FAISAL FARIS BIN RAHIM MOHD HANEESYAH BIN CHE HASSAN NOR SYAKIRA BT ZAUKIFLI ANISAH BT ABD LATIFF
Mar 26, 2015
FAISAL FARIS BIN RAHIM
MOHD HANEESYAH BIN CHE HASSAN
NOR SYAKIRA BT ZAUKIFLI
ANISAH BT ABD LATIFF
OutlineCosts in aggregate planning
Solving in aggregate planning problem
Linear decision rule (LDR)
Modeling management behavior
1. Smoothing Costs2. Holding Costs3. Shortage Costs4. Regular Costs5. Overtime & Subcontracting Costs6. Idle Time Costs
Issues in Aggregate PlanningSmoothing – 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 PlanningPlanning 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 Planning1. 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
Firing costsHiring costs
Cost of Changing the Size of the Workforce
Cost in Aggregate Planning
Cost in Aggregate Planning2. 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 Planning3. 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 Planning4. Regular Time Costs
Involve the cost of producing one unit of output during regular working hours
5. Overtime or Subcontracting CostsCosts 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 Planning6. Idle Time Costs
Under utilization of workforce
SOLVING AGGREGATE PLANNING PROBLEMS
BASIC RELATIONSHIPSWorkforce
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
Regular Time Overtime
January 100 50
February 100 40
March 100 30
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.
Demand for
Supply from January February March
Unused capacit
y (dumm
y)
Total capacit
y availabl
e (Supply
)January Regular 80 20 100
Overtime
50 50
February
Regular 50 50 100Overti
me40 40
March Regular 60 40 100Overti
me30 30
Demand 80 120 150 70 420
Period Demand forecast
Planned producti
on
Beginning
inventory
Ending inventor
y
1 40,000 48,000 9,0002 70,000 48,0003 30,000 48,0004 55,000 48,000
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 Demand forecast
Planned producti
on
Beginning
inventory
Ending inventory
1 40,000 48,000 9,000 17,0002 70,000 48,000 17,000 -5,0003 30,000 48,000 -5,000 13,0004 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.
Period Demand forecast
Planned productio
n
Beginning
inventory
Ending inventory
1 40,000 41,250 9,000 10,2502 70,000 71,250 10,250 11,5003 30,000 31,250 11,500 12,7504 55,000 56,250 12,750 14,000
Inventory is increased by 1250 units in each period: (14,000 - 9,000)/4
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
Required work force
Required number of employees
Available at the end of previous period
HireLayoff
1234
FORMULA= Total Cost Over the T-Period 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)+ 153Ans:………………..
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 noconvincing 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
Construct model for controlling
production level
Created by Bowman (1963)
Avoids problem arise when using
traditional modeling method
Exp : determining the accuracy of assumption that
required by model.
Exp : Avoids determine values of
parameter that difficult to measure
D = forecast demand P = production levelα = smoothing factor / exponential smoothingIN = Smoothing for inventory level β = Relative weighta = for determination of P
Pt = Dt for 1 ≤ t ≥ T
Pt = Dt + α(Pt-1 – Dt)
Pt = Dt + α(Pt-1 – Dt) + β(IN – It-1)
Not given : β, IN , α and a1
2 Not given : a
3
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 = 0.3475 a2 = 0.1211a3 = 0.556 a4 = 0.0663 a5 = 0.0023α = 0.6 β = 0.3 IN = 40,000Dt = 130,000 It-1 = 20,000