Planning the Production Program

1
Chapter 4

• Planning the Production Program

2
Planning the Production Program

• Based on demand forecasts and orders plan the
  production quantities for the (main) products for
  the next periods
• 2 variants
• Aggregate Planning (aggregated view, tactical
  planning, medium run)few product groups for the
  next (months), quarters, or yearscapacities can
  be adjusted (hiring/firing, overtime, holidays,
  subcontracting ...)
• Master Production Scheduling(more detailed view,
  operational planning, short run)all main end
  products for next few shifts, days, or weeks (or
  months)capacities more or less fixed (except for
  overtime)
• Typically solved as an LP model

3
Aggregate Planning

• 2 extreme scenarios in case of seasonal demand
• Always produce the demand (forecast)
  Synchronisation (zero inventory plan)? cost
  of hiring/firing, overtime, subcontracting, idle
  time,
• Always produce average yearly demand (high
  utilization)Emancipation (level workforce
  plan)? inventory holding cost
• Goal
• Trade-off between these costs ? minimize total
  costs
• Solution by column minimum procedure

4
Synchronisation

• Synchronisation
• No active planning, just reaction on demand
  (forecasts) Always produce the demand (forecast)
  
• overview

5
Emancipation

• Emancipation
• More or less constant demand, constant (high)
  resource utilization, fluctuating demand is
  fulfilled by building up and depleting inventory.
• overview

Constant Production
Reduce Inventory
Build up Inventory
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Column Minimum Procedure

• In each period regular capacity can be extended
  at extra cost(overtime, subcontracting, )
• Cope with fluctuating demand (capacity
  shortages)
• Produce more than demand build up inventory, OR
• Use extra capacity
• Solution a special case (just one product group)
  as a TP
• In each cell (row t production period, half row
  k capacity type, and
• column ? demand period) the unit extra cost
  are
• ctk? uk h(? - t)
• where uk ... Extra cost (per unit) of production
  using extra capacity k (e.g. overtime)
• h ... Inventory holding cost per unit and per
  period,
• h(? - t) ... Inventory holding per unit if
  produced ? - t periods early
• Solve as transportation problem using Column
  Minimum Procedure

table
7
Example I

• Given
• 6 Periods
• Normal capacity in each Period 100 units
• Just 1 type of extra capacity k 1max.
  possible extra capacity 10 units
• Cost
• Holding cost h 1 per unit and period
• Cost of extra capacity u1 1,5 for each unit
  produced in overtime k 1
• Determine optimal production plan

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Example I - Table
for period
Period 1 2 3 4 5 6 capacity
1 0,0 1,0 2,0 3,0 4,0 5,0 100
1 1,5 2,5 3,5 4,5 5,5 6,5 10
2 0,0 1,0 2,0 3,0 4,0 100
2 1,5 2,5 3,5 4,5 5,5 10
3 0,0 1,0 2,0 3,0 100
3 1,5 2,5 3,5 4,5 10
4 0,0 1,0 2,0 100
4 1,5 2,5 3,5 10
5 0,0 1,0 100
5 1,5 2,5 10
6 0,0 100
6 1,5 10
Demand 90 110 50 110 100 130
No extra cost
Normal
Extra
Normal
Extra
Normal
Extra
Normal
Extra
Normal
Extra
Normal
Extra
Advance production holding cost h( periods)h
1
production in period
Extra capacity extra cost uin 2nd half rowu
1,5
formula
No shortages permitted (otherwise shortage cost)
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Example I Column Minimum Procedure
Prod Prod
100 100
0 100
100 100
0 100
70 70
0 70
100 100
0 100
100 110
10 110
100 110
10 110
90
10
10
Column Minimum Procedure
100
30
10
50
10
50
40
100
100
10
100
total cost
10
10
30
20
10
10
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Example I Cost Production Plan

• Total cost

590 C
10 1 10 1 10 3
10 2,5 10 1,5
Cost of production using extra capacity
Production cost
Holding cost
table
590 C 90 GE
Production plan
1. Per. 2. Per. 3. Per. 4. Per. 5. Per. 6. Per.
Normal 100 100 70 100 100 100
Extra 0 0 0 0 10 10
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Example II

• 2 sources of extra capacity
• k 1 overtime
• k 2 subcontracing

table
12
Example II Variant 1

• Each row now has 3 sub-rows for 3 sources of
  capayity (normal, overtime, subcontracting)
• Make it completely equivalent to TP by adding
  Dummy Column for unused capacity
• Total capacity 2780Total demand 2550unused
  capacity 2780 - 2550 230
• Initial inventory can be treated in 2
  waysVariant 1 treat as additional (artificial)
  production row 0oder Variant 2 subtract from
  demand of first period

data
13
Example II Variant 2

• Each row now has 3 sub-rows for 3 sources of
  capayity (normal, overtime, subcontracting)
• Make it completely equivalent to TP by adding
  Dummy Column for unused capacity
• Total capacity 2780Total demand 2550unused
  capacity 2780 - 2550 230
• Initial inventory can be treated in 2
  waysVariant 1 treat as additional (artificial)
  production row 0oder Variant 2 subtract from
  demand of first period

data
700
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Example II Solution

• Column minimum procedure

• Total cost 1000(700700700)40(5050)50
  5052150705072 105700

100
50
150