblies, parts, raw materials etc. are required to put a plan into operation i.e. to ensure that the customers’ orders due dates (deadlines) are respected

• Required information:It is much greater than under pull systems, as it is needed to know the master production schedule, the bills of materials and to consider at the same time all the data referred to all the products and departments involved

Information flow

Physical flow

Push planning systemPull planning system

Information flow

Physical flow

BOMs MPS

push

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Characteristics of push (needs / requirements based) systems • Remarks:

Requirements of components directly depend on a plan (e.g. the master production schedule)

Requirements of components are therefore calculated and not estimated (i.e. derived from statistical analyses) as under pull systems

In the end, the objective lies in coordinating the production dates (rendezvous) of components to manufacture finished products (or higher level components in the bill of materials)

• MRPmeans Materials Requirements Planning and it represents the procedure that implement the data processing needed by the push approach to manage inventories

Production date

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Characteristics of push (needs / requirements based) systems • MRP procedure operates – in a recurrent way – according to the so‐called

“3S” approach1. Sum the requirements of the same component coming

from different orders and referred to the same period2. Split the overall requirements per period of each

component according to the lot‐sizing policy3. Shift backward over time the lot‐sized requirements

according to the lead times reported in the bills of materials (to take into account the production routings)

• This leads to a plan of purchasing and manufacturing ordering proposals

• This plan in turn generates gross requirements of lower‐level components of the bill of materials

• The recurrent procedure is finished when the raw materials (i.e. the “leaves” of the BoM) are reached

+÷

Explosion of the bills of materials

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Example of MRP running (1/10)

EngineGear

Exhaust

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Motorcycle

PowerTrainChassis

Front & rear wheels Frame

Finished products (top items)

Components

Raw materials (leaves)

Lead time 3 weeksRe‐order policy Fixed EOQ, 150 piecesInitial inventory 200 piecesReserved stock 30 pieces (1st week)Orders in progress 48 pieces (3rd week)Safety stocks 50 pieces

Scrap rate 10 %Data referred to the

“chassis” and known in advance

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Example of MRP running (2/10)Week 1 2 3 4 5 6 7 8 9 10

Gross internal requirements (chassis) 50 30 20 10 40 60 50 10 10 50

Gross external requirements (chassis) 10 10 10 10 10 20 20 20 20 20

Before entering the first “S” (sum) you should know also the profile (over time) of the gross requirements (i.e. the demand) of your item.

Gross requirements are divided into:1. Internal requirements, i.e. originated from other finished products

(e.g. a different kind of motorcycle)2. External requirements, i.e. originated form customers (e.g. a

chassis sold as spare part)

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Gross total requirements (chassis) 60 40 30 20 50 80 70 30 30 70

Now we enter the first “S” – sum:

The gross total requirements of the chassis are give by the sum period by period of the gross internal requirements and the gross external requirements

+

=

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Initial availability (chassis) 120 60 20

120 = 200 – 30 – 50, i.e.: Initial _inventory

Reserved _stocks

safety stocks

=-

The gross total requirements ‘consume’ the initial availability.

So, at the beginning of period 2, initial availability accounts for 60, i.e. 120 – 60At the beginning of period 3, initial availability accounts for 20, i.e. 60 – 40At the beginning of period 4 initial availability is 0, given that 30 > 20, i.e. the gross total requirements exceed the initial availability

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Requirements (chassis) 10 20 50 80 70 30 30 70

Once the initial availability is finished, all the gross requirements are converted into requirements

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Scraps‐adjusted requirements (chassis) 11 22 55 88 77 33 33 77x 1.1

Now you have to take into account the 10% scrap rateSo, all the requirements are to be multiplied by 1.1

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Scraps‐adjusted requirements (chassis) 11 22 55 88 77 33 33 77

Orders in progress (chassis) 48

Now you have to take into account the orders in progress, i.e. 48 pieces arriving at the beginning of period 3.They represent some sort of additional availability, apart from that they are potentially subject to scraps , while availability is not

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Net requirements (chassis) 40 88 77 33 33 77

The scraps‐adjusted requirements ‘consume’ the orders in progress So, referring to period 3, the net requirements are 0, given that 48 > 11 (and 37 pieces are left)Referring to period 4, the net requirements are 0 again , given that 48 –11 > 22 (and 15 pieces are left)Referring to period 5, the net requirements are 40, i.e. 11 + 22 + 55 – 48

