1 forecasting: first, a firm must forecast demand for aggregate sales over the planning horizon....

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• Forecasting: First, a firm must forecast demand for aggregate sales over the planning horizon.

• Aggregate planning: The forecasts provide inputs for determining aggregate production and workforce levels over the planning horizon.

• Master production schedule (MPS): Recall, that the aggregate production plan does not consider any “real” product but a “fictitious” aggregate product. The MPS translates the aggregate plan output in terms of specific production goals by product and time period.

Hierarchy of Production Decisions

2


Aggregate Planning

Master Production Schedule

Inventory Control

Operations Scheduling

Vehicle Routing

Forecast of Demand

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Suppose that a firm produces three types of chairs:

1.ladder-back chair,

2.kitchen chair

3. desk chair.

The aggregate production considers a fictitious aggregate unit of chair and finds that the firm should produce 550 units of chairs in April. The MPS then translates this output in terms of three product types and four work-weeks in April.



• The MPS suggests that the firm produce 200 units of desk chairs in Week 1, 150 units of ladder-back chair in Week 2, and 200 units of kitchen chairs in Week 3.

• Material Requirements Planning (MRP): A product is manufactured from some components or subassemblies. For example a chair may require two back legs, two front legs, 4 leg supports, etc.

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5

Hierarchy of Production DecisionsMaster Production Schedule

Ladder-back chair

Kitchen chair

Desk chair

1 2

April May

790790

3 4 5 6 7 8

200200

150150

120120

200200

150150

200200

120120

Aggregate production plan for chair family

550550

200200

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While forecasting, aggregate plan and MPS consider the volume of finished products, MRP plans for the components, and subassemblies. A firm may obtain the components by in-house production or purchasing. MRP prepares a plan of in-house production or purchasing requirements of components and subassemblies.

• Scheduling: Scheduling allocates resources over time in order to produce the products. The resources include workers, machines and tools.

• Vehicle Routing: After the products are produced, the firm may deliver the products to some other manufacturers, or warehouses. The vehicle routing allocates vehicles and prepares a route for each vehicle.


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Hierarchy of Production Decisions Materials Requirement Planning

Back slats

Leg supports

Seat cushion

Seat-frameboards

Frontlegs

Backlegs

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Material Requirements Planning

• The demands for the finished goods are obtained from forecasting. These demands are called independent demand.

• The demands for the components or subassemblies depend on those for the finished goods. These demands are called dependent demand.

• Material Requirements Planning (MRP) is used for dependent demand and for both assembly and manufacturing

• If the finished product is composed of many components, MRP can be used to optimize the inventory costs.

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• Next two slides explain the importance of an MRP system. The first one shows inventory levels when an MRP system is not used. The next one shows the same when an MRP system is used.

• The chart at the top shows inventory levels of the finished goods and the chart on the bottom shows the same of the components.

• If the production is stopped (like it is at the beginning of the chart), the finished goods inventory level decreases because of sales. However, the component inventory level remains unchanged. When the production resumes, the finished goods inventory level increases, but the component inventory level decreases.

Importance of an MRP System

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Inventory without an MRP System


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Inventory with an

MRP System


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• Without an MRP system:– Component is ordered at time A, when the inventory

level of the component hits reorder point, R– So, the component is received at time B. – However, the component is actually needed at time

C, not B. So, the inventory holding cost incurred between time B and C is a wastage.

• With an MRP system:– We shall see in this lesson that given the production

schedule of the finished goods and some other information (see the next slide), it is possible to predict the exact time, C when the component will be required. Order is placed carefully so that it is received at time C.


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• MRP Inputs:– Master Production Schedule (MPS): The MPS of

the finished product provides information on the net requirement of the finished product over time.

– Bill of Materials: For each component, the bill of materials provides information on the number of units required, source of the component (purchase/ manufacture), etc. There are two forms of the bill of materials:

• Product Structure Tree: The finished product is shown at the top, at level 0. The components assembled to produce the finished product is shown at level 1 or below. The sub-components used to produce the components at level 1 is

MRP Input and Output

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MRPcomputerprogram

MRPcomputerprogram

Bill ofMaterials

file

Bill ofMaterials

file

Inventoryfile

Inventoryfile

Master Production

Schedule

Master Production

Schedule

ReportsReportsTo Production To Purchasing

ForecastsOrders


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shown at level 2 or below, and so on.

The number in the parentheses shows the requirement of the item. For example, “G(4)” implies that 4 units of G is required to produce 1 unit of B.

The levels are important. The net requirements of the components are computed from the low levels to high. First, the net requirements of the components at level 1 is computed, then level 2, and so on.


