1. Chapter 8 Aggregate Planning in the Supply Chain
Supply Chain Management
Chapter 8 Aggregate Planning in the Supply Chain

2. Production System
In a broader sense, a production system is anything that takes inputs and transforms them into outputs.
Production system is the collection of people, equipment, and procedures organized to accomplish the operations of a company (or other organization).
Manufacturing
Service

3. Production Planning
Production Planning is the analysis, design and management of production systems.
Objective: Transform a variety of inputs (such as raw material, labor, capital, etc.) into outputs (goods and services) in a manner that is both efficient in using resources and effective in achieving high customer satisfaction.
In today’s competitive business environment it is important to know methods and specific analysis tools for operational decisions to effectively manage these systems.

4. Production Planning Decisions
Long-term (Strategic) Decisions:
Top Management Decisions
3-10 years
Decisions: Capacity, Product, Supplier needs, Quality Policy
Intermediate-term (Tactical) Decisions:
Middle Management Decisions
6 months - 3 years
Decisions: Work-force levels, processes, production rates, inventory levels, contracts with suppliers, quality level, quality costs
Short-term (Operational) Decisions:
Operational Management Decisions
1 week - 6 months
Decisions: Allocation of jobs to machines, overtime, undertime, subcontracting, delivery dates for suppliers, product quality

5. Production Planning and Control General Framework
Aggregate
Planning
Master Production
Scheduling
Detailed M a
terial
Material and
Capac
ity Plans
Purchasing
Demand
Management
Resources
Rough -
cut
Capacity
Detailed C
apacity
Shop Floor
Systems

6. Role of Aggregate Planning in a Supply Chain
process by which a company determines levels of capacity, production, subcontracting, inventory, stockouts, and pricing over a specified time horizon
goal is to maximize profit
decisions made at a product family level
time frame of 3 to 18 months
how can a firm best use the facilities it has?

7. Role of Aggregate Planning in a Supply Chain
Specify operational parameters over the time horizon:
production rate
workforce
overtime
machine capacity level
subcontracting
backlog
inventory on hand
All supply chain stages should work together on an aggregate plan that will optimize supply chain performance

8. The Aggregate Planning Problem
Given the demand forecast for each period in the planning horizon, determine the production level, inventory level, and the capacity level for each period that maximizes the firm’s (supply chain’s) profit over the planning horizon
Specify the planning horizon (typically 3-18 months)
Specify the duration of each period
Specify key information required to develop an aggregate plan

9. Information Needed for an Aggregate Plan
Demand forecast in each period
Production costs
labor costs, regular time ($/hr) and overtime ($/hr)
subcontracting costs ($/hr or $/unit)
cost of changing capacity: hiring or layoff ($/worker) and cost of adding or reducing machine capacity ($/machine)
Labor/machine hours required per unit
Inventory holding cost ($/unit/period)
Stockout or backlog cost ($/unit/period)
Constraints: limits on overtime, layoffs, capital available, stockouts and backlogs

10. Outputs of Aggregate Plan
Production quantity from regular time, overtime, and subcontracted time: used to determine number of workers and supplier purchase levels
Inventory held: used to determine how much warehouse space and working capital is needed
Backlog/stockout quantity: used to determine what customer service levels will be
Machine capacity increase/decrease: used to determine if new production equipment needs to be purchased
A poor aggregate plan can result in lost sales, lost profits, excess inventory, or excess capacity

11. Fundamental Tradeoffs in Aggregate Planning
Capacity (regular time, overtime, subcontract)
Inventory
Backlog / lost sales
Basic Strategies
Chase strategy
Time flexibility from workforce or capacity
Level strategy
Notes:

12. Aggregate Planning Strategies
Trade-off between capacity, inventory, backlog/lost sales
Chase strategy – using capacity as the lever
Time flexibility from workforce or capacity strategy – using utilization as the lever
Level strategy – using inventory as the lever
Mixed strategy – a combination of one or more of the first three strategies

13. Chase Strategy
Production rate is synchronized with demand by varying machine capacity or hiring and laying off workers as the demand rate varies
However, in practice, it is often difficult to vary capacity and workforce on short notice
Expensive if cost of varying capacity is high
Negative effect on workforce morale
Results in low levels of inventory
Should be used when inventory holding costs are high and costs of changing capacity are low