Once the orders in progress are finished, all the requirements are converted into net requirements

= 55 – 15

37 left 15 left

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Lot‐sized requirements (chassis) 150 150 150

Now you have to split (S2) net requirements by economic lots (of 150 pieces)

150 – 40 = 110 left

110 – 88 = 22 left

150 + 22 – 77 = 95 left

95 – 33 = 62 left 62 – 33 = 29 left

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Orders to issue (chassis) 150 150 150

Finally you have to shift backward over time (S3) lot sized requirements by the lead time (3 periods)

Lead time = 3

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The recurrent approach of MRP • Now you have on hand the plan of orders for the chassis• It has to be converted into gross requirements of the wheels and of the

frame, i.e. of the lower‐level components (raw materials in the example)

• These gross internal requirements of wheels coming from the chassis maybe have to be summed up with gross internal requirements coming from other products and with gross external requirements (of the wheels) if they are sold as spare parts

Week 1 2 3 4 5 6 7 8 9 10


Gross internal requirements (wheels ) coming from the chassis 0 300 0 300 0 0 300 0 0 0

x 2

“2” factor comes from the coefficient of use

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Limits of MRP procedures• Three major areas are referred to as “critical system design features”

(Orlicky, 1974)

1. Production capacity is infinite While all the production systems are capacity‐constrained

2. Lead times are fixed and pre‐determined (a priori, outside MRP) While lead times result form the planning activity

3. Data used by MRP require a huge amount of space And MRP is subject to the garbage‐in‐garbage‐out (GIGO) law

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Limits of MRP procedures1. Production capacity is infinite

MRP basically operates at infinite capacity, so the load of work centers is optimized only indirectly, through lot‐sizing rules.

100300

170300 40 300 260

230 30 130

0

200

400

600

1 2 3 4 5 6 7 8 9 10Periods

Orders to issue

MRP procedure “by itself” is unable to manage the peaks

of workload

Production capacity

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100300

170300 40 300 260

230 30 130

0

200

400

600

1 2 3 4 5 6 7 8 9 10

100

300

170

300

40

300260

200 30

130

30

0

50

100

150

200

250

300

350

1 2 3 4 5 6 7 8

100

300

170

300

200 3030

0

50

100

150

200

250

300

350

1 2 3 4


Limits of MRP procedures1. Production capacity is infinite

Production capacity is managed through finite‐capacity post‐processors which are often based on (complex) linear programming (LP) and/or theory of constraints (ToC) approaches

Step 1: initial infeasibility Step 2: Overloaded is either avoided or reduced by shifting orders backward

Step 3: Overloaded is removed by shifting orders forward

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Limits of MRP procedures2. Lead times are fixed and pre‐determined (a priori, outside MRP)

Lead times are used as input variables and they are not considered as function of (dependent on) the work load No protection is assured against the “orders in the past” phenomenon i.e. the orders that fall in periods prior to period 1, i.e. orders that would have had

to be issued “in the past” (yesterday, last week / month etc.)

• Go back to the example of MRP running and suppose that the lead time of the chassis is 5 weeks instead of 3

week 1 2 3 4 5 6 7 8 9 10




Lead time = 5

Order in the past

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Limits of MRP procedures2. Lead times are fixed and pre‐determined (a priori, outside MRP)

• MRP uses lead times as input, while their actual value is an output Lead times are variable “by nature”, due to technology and organization‐

related factors No protection is assured against the “orders in the past” phenomenon

i.e. the orders that fall in periods prior to period 1, i.e. orders that would have had to be issued “in the past” (yesterday, last week / month etc.)

• In the end, lead times estimation is critical: Underestimating lead times leads to stock‐out (of components) and therefore

it puts the entire logic of the production dates” in crisis Overestimating lead times causes the planning horizon expansion, which

implies: A lower data reliability, since in the long term the portfolio will be composed of

forecasts and fewer certain orders An increase of components stock holding costs as they are manufactured longer

before the time they are actually needed

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Limits of MRP procedures2. Lead times are fixed and pre‐determined (a priori, outside MRP)• Lead times can be managed by shortening time buckets

E.g. by using days as buckets instead of weeks

• Shortening time buckets requires (more) accurate forecasts and (more) frequent planning Example:

