FAISAL FARIS BIN RAHIM
MOHD HANEESYAH BIN CHE HASSAN
NOR SYAKIRA BT ZAUKIFLI
ANISAH BT ABD LATIFF
Outline
 Costs in aggregate planning
 Solving in aggregate planning problem
 Linear decision rule (LDR)
 Modeling management behavior
1.
2.
3.
4.
5.
6.
Smoothing Costs
Holding Costs
Shortage Costs
Regular Costs
Overtime & Subcontracting Costs
Idle Time Costs
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)
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
Cost in Aggregate Planning
1. 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
Cost in Aggregate Planning
Cost of Changing the Size of the Workforce
Firing costs
Hiring costs
Cost in Aggregate Planning
2. 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)
(e.g. 100 $/month for one item)
Cost in Aggregate Planning
3. 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.
Cost in Aggregate Planning
4. Regular Time Costs
 Involve the cost of producing one unit of output during
regular working hours
5. 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;
Cost in Aggregate Planning
6. Idle Time Costs
 Under utilization of workforce
SOLVING AGGREGATE
PLANNING PROBLEMS
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
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 - 120 units.
• March - 150 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
100
40
March
100
30
Demand for
Unused Total
capacity capacity
Supply from
January February
March (dummy) available
(Supply)
January Regular
80
20
100
Overtime
50
50
February Regular
50
50
100
Overtime
40
40
March Regular
60
40
100
Overtime
30
30
Demand
80
120
150
70
420
a) 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
1
2
3
4
Demand Planned Beginning Ending
forecast production inventory inventory
40,000
48,000
9,000
70,000
48,000
30,000
48,000
55,000
48,000
Period
1
2
3
4
Demand Planned Beginning Ending
forecast production inventory inventory
40,000 48,000
9,000
17,000
70,000 48,000
17,000
-5,000
30,000 48,000
-5,000
13,000
55,000 48,000
13,000
6,000
Note that ending inventory = beginning inventory +
planned production - demand forecast
b) 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 - 9,000)/4
Period
1
2
3
4
Demand Planned Beginning Ending
forecast production inventory inventory
40,000
41,250
9,000
10,250
70,000
71,250
10,250
11,500
30,000
31,250
11,500
12,750
55,000
56,250
12,750
14,000
c) 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
1
2
3
4
Required
work force
Required
number of
employees
Available at the
end of previous
period
Hire
Layoff
Period Required work Required Available at the
number of end of previous
force
employees
period
1 41,250/4,000
10
10
= 10.3
2 71.250/4,000
18
10
= 17.8
3 31,250/4,000
8
18
= 7.8
4 56,250/4,000
14
8
= 14.1
Hire Layoff
8
10
6
FORMULA= Total Cost Over the TPeriod Planning Horizon
FORMULA= Optimal Production
Level in Period t
The terms of a,b,c and d are constant
that depend on the cost parameters
EXAMPLE:
 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) + 0.234(164)+ 0.111(185)+ 0.046(193)+
0.993(180)– 0.464(45)+ 153
 Ans:………………..
W t = 0.010D t + 0.0088D t+1 + 0.0071D t+2 + 0.0054D t+2
+0.743W t-1 – 0.01I t-1 – 2.09
Ans:………………….
THE
ADVANTAGES
•The result is optimal production
in period t will be form.
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.
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.
Pt = Dt
1
2
Pt = Dt + α(Pt-1 – Dt)
Pt = Dt + α(Pt-1 – Dt) + β(IN – It-1)
for 1 ≤ t ≥ T
Not given : β, IN , α and a
Not given : a
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
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
a3 = 0.556
α = 0.6
Dt = 130,000
a1 = 0.3475
a4 = 0.0663
β = 0.3
It-1 = 20,000
a2 = 0.1211
a5 = 0.0023
IN = 40,000