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Aggregate Planning

L.A FISH

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Aggregate Planning: used for Medium range capacity planning (usually 3 to 12 months)
Goal: achieve production plan that will effectively utilize resources to meet expected demand.  Therefore, must make decisions on output rates, employment levels & changes, inventory levels and changes, backorders and subcontracting

I)     Introduction:   
A) Long-term decisions -
B) Aggregate decisions -
C) Short term decisions -

II)      Purpose & Scope of Aggregate Planning
A) Purpose
: minimize costs while balancing expected demand & capacity over entire period

Develop feasible production plan to achieve balance of expected demand & capacity over planning horizon

B) Inputs to Aggregate Planning:
     1) Available resources over period must be known

     2) "Known"/forecast expected demand

     3) Employment policies

C) Demand & Capacity - pricing changes, promotions, backlogging orders using overtime, part time employees, subcontracting, +/- extra shifts & stockpiling inventories, pricing & promotions


1) Demand
:
a) Pricing - shift demand from peak periods to off-peak periods; consider degree of price elasticity
b) Promotion - very effective in shifting demand so that it conforms more closely to capacity
c) Backorders - cost would include lost sales, lost customers & paperwork
d) New demand/ Counter-seasonal Demand

2) Capacity:
a) Hire & Fire workers (Layoffs) - including recruitment, screening & training; fire: severance pay, realigning workers, worker motivation, loss of moral
b) Overtime  - can be implemented relatively quickly; firm employee base; may result in lower productivity, poorer quality, safety & payroll costs increasing
c) Part-time workers - generally cost less than regular workers in both wages & fringe benefits
d) Inventories - use for finished goods; includes storage costs, cost of insurance, obsolescence, deterioration, spoilage & breakage
e) Subcontracting - enables planners to acquire temporary capacity; decisions on available capacity, relative expectations on quality & costs & demand expectations

Ex: Cost Worksheet: Create one feasible plan, given the following information: regular time cost per unit = $2 /unit, overtime cost per unit = $3 /unit, subcontracting cost per unit = $6 / unit, inventory carrying cost = $1/unit/period, and backordering cost = $5/unit per period. Regular production produces 300 units per period, overtime can produce 100 units, and subcontracting can be used for an additional 50 units per period.


Period

1

2

3

4

Forecast

200

200

300

400

Output:

 

 

 

 

Regular

 

 

 

 

Overtime

 

 

 

 

Subcontract

 

 

 

 

Output-Forecast

 

 

 

 

Inventory:

 

 

 

 

Beginning

 

 

 

 

Ending

 

 

 

 

Average

 

 

 

 

 

 

 

 

 

Costs:

 

 

 

 

Regular

 

 

 

 

Overtime

 

 

 

 

Subcontract

 

 

 

 

Inventory

 

 

 

 

Backorders

 

 

 

 

Total

 

 

 

 




Computer Solution:

 

Demand

Regular time Capacity

Overtime Capacity

Subcontract Capacity

Regular time production

Inventory (end PD)

Initial Inventory

 

 

 

 

 

 0

Period 1

200

300

100

50

300

100

Period 2

200

300

100

50

300

200

Period 3

300

300

100

50

300

200

Period 4

400

300

100

50

300

100

Total(units)

1100

1200

400

200

1200

600

 

 

 

 

 

@$2 /unit

@$1 /unit

Subtotal Costs

 

 

 

 

$2,400.

$600.

Total Cost

$3,000.

 

 

 

 

 



III)    Basic Strategies for Uneven Demand
1) Level Capacity - maintain steady rate of regular time output while meeting variations in demand by combinations of options; use subcontracting, backlogging & use of inventories to absorb fluctuations

             2) Chase Demand - match capacity to demand; planned output for a period would be equal to expected demand for that period;




              3) Hybrid – combination of level and chase used over time to balance demand versus capacity


IV) Choosing a strategy:


A) Assumptions:

  1) Regular capacity in all periods

  2) Cost is linear function

  3) Plans are feasible

  4) All costs associated can be represented by lump sum or unit costs

  5) Cost figures can be reasonably estimated and are constant

  6) Inventories change @ uniform rate

B) Techniques:
1) Informal techniques: graphing & charting

2) Mathematical techniques:
a) Linear programming/ Transportation Method - optimal solution; minimize cost or maximize profit;
Ex: Transportation Formulation

Variables:
  r = regular production cost per unit
  o = overtime cost per unit
  s = subcontracting costs per unit
  h = holding costs per unit per period
  b = backorder cost per unit per period
  n = # periods in planning horizon


Period

1

2

3

....

End Inv.

Capacity

Beg. Inv.