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• Bill of Materials: For each item, the name, number, source, and lead time of every component required is shown on the bill of materials in a tabular form.

– Inventory file: For each item, the number of units on hand is obtained from the inventory file.

• MRP Output:– Every required item is either produced or purchased.

So, the report is sent to production or purchasing.


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Bill of Materials: Product Structure Tree

Level 1

Level 0

Level 2

Level 3

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BILL OF MATERIALS Product Description: Ladder-back chair Item: A

ComponentItem Description

QuantityRequired

Source

B Ladder-back 1 ManufacturingC Front legs 2 PurchaseD Leg supports 4 PurchaseE Seat 1 Manufacturing

Bill of Materials

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BILL OF MATERIALS Product Description: Seat Item: E

ComponentItem Description

QuantityRequired

Source

H Seat frame 1 ManufacturingI Seat cushion 1 Purchase

Bill of Materials

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Component Units in Lead Inventory time (weeks)

Seat Subassembly 25 2

Seat frame 50 3

Seat frame boards 75 1

On Hand Inventory and Lead time

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• Suppose that 150 units of ladder-back chair is required.

• The net requirement is computed from top to bottom. Since 150 units of ladder-back chair is required, and since 1 unit of seat subassembly is required for each unit of ladder-back chair, the gross requirement of seat-subassembly is 150*1 =150 units. Since there are 25 units of seat-subassembly in the inventory, the net requirement of the seat-subassembly is 150-25 = 125 units.

• Since 1 unit of seat frames is required for each unit of seat subassembly, the gross requirement of the seat frames is 125*1 = 125 units. Since there are 50 units of seat frames in the inventory, the net requirement of the seat frames is 125-50 = 75 units.

MRP Calculation

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• Scheduled Receipts: – Items ordered prior to the current planning period

and/or– Items returned from the customer

• Lot-for-lot (L4L)– Order quantity equals the net requirement – Sometimes, lot-for-lot policy cannot be used. There

may be restrictions on minimum order quantity or order quantity may be required to multiples of 50, 100 etc.

MRP Calculation: Some Definitions

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Level 0

Level 1

Level 2

Example 1:MRP Calculation

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Items A, C, D, and E have on-hand inventories of 20, 10, 20, and 10 units, respectively.

Item B has a scheduled receipt of 10 units in period 1, and C has a scheduled receipt of 50 units in Period 1.

Lot-for-lot (L4L) is used for Items A and B. Item C requires a minimum lot size of 50 units. D and E are required to be purchased in multiples of 100 and 50, respectively.

Lead times are 1 period for Items A, B, and C, and 2 periods for Items D and E. The gross requirements for A are 30 in Period 2, 30 in Period 5, and 40 in Period 8. Find the planned order releases for all items.

Example 1:MRP Calculation

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MRP Calculation

Period 1 2 3 4 5 6 7 8 9 10GrossRequirementsScheduledreceiptsOn hand fromprior periodNetrequirementsTime-phased NetRequirementsPlanned orderreleases

Item

A

LT=

Q=

Planned orderdelivery

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MRP Calculation

1WK

L4L


Item

A

LT=

Q=


30 30 40

20

All the information above are given.

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MRP Calculation

1WK

L4L


Item

A

LT=

Q=


30 30 40

--

20 20

20 units are just transferred from Period 1 to 2.

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MRP Calculation

1WK

L4L


Item

A

LT=

Q=


30 30 40

--

20 20

10

10

10

10

The net requirement of 30-20=10 units must be ordered in week 1.

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MRP Calculation

1WK

L4L


Item

A

LT=

Q=


30 30 40

--

20 20 0 0 0

10

10

10

10

On hand in week 3 is (20+10)-30=0 unit.

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MRP Calculation

1WK

L4L


Item

A

LT=

Q=


30 30 40

--

20 20 0 0 0

10 30

3010

10 30

10 30


31


Item

A

LT=

Q=


MRP Calculation

30 30 40

1WK

L4L

--

20 20 0 0 0 0 0 0

10 30 40

30 4010

10 30 40

10 30 40


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Item

A

LT=

Q=


MRP Calculation

30 30 40

1WK

L4L

--

20 20 0 0 0 0 0 0 0 0

10 30 40

30 4010

10 30 40

10 30 40


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MRP Calculation


Item

B

LT=

Q=


Exercise

34

MRP Calculation


Item

C

LT=

Q=


Exercise

35

MRP Calculation


Item

D

LT=

Q=


Exercise

36

MRP Calculation


Item

E

LT=

Q=


Exercise

37

• Lot Sizing Methods– Lot-for-Lot (L4L)– EOQ– Silver-Meal Heuristic– Least Unit Cost (LUC)– Part Period Balancing

LOT SIZING

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Lot-for-Lot

– Order production or purchasing as much as it is needed.