14. Level Strategy
Maintain stable machine capacity and workforce levels with a constant output rate
Shortages and surpluses result in fluctuations in inventory levels over time
Inventories that are built up in anticipation of future demand or backlogs are carried over from high to low demand periods
Better for worker morale
Large inventories and backlogs may accumulate
Should be used when inventory holding and backlog costs are relatively low

15. Time Flexibility Strategy
Can be used if there is excess machine capacity
Workforce is kept stable, but the number of hours worked is varied over time to synchronize production and demand
Can use overtime or a flexible work schedule
Requires flexible workforce, but avoids morale problems of the chase strategy
Low levels of inventory, lower utilization
Should be used when inventory holding costs are high and capacity is relatively inexpensive

16. Comparison of production planning strategies
Item
Chase Demand
Level Capacity
Labor skill required
Low
High
Job discretion
Working conditions
Sweatshop
Pleasant
Training required
Labor turnover
Supervision required

17. Aggregate Planning Problem
Costs in Aggregate Planning:
Material Cost
Inventory Holding Cost
Shortage cost
Regular Time Costs
Overtime and Subcontracting Costs
Hiring and Firing Costs
Idle Time Costs
Backlogging costs
Costs associated with lost sales
Control system cost.

18. Data for the aggregate planning problem
Item
January
February
March
April
May
June
Totals
Demand Forecast
2250
1425
1000
850
1150
1725
8400
Number of Working Days 22 19 21 20
125
Costs:
Materials
100
Inventory holding cost
1.5
Marginal cost of stockout 5
Marginal cost of subcontracting
Hiring and training cost
200
Layoff cost
250
Labor hours required
Straight-line cost (first eight hours each day) 4
Overtime cost (time and a half) 6
Beginning Inventory
400
Production Requirement (Demand Forecast - Beginning Inventory)
1,850
1,425
1,000
1,150
1,725

19. Production Plan 1: Exact Production; Vary Workforce
Item
January
February
March
April
May
June
Total
Production Requirement
1,850
1,425
1,000
850
1,150
1,725
Production Hours Required (Production Requirement x 5 Hr./Unit)
9,250
7,125
5,000
4,250
5,750
8,625
Working Days per Month 22 19 21 20
Hours per Month per Worker (Working Days x 8 Hrs/Day)
176
152
168
160
Workers Required (Production Hours Required/Hours per Month per Worker, must round this number up) 53 47 30 25 33 54
New Workers Hired (Assuming opening workforce equal to first month's requirement of 53 workers.) 8
Hiring Cost (new Workers Hired x $200) $0
$1,600
$4,200
$5,800
Workers Laid Off 6 17 5
Layoff Cost (Workers Laid Off x $250)
$1,500
$4,250
$1,250
$7,000
Straight Time Cost (Production Hours Required x $4)
$37,000
$28,500
$20,000
$17,000
$23,000
$34,500
$160,000
Total Cost
$172,800

21. Production Plan 3: Constant Low Workforce; Subcontract
January
February
March
April
May
June
Total
Production Requirement
1,850
1,425
1,000
850
1,150
1,725
Working Day per Month 22 19 21 20
Production Hours Available (Working Day x 8 Hrs./Day x 25 Workers)*
4,400
3,800
4,200
4,000
Actual Production (Production Hours Available/5 hr.per Unit)
880
760
840
800
Units Subcontracted (Production Requirement - Actual Production)
970
665
160 10
270
925
Subcontracting Cost (Units Subcontracted x $20)
$19,400
$13,300
$3,200
$200
$5,400
$18,500
$60,000
Straight Time Cost (Production Hours Available x $4)
$17,600
$15,200
$16,800
$16,000
$100,000
*Minimum production requirement. In this example, April is minimum of 850 units. Number of workers required for April is (850 x 5)/(21 x 8) = 25
Total Cost
$160,000