             0
I11

             h
I12

          2h
I13

 

           Nh
I1n

 Io

Period 1:
Regular

             r
R11

          r+h
R12

      r + 2h
R13

 

      r +nh
R1n

R1

Overtime


            O
O11

          o+h
O12

      o+2h
O13

 

      o+nh
O1n

O1

Subcontract


             s
S11

          s+h
S12

       s+2h
S13

 

       s+nh
S1n

S1

Period 2:
Regular

        r+b
R21

             r
R22

        r+h
R23

 

   r+(n-1)h
R2n

R2

Overtime


        o+b
O21

             o
O22

        o+h
O23

 

  o+(n-1)h
O2n

O2

Subcontract


        s+b
S21

             s
S22

        s+h
S23

 

   s+(n-1)h
S2n

S2

.
.
.

 

 

 

 

 

 

Demand

D1

D2

D3

 

End Inv.

 


Bowman Formulation:
Min TC = 0 I11 + h I12 + 2h I13 + r R11 + (r+h) R12 + (r+2h) R13 +
o O11 + (o+h) O12 + (o + 2h) O13 + s S11 + (s+h) S12 +
(s + 2h) S13 + …….+ (s+h) S23

st: (rows)
I11 + I12 + I13 = Io
R11 + R12 + R13 = R1
O11 + O12 + O13 = O1
S11 + S12 + S13 = S1
…..
(columns)
I11 + R11 + O11 + S11 + R21 + O21 + S21 + …. = D1
I12 + R12 + O12 + S12 + R22 + O22 + S22 + ….
= D2
….
(demand = capacity)
D1 + D2 + D3 + …. = Io + R1 + O1 + S1 + R2 + O2 + S2

All variables > 0
Ex:     The demand for "widgets" is 10 in period 1 and 15 in period 2. The capacity to manufacture widgets on regular time is 10 per period and 2 per period on overtime. There is 1 unit available at the beginning of the period. It costs $2 per unit to produce the product during regular time and $3 per unit to produce the product during overtime. The cost to hold product in inventory is $1 per unit per period. Cost to backorder is $100 per unit per period.  Given that there is 1 unit in inventory at the start of period 1, develop (1) solution to this problem, and calculate the total cost to manufacture product in this manner.


Period

1

2

End Inv.

Capacity

Beg. Inv.



            


 

 

 

Period 1:
Regular


            

 

 

 

Overtime



         

 

 

 

Period 2:
Regular


      

 

 

 

Overtime



       

 

 

 

Demand


 

 

 

 




Computer Solution:

Optimal cost =  $55

Period 1

Period 2

End Inv.

Beg. Inventory

 1

 

 

Period 1: Regular

 9

 1

 

             Overtime

 

 2

 

Period 2: Regular

 

 10

 

             Overtime

 

 2

 0


Marginal Costs:

 

Period 1

Period 2

End Inv.

Beg. Inventory

 

 0

 0

Period 1: Regular

 

 

 0

             Overtime

 0

 

 0

Period 2: Regular

 101

 

 0

             Overtime

 101

 

 


Shipments with Costs

 

Period 1

Period 2

End Inv.

Beg. Inventory

 1/$0

 

 

Period 1: Regular

 9/$18

 1/$3

 

             Overtime

 

 2/$8

 

Period 2: Regular

 

 10/$20

 

             Overtime

 

 2/$6

 0/$0


Shipping List

From

To

Shipment

Cost per unit

Shipment cost

Beg. Inventory

Period 1

1

0

0

Period 1: Regular

Period 1

9

2

18

Period 1: Regular

Period 2

1

3

3

             Overtime

Period 2

2

4

8

Period 2: Regular

Period 2

10

2

20

             Overtime

Period 2

2

3

6

             Overtime

End Inv.

0

4

0



            V) Disaggregating Aggregate Plan:
Breakdown the aggregate plan into specific product requirements in order to determine labor requirements, materials & inventory requirements

Master schedule = quantity & timing of specific end items for schedule horizon; short- range planning

Rough-cut capacity planning = approximate balancing of capacity & demand to test feasibility of master schedule

A) Master Production Schedule (MPS) - quantity & timing of planned production & on-hand inventory

     a) Inputs =      1) beginning inventory,
               2) forecasts for demand  
               3) customer orders

     b) Outputs = projected inventory, production requirements, uncommitted inventory (available to promise inventory - ATP); can use to provide realistic delivery dates to customers

 
Projected On-Hand Inventory
=     Previous Inventory  Level -   Current Requirements


Note: Current Requirements = larger of forecast and customer orders

Available to     = MPS quantity -
"Current customer orders until build product again"
Promise (ATP)

Demand Time Fence =  The point in time inside of which the forecast is no longer included in total demand and projected available inventory calculations; inside this point, only customer orders are considered.

Planning Time Fence = a point in time denoted in the planning horizon of the master scheduling process that marks a boundary inside of which changes to the schedule can manually be made by the master scheduler. The customer requirements within this time fence are the larger of the forecast or customer orders.

Example: Given the lot size = 100, beginning inventory = 60, demand time fence is 1 month, and planning time fence is 4 months. Complete the following master production schedule:
                         Month




1

2

3

4

Forecast



50

50

50

50

Customer Orders



10

20

25

60

Projected On-Hand



 

 

 

 

MPS



 

 

 

 

ATP



 

 

 

 




Bibliography:

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