– Exception are only the cases in which there are constraints on the order quantity.

– For example, it may be required to order at least 50 units or multiples of 50.

• The motivation behind using lot for lot policy is minimizing inventory.

• If we order as much as it is needed, there will be no ending inventory at all!

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Lot-for-Lot

• However, lot for lot policy requires that an order be placed each period. So, the number of orders and ordering cost are maximum.

• So, if the ordering cost is significant, one may naturally try to combine some lots into one in order to reduce the ordering cost. But then, inventory holding cost increases.

• Therefore, a question is what is the optimal size of the lot? How many periods will be covered by the first order, the second order, and so on until all the periods in the planning horizon are covered.

• This is the concern of lot sizing methods.

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Lot-Sizing Problem

• The lot sizing problem is as follows: • Given net requirements of an item over the

next T periods, T >0, find order quantities that minimize the total holding and ordering costs over T periods.

• Note that this is a case of deterministic demand and the inventory holding cost is only charged on ending inventory of each period.

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Lot-Sizing

• Some heuristic methods:– Lot-for-Lot (L4L):

• Order as much as it is needed. • L4Lminimizes inventory holding cost, but maximizes

ordering cost.– EOQ:

• Every time it is required to place an order, lot size equals EOQ.

• EOQ method may choose an order size that covers partial demand of a period. For example, suppose that EOQ is 15 units. If the demand is 12 units in period 1 and 10 units in period 2, then a lot size of 15 units covers all of period 1 and only (15-12)=3 units of period 2. So, one does not save the ordering cost of period 2, but carries some 3 units in

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Lot-Sizing

• Some heuristic methods:

the inventory when that 3 units are required in period 2. This is not a good idea because if an order size of 12 units is chosen, one saves on the holding cost without increasing the ordering cost!

• So, what’s the mistake? Generally, if the order quantity covers a period partially, one can save on the holding cost without increasing the ordering cost. The next three methods, Silver-Meal heuristic, least unit cost and part period balancing avoid order quantities that cover a period partially. These methods always choose an order quantity that covers some K periods, K >0.

• Be careful when you compute EOQ. Express both holding cost and demand over the same period. If the holding cost is annual, use annual demand. If the holding cost is weekly, use weekly demand.

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Lot-Sizing

• Some heuristic methods:– Silver-Meal Heuristic

• As it is discussed in the previous slide, Silver-Meal heuristic chooses a lot size that equals the demand of some K periods in future, where K>0.

• If K =1, the lot size equals the demand of the next period. • If K =2, the lot size equals the demand of the next 2 periods.• If K =3, the lot size equals the demand of the next 3 periods,

and so on.• The average holding and ordering cost per period is computed

for each K=1, 2, 3, etc. starting from K=1 and increasing K by 1 until the average cost per period starts increasing. The best K is the last one up to which the average cost per period decreases.

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Lot-Sizing

• Some heuristic methods:– Least Unit Cost (LUC)

• As it is discussed before, least unit cost heuristic chooses a lot size that equals the demand of some K periods in future, where K>0.

• The average holding and ordering cost per unit is computed for each K=1, 2, 3, etc. starting from K=1 and increasing K by 1 until the average cost per unit starts increasing. The best K is the last one up to which the average cost per unit decreases.

• Observe how similar is Silver-Meal heuristic and least unit cost heuristic. The only difference is that Silver-Meal heuristic chooses K on the basis of average cost per period and least unit cost on average cost per unit.

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Lot-Sizing

• Some heuristic methods:– Part Period Balancing

• As it is discussed before, part period balancing heuristic chooses a lot size that equals the demand of some K periods in future, where K>0.

• Holding and ordering costs are computed for each K=1, 2, 3, etc. starting from K=1 and increasing K by 1 until the holding cost exceeds the ordering cost. The best K is the one that minimizes the (absolute) difference between the holding and ordering costs.

• Note the similarity of this method with the Silver-Meal heuristic and least unit cost heuristic. Part period balancing heuristic chooses K on the basis of the (absolute) difference between the holding and ordering costs.

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• Some important notes– Inventory costs are computed on the ending inventory.– L4L minimizes carrying cost– Silver-Meal Heuristic, LUC and Part Period Balancing

are similar– Silver-Meal Heuristic and LUC perform best if the costs

change over time– Part Period Balancing perform best if the costs do not

change over time– The problem extended to all items is difficult to solve

Lot-Sizing

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Example 2: The MRP gross requirements for Item A are shown here for the next 10 weeks. Lead time for A is three weeks and setup cost is $10. There is a carrying cost of $0.01 per unit per week. Beginning inventory is 90 units.