Finished product

Raw materials

Components

LT = 7 days, i.e. 2 weeks

LT = 8 days, i.e. 2 weeks

Week 1 Week 2

M T W T F

Past FutureWeek "‐1" Week 1 Week 2 Week 3 Week 4M T W T F M T W T F M T W T F M T W T F M T …

Finished productComponentsRaw materials

Planning under weekly time bucketing Planning under daily time bucketing

A requirement scheduled for week 4 (if not “absorbed” by either availability or orders in progress) gives rise to an order “in the past” at the raw materials stage under a weekly bucketing approach, while it gives rise to an order for today under a daily bucketing approach

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Limits of MRP procedures3. Data used by MRP require a huge amount of space

The volume of data is relevant, mainly for the bills of materials (BOMs) Consider “Taurus” tractor, equipped with different devices that

correspond to various configurations of the same “basic” product To fully represent all the available alternatives for this (very

simplified) example the (huge) numberof bills of materials required is:

3 x 2 x 5 x 2 x 2 x 3 x 3 = 1,080

Feature Alternatives Description

Number of wheels 3 4 (2‐motion); 4‐motion; 1 rear & 2 front

Fuel engine 2 Petrol; diesel

Power 5 20, 60, 80, 120, 200 kW

Gears 2 Normal; normal & overdrive

Steering 2 Normal; power‐steering

Rear tow‐hook 3 Normal; strengthened; special

Power takeoff 3 Absent; normal; special

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Limits of MRP procedures3. Data used by MRP require a huge amount of space• To save space you can have to resort to super bills (product configurators)

Through the analysis of commonalities, the bills of materials are arranged in modules (also called modular bills) Each module is a fictitious (artificial) bills that contains all the codes of one single

option

Taurus tractor

Common to all

Wheels Engine Gearbox Steering Tow hook Takeoff

petrol

normal

1

overdrive

2diesel

3

44, 2‐motion

normal

absent

Power

normal

4‐motion

1 rear, 2‐front

20 kWnormal

60 kW

80 kW

120 kW

200 kW

power steering

strength‐ened

special

special

Specific

…

n

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Limits of MRP procedures3. Data used by MRP require a huge amount of space• Strengths of super bills

1. They reduce the required space by 1/100 ore even more E.g. in the example of the Taurus tractor the

number of bills of materials required is: Which is anyway much less than:

3 x 2 x 5 x 2 x 2 x 3 x 3 = 1,080, i.e. the number of BoMs without super bills

2. They remarkably help data maintenance and to keep data consistency

1 + 3 + 2 + 5 + 2 + 2 + 3 + 3 + n = 21 + n

Taurus tractor

Gearbox Steering

normal

overdrive

Power

Taurus tractor

Gearbox

normal

overdrive

special

Taurus tractor

Gearbox

normal

overdrive

You can easily add or remove features without having to resort to multiple data

operations

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Limits of MRP procedures3. Data used by MRP require a huge amount of space• Strengths of super bills

3. They dramatically improve accuracy of the forecasting process The sales forecasts over the medium‐long term, usually calculated only by product

type (e.g. Taurus tractor) are converted into (equally) reliable forecasts at the components / single option (part number) level

This allows a longer Master Production Schedule (MPS) horizon Taurus tractor

Common to all

Wheels Engine

petrol

diesel

4, 2‐motion

Power

4‐motion

1 rear, 2‐front

20 kW

60 kW

80 kW

120 kW

200 kW

1.00 1.00 1.00 1.00

0.2

0.8

0.8

0.1

0.1

0.15

0.05

0.1

0.3

0.4

…The coefficients of use (expressed as %)

represent how “popular” is the addressed product within the sales mix

Through the coefficients of use the forecast for Taurus tractor is

translated (with the same reliability) into corresponding forecasts for each

component

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Executive summary • Materials Requirement Planning (MRP) systems make the ‘explosion’ of the

bills of materials, by calculating (not estimating) which, how many and when components, sub‐assemblies, parts, raw materials etc. are required to ensure that the customers’ orders due dates (deadlines) are respected In the end MRPs coordinate the production dates (rendezvous) of components

to manufacture finished products (or higher level components in the BoM)

• MRP is very useful to protect the inventory system against the bullwhip effect

• However, three major areas are referred to as critical system design features of MRP: MRP basically operates at infinite capacity Lead times are assumed as fixed and pre‐determined MRP requires a high volume of data

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Further (suggested) readings• Masuchun, W., Davis, S., Patterson, J.W. (2004) “Comparison of push and

pull control strategies for supply network management ina make‐to‐stock environment”, International Journal of Production Research, Vol. 42, No. 20, pp. 4401‐4419

• Butman, J. (2002) “A pain in the (supply) chain”, Harvard Business Review, May, pp. 31‐36

• Caridi, M., Cigolini, R. (2002) “Improving materials management effectiveness: a step towards agile enterprise”, International Journal of Physical Distribution and Logistics Management, Vol. 32, No. 7, pp. 556‐576.

