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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

This last method shows that the intuitive decision a good manager will take is similar to that which is provided by the linear decision rule.

1. Produce what is required

However, this could result in large changes in production level and workforce.

2. Smooth production over timeIt could therefore be useful to introduce smoothing factor α. It is decided to select a production level P(t) which is a compromise between the current demand and the last production level.

3. Reach target inventoryIntroduce an additional factor β.

4. Incorporate demand forecastsLook at the future demands could avoid problems in the future

The result is very similar to what the LDR proposed.The main drawback of the approach is the arbitrary character of all the choices.

ExampleUsing 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

D = forecast demand P = production levelα = smoothing factor / exponential smoothingIN = Smoothing for inventory level β = Relative weighta = for determination of P