Week Gross requirements Week Gross requirements

1 30 6 80

2 50 7 20

3 10 8 60

4 20 9 200

5 70 10 50

Determine the lot sizes.

Lot-Sizing

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Period 1 2 3 4 5 6 7 8 9 10GrossRequirements

30 50 10 20 70 80 20 60 200 50

BeginningInventory

90 60 10 0

NetRequirements

0 0 0 20

Time-phased NetRequirementsPlanned orderReleasePlannedDeliveriesEndingInventory

60 10 0

Lot-Sizing: Lot-for-Lot

Use the above table to compute ending inventory of various periods.

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30 50 10 20 70 80 20 60 200 50

BeginningInventory

90 60 10 0

NetRequirements

0 0 0 20


60 10 0


20

Week 4 net requirement = 20 > 0. So, an order is required.

50


30 50 10 20 70 80 20 60 200 50

BeginningInventory

90 60 10 0

NetRequirements

0 0 0 20


60 10 0


20

20

20

A delivery of 20 units is planned for the 4th period..

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30 50 10 20 70 80 20 60 200 50

BeginningInventory

90 60 10 0

NetRequirements

0 0 0 20


60 10 0


0

70

20

20

0

20

The net requirement of the 5th period is 70 periods.

Exercise

52

Lot-Sizing: EOQ

• First, compute EOQ– Annual demand is not given. Annual demand is

estimated from the known demand of 10 weeks.

– Compute annual holding cost per unit

units/year

502006020807020105030

r weeks/yea weeks10 over demand Total

demand, annual Estimated

068,3

5210

590

5210

5210

/year$0.52/unit/unit/week 01.0$h

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Lot-Sizing: EOQ

• First, compute EOQ

• Therefore, whenever it will be necessary to place an order, the order size will be 344 units. This will now be shown in more detail.

units EOQ

/unit/year$

/order

units/year

34451.34352.0

068,31022

52.0

10$

068,3

h

K

h

K

54


30 50 10 20 70 80 20 60 200 50

BeginningInventory

90 60 10 0

NetRequirements

0 0 0 20


60 10 0

Lot-Sizing: EOQ


55


30 50 10 20 70 80 20 60 200 50

BeginningInventory

90 60 10 0

NetRequirements

0 0 0 20


60 10 0

Lot-Sizing: EOQ

20


56


30 50 10 20 70 80 20 60 200 50

BeginningInventory

90 60 10 0

NetRequirements

0 0 0 20


60 10 0

Lot-Sizing: EOQ

20

344

344

Order size = EOQ = 344, whenever it is required to place an order.

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30 50 10 20 70 80 20 60 200 50

BeginningInventory

90 60 10 0

NetRequirements

0 0 0 20


60 10 0

Lot-Sizing: EOQ

20

344

324

344

324

Week 5 b. inv=344-20=324>70= gross req. So, no order is required.

Exercise

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j 1 2 3 4 5 6 7r j 20 70 80 20 60 200 50 Per

H. Ord. PeriodOrder for weeks Q 4 5 6 7 8 9 10 Cost Cost Cost1 week, week 4

2 weeks, weeks 4 to 53 weeks, weeks 4 to 64 weeks, weeks 4 to 75 weeks, weeks 4 to 86 weeks, weeks 4 to 9

7 weeks, weeks 4 to 10

Units in the inventory at the end of Week

Lot-Sizing: Silver-Meal-Heuristic

The order is placed for K periods, for some K>0. Use the above table to find K.

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j 1 2 3 4 5 6 7r j 20 70 80 20 60 200 50 Per






20 0.00 10 10.0

If K=1, order is placed for 1 week and the order size = 20. Then, the ending inventory = inventory holding cost =0. The order cost = $10. Average cost per period = (0+10)/1=$10.

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j 1 2 3 4 5 6 7r j 20 70 80 20 60 200 50 Per






20 0.01 10 10.090 70 0.70 10 5.35

If K=2, order is placed for 2 weeks and the order size = 20+70=90.Then, inventory at the end of week 4 = 90-20=70 and holding cost =70 0.01. = 0.70. Average cost per period = (0.70+10)/2=$5.35.