• Koh, S.C.L., Saad, S.M., Jones, M.H. (2002) “Uncertainty under MRP‐planned manufacture: review and categorization”, International Journal of Production Research, Vol. 40, No. 10, pp. 2399‐2421

• Barzizza, R., Caridi, M., Cigolini, R. (2001) “Engineering change: a theoretical assessment and a case study”, Production Planning and Control, Vol. 12, No. 7, pp. 717‐726

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Practice 1Company Alpha manufactures product Beta, made up from 2 critical components (B and C), according to the represented relevant data, while the table reports the gross total requirements of Beta

You are required to calculate the gross requirements of B and C coming from Beta

Lead time 2 periodsRe‐order policy Fixed EOQ, 250 piecesInitial inventory 350 piecesReserved stock 100 pieces (1st period)Orders in progress 100 pieces (3rd period)Safety stock 50 pieces

Scrap rate 5 %

Beta

B C

3210% scrap rate 20% scrap rate

Period 1 2 3 4 5 6 7 8

Gross total requirements 90 100 120 150 80 110 90 85

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Practice 1 ‐ short discussion

Period 1 2 3 4 5 6 7 8 Gross total requirements 90 100 120 150 80 110 90 85 Initial availability 200 110 10 Scraps-adjusted requirements 116 158 84 116 95 90 Orders in progress 100 Net requirements 16 158 84 116 95 90 Lot-sized requirements 250 250 250Orders to issue (of Beta) 250 250 250 Gross requirements of B 550 550 550 Gross requirements of C 900 900 900

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Practice 2Consider the represented bill of materials and the relevant data reported in the tables together with the gross total requirements of A

You are required to calculate the plan of orders to issue for all the involved components (i.e. B, C, D, E)

A

B C

D E

Code Coefficient of use

Lead time

(weeks)

Initial inventory (pieces)

Safety stock

(pieces)

Re-order policy

A - 1 3 0 L4L B 2 1 20 10 L4L C 20 2 100 40 EOQ = 50D 2 1 150 0 L4L E 4 2 500 200 EOQ = 200

Week 1 2 3 4 5 6Gross total requirements of A 1 2 2 3 3 1

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Practice 2 ‐short discussion

Period -1 1 2 3 4 5 6 Gross requirements (of A) 1 2 2 3 3 1 Initial availability (of A) 3 2 0 0 0 0 Scraps-adjusted requirements (of A) 0 0 2 3 3 1 Lot-sized requirements (of A) 0 0 2 3 3 1 Orders to issue (of A) 0 2 3 3 1 Gross requirements (of B) 0 4 6 6 2 Gross requirements (of C) 0 40 60 60 20 Initial availability (of B) 10 10 6 0 0 Scraps-adjusted requirements (of B) 0 0 0 6 2 Lot-sized requirements (of B) 0 0 0 6 2 Orders to issue (of B) 0 0 6 2 Gross requirements (of C) 0 40 60 60 20 Initial availability (of C) 60 60 20 0 0 Scraps-adjusted requirements (of C) 0 0 40 60 20 Net requirements (of C) 0 0 40 60 20 Lot-sized requirements (of C) 0 0 50 50 50 Orders to issue (of C) 50 50 50 Gross requirements (of D) 100 100 100 Gross requirements (of E) 200 200 200 Initial availability (of D) 150 50 0 Scraps-adjusted requirements (of D) 0 50 100 Lot-sized requirements (of D) 0 50 100 Orders to issue (of D) 50 100 Gross requirements (of E) 200 200 200 Initial availability (of E) 300 100 0 Scraps-adjusted requirements (of E) 0 100 200 Lot-sized requirements (of E) 0 200 200 Orders to issue (of E) 200 200

Order in the past,

manageable e.g. through safety stock

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3 - MRP Model · 2017. 5. 12. · •MRP procedure operates –in a recurrentway –according to...

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