22. Production Plan 4: Constant Low Workforce; Overtime
January
February
March
April
May
June
Total
Production Requirement
1,850
1,425
1,000
850
1,150
1,725
Working Day per Month 22 19 21 20
Production Hours Available (Working Day x 8 Hrs./Day x 25 Workers)*
4,400
3,800
4,200
4,000
Regular Production (Production Hours Available/5 hr.per Unit)
880
760
840
800
Units Produced with Overtime (Production Requirement - Actual Production)
970
665
160 10
270
925
Overtime Cost (Overtime Units x5hr/unit x $6)
$29,100
$19,950
$4,800
$300
$8,100
$27,750
$90,000
Straight Time Cost (Production Hours Available x $4)
$17,600
$15,200
$16,800
$16,000
$100,000
*Minimum production requirement. In this example, April is minimum of 850 units. Number of workers required for April is (850 x 5)/(21 x 8) = 25
Total Cost
$190,000

23. Aggregate Planning at Red Tomato Tools
Notes:

24. Aggregate Planning
Notes:

25. Aggregate Planning (Define Decision Variables)
Wt = Workforce size for month t, t = 1, ..., 6
Ht = Number of employees hired at the beginning of month t, t = 1, ..., 6
Lt = Number of employees laid off at the beginning of month t, t = 1, ..., 6
Pt = Production in month t, t = 1, ..., 6
It = Inventory at the end of month t, t = 1, ..., 6
St = Number of units stocked out at the end of month t, t = 1, ..., 6
Ct = Number of units subcontracted for month t, t = 1, ..., 6
Ot = Number of overtime hours worked in month t, t = 1, ..., 6
Notes:

26. Aggregate Planning (Define Objective Function)
Notes:

27. Aggregate Planning (Define Constraints Linking Variables)
Workforce size for each month is based on hiring and layoffs
Notes:

28. Aggregate Planning (Constraints)
Production for each month cannot exceed capacity
Notes:

29. Aggregate Planning (Constraints)
Inventory balance for each month
Notes:

30. Aggregate Planning (Constraints)
Over time for each month
Notes:

31. Scenarios Increase in holding cost (from $2 to $6)
Overtime cost drops to $4.1 per hour
Increased demand fluctuation
Notes:

32. Increased Demand Fluctuation
Notes:

33. Aggregate Planning in Practice
Think beyond the enterprise to the entire supply chain
Make plans flexible because forecasts are always wrong
Rerun the aggregate plan as new information emerges
Use aggregate planning as capacity utilization increases

34. Production Planning and Control General Framework
Aggregate
Planning
Master Production
Scheduling
Detailed M a
terial
Material and
Capac
ity Plans
Purchasing
Demand
Management
Resources
Rough -
cut
Capacity
Detailed C
apacity
Shop Floor
Systems

35. Aggregate Production Plan and Master Production Schedule
Actual production plan should consider individual products, smaller time units, production sequence etc.
Aggregate production plan is disaggregated to form the master production schedule(MPS).

36. Aggregate Production Plan and Master Production Schedule

37. Capacity Planning and Material Requirements Planning
Rough-cut Capacity Planning: To check feasibility of MPS.
Quick check on capacity of key resources
Use Bill of Resource (BOR) for each item in MPS
Infeasibilities addressed by altering MPS or adding capacity (e.g., overtime)
Material Requirements Planning(MRP): Breaking the MPS into a production schedule for each component of an end-item. Determines the material requirements and timings for each phase of production.
Detailed Capacity Planning: To check feasibility of MRP. Supplements the process of checking material shortage.
Uses routing data (work centers and times) for all items
Generates usage profile of all work centers
Identifies overload conditions
More detailed than RCCP

38. Materials Requirements Planning (MRP)
Materials Requirements Planning (MRP) determines time-phased requirements (period-by-period) for all purchased and manufactured parts such as raw materials, components, parts, subassemblies, etc.
Three major inputs are MPS, Inventory Status and Bill of Materials (BOM), also called the Product Structure.
The major output of MRP is planned-order releases: Purchase orders and work orders(production plan).