Exercise

61


30 50 10 20 70 80 20 60 200 50

BeginningInventory

90 60 10 0

NetRequirements

0 0 0 20


60 10 0



62


30 50 10 20 70 80 20 60 200 50

BeginningInventory

90 60 10 0

NetRequirements

0 0 0 20


60 10 0


20


Exercise

63

j 1 2 3 4 5 6 7r j 20 70 80 20 60 200 50

H. Ord. UnitOrder for weeks Q 4 5 6 7 8 9 10 Cost Cost Cost1 week, week 4




Lot-Sizing: Least Unit Cost


64

j 1 2 3 4 5 6 7r j 20 70 80 20 60 200 50






20 0.01 10 .500

If K=1, order is placed for 1 week and the order size = 20. Then, the ending inventory = inventory holding cost =0. The order cost = $10. Average cost per unit = (0+10)/20=$0.50

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j 1 2 3 4 5 6 7r j 20 70 80 20 60 200 50






20 0.01 10 .50090 70 0.70 10 .119

If K=2, order is placed for 2 weeks and the order size = 20+70=90.Then, inventory at the end of week 4 = 90-20=70 and holding cost =70 0.01. = 0.70. Average cost per unit = (0.70+10)/90=$0.119.

Exercise

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30 50 10 20 70 80 20 60 200 50

BeginningInventory

90 60 10 0

NetRequirements

0 0 0 20


60 10 0


67



30 50 10 20 70 80 20 60 200 50

BeginningInventory

90 60 10 0

NetRequirements

0 0 0 20


60 10 0

20


Exercise

68

Lot-Sizing: Part Period Balancing

j 1 2 3 4 5 6 7r j 20 70 80 20 60 200 50

H. Ord. DiffOrder for weeks Q 4 5 6 7 8 9 10 Cost Cost1 week, week 4





69


j 1 2 3 4 5 6 7r j 20 70 80 20 60 200 50

H. Ord. DiffOrder for weeks Q 4 5 6 7 8 9 10 Cost Cost1 week, week 4




20 0.00 10 10.090 70 0.70 10 9.30

170 150 80 2.30 10 7.70190 170 100 20 2.90 10 7.10250 230 160 80 60 5.30 10 4.70450 430 360 280 260 200 15.30 10 5.30

NOT COMPUTED1 week, week 92 weeks, weeks 9 to 10

200 0.00 10 10.0250 50 0.50 10 9.50

The above computation is similar to that of the Silver-Meal heuristic. The primary difference is that the (absolute) difference between holding and ordering cost is shown in the last column.

70



30 50 10 20 70 80 20 60 200 50

BeginningInventory

90 60 10 0

NetRequirements

0 0 0 20


60 10 0


71



30 50 10 20 70 80 20 60 200 50

BeginningInventory

90 60 10 0

NetRequirements

0 0 0 20


60 10 0

200

20 200

250 250

230 160 80 60 0 50 0

250 250

230 160 80 60 0 50

The computation is similar to that of the Silver-Meal heuristic.

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• Lot-for-Lot– See the last slide entitled “lot-sizing: lot-for-lot”– Number of orders: 7– Ordering cost = 7 $10/order = $70– Holding cost = (60+10) $0.01/unit/week = $0.70– Total cost = 70+0.70 =$70.70

• EOQ– See the last slide entitled “lot-sizing: EOQ”– Number of orders: 2– Ordering cost = 2 $10/order = $20– Holding cost = (60 +10 +324 +254 +174 +154 +94

+237 +187) $0.01/unit/week = $14.94– Total cost = 20+14.94 =$34.94

Cost Comparison

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• Silver-Meal Heuristic– See the last slide entitled “lot-sizing: Silver-Meal

heuristic”– Number of orders: 2– Ordering cost = 2 $10/order = $20– Holding cost = (60 +10 +230 +160 +80 +60 +50)

$0.01/unit/week = $6.50– Total cost = 20+6.50 =$26.50

• Least Unit Cost– See the last slide entitled “lot-sizing: least unit cost”– Number of orders: 2– Ordering cost = 2 $10/order = $20– Holding cost = (60 +10 +430 +360 +280 +260 +200)


Cost Comparison

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• Part-Period Balancing– See the last slide entitled “lot-sizing: part-period

balancing”– Number of orders: 2– Ordering cost = 2 $10/order = $20– Holding cost = (60 +10 +230 +160 +80 +60 +50)


• Conclusion: In this particular case, Silver-Meal heuristic and part period balancing yield the least total holding and ordering cost of $26.50 over the planning period of 10 weeks.

Cost Comparison

1 forecasting: first, a firm must forecast demand for aggregate sales over the planning horizon....

Documents

plan of inhouse production

aggregate planning

master production schedule

fictitious aggregate

requirements of components

mrp system

aggregate plan output

chair family550200