3 - mrp model · 2017. 5. 12. · •mrp procedure operates –in a recurrentway –according to...
TRANSCRIPT
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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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Inventory systems for dependent demand
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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Inventory systems for dependent demand
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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Inventory systems for dependent demand
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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Inventory systems for dependent demand
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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Inventory systems for dependent demand
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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Inventory systems for dependent demand
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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Inventory systems for dependent demand
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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Inventory systems for dependent demand
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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Inventory systems for dependent demand
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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Inventory systems for dependent demand
Example of MRP running (3/10)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
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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Inventory systems for dependent demand
Example of MRP running (4/10)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
Gross total requirements (chassis) 60 40 30 20 50 80 70 30 30 70
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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Inventory systems for dependent demand
Example of MRP running (5/10)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
Gross total requirements (chassis) 60 40 30 20 50 80 70 30 30 70
Initial availability (chassis) 120 60 20
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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Inventory systems for dependent demand
Example of MRP running (6/10)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
Gross total requirements (chassis) 60 40 30 20 50 80 70 30 30 70
Initial availability (chassis) 120 60 20
Requirements (chassis) 10 20 50 80 70 30 30 70
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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Inventory systems for dependent demand
Example of MRP running (7/10)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
Gross total requirements (chassis) 60 40 30 20 50 80 70 30 30 70
Initial availability (chassis) 120 60 20
Requirements (chassis) 10 20 50 80 70 30 30 70
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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Inventory systems for dependent demand
Example of MRP running (8/10)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
Gross total requirements (chassis) 60 40 30 20 50 80 70 30 30 70
Initial availability (chassis) 120 60 20
Requirements (chassis) 10 20 50 80 70 30 30 70
Scraps‐adjusted requirements (chassis) 11 22 55 88 77 33 33 77
Orders in progress (chassis) 48
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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Inventory systems for dependent demand
Example of MRP running (9/10)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
Gross total requirements (chassis) 60 40 30 20 50 80 70 30 30 70
Initial availability (chassis) 120 60 20
Requirements (chassis) 10 20 50 80 70 30 30 70
Scraps‐adjusted requirements (chassis) 11 22 55 88 77 33 33 77
Orders in progress (chassis) 48
Net requirements (chassis) 40 88 77 33 33 77
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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Inventory systems for dependent demand
Example of MRP running (10/10)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
Gross total requirements (chassis) 60 40 30 20 50 80 70 30 30 70
Initial availability (chassis) 120 60 20
Requirements (chassis) 10 20 50 80 70 30 30 70
Scraps‐adjusted requirements (chassis) 11 22 55 88 77 33 33 77
Orders in progress (chassis) 48
Net requirements (chassis) 40 88 77 33 33 77
Lot‐sized requirements (chassis) 150 150 150
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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Inventory systems for dependent demand
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
Orders to issue (chassis) 150 150 150
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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Inventory systems for dependent demand
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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Inventory systems for dependent demand
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
Inventory systems for dependent demand
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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Inventory systems for dependent demand
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
Net requirements (chassis) 40 88 77 33 33 77
Lot‐sized requirements (chassis) 150 150 150
Orders to issue (chassis) 150 150 150
Lead time = 5
Order in the past
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Inventory systems for dependent demand
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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Inventory systems for dependent demand
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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Inventory systems for dependent demand
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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Inventory systems for dependent demand
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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Inventory systems for dependent demand
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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Inventory systems for dependent demand
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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Inventory systems for dependent demand
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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Inventory systems for dependent demand
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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Inventory systems for dependent demand
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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Inventory systems for dependent demand
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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Inventory systems for dependent demand
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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Inventory systems for dependent demand
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