39. Product Structure Example

40. Product and Part Complexity
Approximate number of components
Mechanical pencil (modern) 10
Ball bearing (modern) 20
Rifle (1800) 50
Sewing machine (1875)
150
Bicycle chain
300
Bicycle (modern)
750
Early automobile (1910)
2000
Automobile (modern)
20000
Commercial airplane (1930)
100000
Commercial airplane (modern)
Space shuttle (modern)

41. Steps in MRP
Explosion: Evaluating the gross requirements of each component
Netting: Adjusting gross requirements to account for on-hand inventory or quantity on order.
Offsetting:Determining the timing of order releases
Lot Sizing: Determining the batch size to be purchased or produced

42. MRP Example Trumpet Total Lead Time= 7 wks Bell Assembly (1)
Valve Casing Assembly (1)
Lead Time=4 wks
Slide Assemblies (3)
Lead Time=2 wks
Valves (3)
Lead Time=3 wks
Total Lead Time= 7 wks

43. Product Structure Example
Valve Casing Assembly:
Valves: (Assume an inventory of 282 at hand at week 3)

44. Lot Sizing
Setup/Ordering Costs: Every time a new production is started, a setup of machines/labor is required and there is an associated cost with it.
Similarly, every time an order is given for a product, there is an ordering cost for transportation, managerial issues etc. Thus, every time we start a new production or give a new order, we want it to be for high quantities.
However, if we order for high quantities, we have to carry high levels of inventory. Thus, there is a tradeoff between inventory costs and setup costs.
Question: What is the optimal time and amount to order?

45. Min ∑(h(t)I(t) + A(t)O(t)) s.t. I(t) = I(t-1)+X(t)-D(t) X(t) ≤ O(t).M
Lot Sizing
Parameters:
h(t):unit inventory holding cost in period t.
A(t): setup/ordering cost in period t.
Decision variables:
X(t): Amount ordered in period t.
O(t) = 1 if an order is given in period t
= 0 otherwise
I(t): Inventory level at the end of period t.
Min ∑(h(t)I(t) + A(t)O(t))
s.t. I(t) = I(t-1)+X(t)-D(t)
X(t) ≤ O(t).M
I(t), X(t)≥0, O(t) = 0 or 1

46. Lot Sizing
Ex: Over the next 5 weeks, the net requirement of our company for a product is 18, 30, 20, 5, 20. The holding cost is $2 per unit per week and the ordering cost is $80. What are the optimal times and amounts to order?
Simple Rules
Lot for Lot (L4L): Order 1 period of future demand
Fixed period demand: Order m periods of future demand
Fixed Order Quantity: Order fixed amounts
Heuristic Methods
Silver-Meal Method: Decision based on average cost per period
Least unit cost: Decision based on average cost per unit
Part-Period Balancing: Decision based on total variable cost per order
Exact Methods:
Wagner-Whitin Algorithm
Integer Programming

47. Lot Sizing Example
Ex: Over the next 5 weeks, the net requirement of our company for a product is 18, 30, 20, 5, 20. The holding cost is $2 per unit per week and the ordering cost is $80. What are the optimal times and amounts to order?
Silver-Meal Heuristic:
C(T)=Average cost per period if the current order is for the next T periods.
Evaluate C(T) for T=1,2… and stop when C(T)>C(T-1).
C(1)=80/1=80
C(2)=(80+2*30)/2=70
C(3)=(80+2*30+2*2*20)/3=73.33 Stop
Order 48 units at week 1.

48. Lot Sizing Example Now go to week 3 and start over. C(1)=80/1=80
C(3)=(80+2*5+2*2*20)/3=56.67 Stop
Order 25 units at week 3.
Go to week 5. Since week 5 is the final week, order
20 units at week 5.
Total Cost=80+2* *5+80=310
Is it optimal? No, because
If we consider ordering 18 at week 1, 55 at week 2 and
20 at week 5. Then,
Total Cost= *20+2*2*5+80=300<310

