1. Aggregate Planning FAISAL FARIS BIN RAHIM
MOHD HANEESYAH BIN CHE HASSAN
NOR SYAKIRA BT ZAUKIFLI
ANISAH BT ABD LATIFF

2. Outline Costs in aggregate planning
Solving in aggregate planning problem
Linear decision rule (LDR)
Modeling management behavior

3. Costs in Aggregate Planning
Smoothing Costs
Holding Costs
Shortage Costs
Regular Costs
Overtime & Subcontracting Costs
Idle Time Costs

4. Issues in Aggregate Planning
Smoothing – refer to the cost of changing production and workforce level between periods. (Firing & Hiring Costs)
Bottleneck Problem – Inability to respond to sudden changes in demand as a result of capacity restrictions (High demand in one period & breakdown of a vital piece of equipment)

5. Issues in Aggregate Planning
Planning Horizon- Number of periods for which the demand forecast and aggregate planning are done.
If it is too small ( current aggregate plan may lead into not meeting the demand beyond planning horizon)
If it is too large ( forecasts into far future will be less accurate)
End-of-horizon effect

6. Cost in Aggregate Planning
Smoothing Cost
Hiring costs (advertising, interviewing & training)
Firing costs ( lack of labor force in future)
Assumed to be a linear function of the number of workers

7. Cost in Aggregate Planning
Cost of Changing the Size of the Workforce
Firing costs Hiring costs

8. Cost in Aggregate Planning
Holding Costs
Occurs as a result of having capital tied up in inventory.
Assumed to be linear in the level of inventory
For aggregate planning, it is expressed in terms of dollars per unit held per planning period; (e.g. 100 $/month for one item)

9. (e.g. 100 $/month for one item)

10. Cost in Aggregate Planning
Shortage Costs
Shortage occurs when demands are higher than anticipated
For aggregate planning, it is assumed that excess demand is backlogged and filled in a future period.
In a highly competitive situation, the excess demand may be lost---lost sales.

11. Cost in Aggregate Planning
Regular Time Costs
Involve the cost of producing one unit of output during regular working hours
Overtime or Subcontracting Costs
Costs of production units not produced on regular time.
Overtime-production by regular-time employees beyond work day;
Subtracting-the production of items by an outside supplier;

12. Cost in Aggregate Planning
Idle Time Costs
Under utilization of workforce

13. SOLVING AGGREGATE PLANNING PROBLEMS

14. BASIC RELATIONSHIPS Workforce
Number of workers in a period = Number of workers at end of previous period + Number of new workers at the start of the period- Number of laid off workers at start of the period
Inventory
Inventory at the end of a period = Inventory at end of the previous period + production in current period – Amount used to satisfy demand in current period
Cost
Cost for a period = Output Cost( Reg + OT+ Sub) +Hire/Lay off Cost +Inventory Cost +Back-order Cost

15. PROBLEM 1
A firm producing one product is scheduling (allocating) its January-March production capabilities. Part of the decision involves scheduling overtime work.
A unit produced on overtime costs an extra $300. Similarly, a unit made one month before it is needed incurred an inventory carrying cost of $100; two months costs $200 per unit.
The units delivered according to this schedule follows:
January - 80 units.
February units.
March units.
Production capacities are:
Formulate the production scheduling problem as a transportation problem and solve it by the Northwest Corner Rule.
Regular Time
Overtime
January
100 50
February 40
March 30

16. SOLUTION: Demand for Supply from January February March
Unused capacity (dummy)
Total capacity available (Supply)
Regular 80 20
100
Overtime 50 40 60 30
Demand
120
150 70
420

17. PROBLEM 2 Period Demand forecast Planned production
The production planner of Omega Research, a maker of industrial lenses, devised the following level output aggregate plan for the next 4 periods. Calculate the projected beginning and ending inventory for each period. Possible backorders may be shown by a negative number.
Period
Demand forecast
Planned production
Beginning inventory
Ending inventory 1
40,000
48,000
9,000 2
70,000 3
30,000 4
55,000

18. SOLUTION: Period Demand forecast Planned production
Beginning inventory
Ending inventory 1
40,000
48,000
9,000
17,000 2
70,000
-5,000 3
30,000
13,000 4
55,000
6,000
Note that ending inventory = beginning inventory + planned production - demand forecast

19. Develop a chase demand strategy that gradually increases the inventory level to 14,000 units by the end of period 4. Show the effect of the plan on inventory level for each period.
Inventory is increased by 1250 units in each period: (14, ,000)/4
Period
Demand forecast
Planned production
Beginning inventory
Ending inventory 1
40,000
41,250
9,000
10,250 2
70,000
71,250
11,500 3
30,000
31,250
12,750 4
55,000
56,250
14,000

20. Assume that the company currently has 10 employees and each employee, on average, can produce 4,000 units per period. Develop a staffing plan showing the number of employees that should be hired or laid off at the beginning period, using the following worksheet format.
Period
Required work force
Required number of employees
Available at the end of previous period
Hire
Layoff 1 2 3 4

21. SOLUTION: Period Required work force Required number of employees
Available at the end of previous period
Hire
Layoff 1
41,250/4,000= 10.3 10 2
71.250/4,000= 17.8 18 8 3
31,250/4,000= 7.8 4
56,250/4,000= 14.1 14 6

22. Linear Decision Rule (LDR)

23. FORMULA= Total Cost Over the T-Period Planning Horizon

24. FORMULA= Optimal Production Level in Period t
The terms of a,b,c and d are constant that depend on the cost parameters

25. EXAMPLE:

26. a) Compute the values of the aggregate production level and the number of workers that the company should be using in the current period:
Solution:
Pt= 0.463(150) (164) (185) (193) (180)– 0.464(45)+ 153
Ans:………………..
W t = 0.010D t D t D t D t W t-1 – 0.01I t-1 – 2.09
Ans:………………….

27. The result is optimal production in period t will be form.
THE ADVANTAGES
The result is optimal production in period t will be form.

28. convincing argument to justify such cost curves.
THE DRAWBACKS
The main weakness of the method is that it requires symmetric cost functions and there is no
convincing argument to justify such cost curves.
The quadratic lead to LDR there is no guarantee that the solution will be non-negative.

29. Modeling Management Behavior
Created by Bowman (1963)
Construct model for controlling production level
Avoids problem arise when using traditional modeling method
Exp : Avoids determine values of parameter that difficult to measure
Exp : determining the accuracy of assumption that required by model.

30. Pt = Dt + α(Pt-1 – Dt) + β(IN – It-1)
Pt = Dt for 1 ≤ t ≥ T 1
Pt = Dt + α(Pt-1 – Dt)
Not given : β, IN , α and a 2
Not given : a
Pt = Dt + α(Pt-1 – Dt) + β(IN – It-1) 3
D = forecast demand P = production level
α = smoothing factor / exponential smoothing
IN = Smoothing for inventory level β = Relative weight
a = for determination of P

31. Example
Using the following values of management coefficient for Bowman smoothed production model, determine the production level should plan in the coming year with demand of 100,000 packages. Assume current production level is 150,000 packages
Given :
Pt-1 = 150,000 a1 = a2 =
a3 = a4 = a5 =
α = 0.6 β = 0.3 IN = 40,000
Dt = 130,000 It-1 = 20,000