49. Lot Sizing Example Least Unit Cost Heuristic:
C(T)=Average cost per unit if the current order is for the next T periods.
Evaluate C(T) for T=1,2… and stop when C(T)>C(T-1).
C(1)=80/18=4.4
C(2)=(80+2*30)/48=2.9
C(3)=(80+2*30+2*2*20)/68=3.23 Stop
Order 48 units at week 1.
Now go to week 3 and start over.
C(1)=80/20=4
C(2)=(80+2*5)/25=3.6
C(3)=(80+2*5+2*2*20)/45=3.77 Stop
Order 25 units at week 3.
Go to week 5. Since week 5 is the final week, order 20 units at week 5.
Total Cost=80+2* *5+80=310

50. Lot Sizing Example Part Period Balancing
C(T)=Total inventory cost for the current order if the order is for the next T periods.
Evaluate C(T) for T=1,2… and stop when C(T)>A=80.
C(1)=0
C(2)=2*30<80
C(3)=(2*30+2*2*20)>80 Stop
Order 48 units at week 1.
Now go to week 3 and start over.
C(2)=2*5<80
C(3)=(2*5+2*2*20)>80 Stop
Order 25 units at week 3.
Go to week 5. Since week 5 is the final week, order 20 units at week 5.
Total Cost=80+2* *5+80=310

51. Dynamic Lot Sizing Notation
t a period (e.g., day, week, month); we will consider t = 1, … ,T, where T represents the planning horizon.
Dt demand in period t (in units)
ct unit production cost (in dollars per unit), not counting setup or inventory costs in period t
At fixed or setup cost (in dollars) to place an order in period t
ht holding cost (in dollars) to carry a unit of inventory from period t to period t +1
Qt the unknown size of the order or lot size in period t
decision variables

52. Wagner-Whitin Example
Data
Lot-for-Lot Solution
Since production cost c is constant, it can be ignored.

53. Wagner-Whitin Example (cont.)
Data
Fixed Order Quantity Solution

54. Wagner-Whitin Property
A key observation
If we produce items in t (incur a setup cost) for use to satisfy demand in t+1, then it cannot possibly be economical to produce in t+1 (incur another setup cost) .
Either it is cheaper to produce all of period t+1’s demand in period t, or all of it in t+1; it is never cheaper to produce some in each.
Under an optimal lot-sizing policy
either the inventory carried to period t+1 from a previous period will be zero (there is a production in t+1)
or the production quantity in period t+1 will be zero (there is no production in t+1)
Does fixed order quantity solution violate this property? Why?

55. Basic Idea of Wagner-Whitin Algorithm
By WW Property, either Qt=0 or Qt=D1+…+Dk for some k.
If jk* = last period of production in a k period problem,
then we will produce exactly Dk+…DT in period jk*. Why?
We can then consider periods 1, … , jk*-1 as if they are an independent jk*-1 period problem.

56. Wagner-Whitin Example
Step 1: Obviously, just satisfy D1 (note we are neglecting production cost, since it is fixed).
Step 2: Two choices, either j2* = 1 or j2* = 2.

57. Wagner-Whitin Example (cont.)
Step3: Three choices, j3* = 1, 2, 3.

58. Wagner-Whitin Example (cont.)
Step 4: Four choices, j4* = 1, 2, 3, 4.

59. Planning Horizon Property
In the Example:
Given fact: we produce in period 4 for period 4 of a 4 period problem.
Question: will we produce in period 3 for period 5 in a 5 period problem?
Answer: We would never produce in period 3 for period 5 in a 5 period problem.
If jt*=t, then the last period in which production occurs in an optimal t+1 period policy must be in the set t, t+1,…t+1. (this means that it CANNOT be t-1, t-2……)

60. Wagner-Whitin Example (cont.)
Step 5: Only two choices, j5* = 4, 5.
Step 6: Three choices, j6* = 4, 5, 6.
And so on.

61. Wagner-Whitin Example Solution
Produce in period 1 for 1, 2, 3 ( = 80 units)
Produce in period 4 for 4, 5, 6, 7 ( = 130 units)
Produce in period 8 for 8, 9, 10 ( = 90 units

62. Wagner-Whitin Example Solution (cont.)
Optimal Policy:
Produce in period 8 for 8, 9, 10 ( = 90 units)
Produce in period 4 for 4, 5, 6, 7 ( = 130 units)
Produce in period 1 for 1, 2, 3 ( = 80 units)