Post on 14-Jan-2016
Chapter 4/1
Chapter 4
Planning the Production Program
Chapter 4/2
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
Chapter 4/3
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
Chapter 4/4
Synchronisation
Synchronisation: No active planning, just reaction on demand (forecasts) Always produce the demand (forecast)
overview
Chapter 4/5
Emancipation
Emancipation:More or less constant demand, constant (high) resource utilization, fluctuating demand is fulfilled by building up and depleting inventory.
overview
Constant Production
Build up Inventory
Reduce Inventory
Chapter 4/6
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 TPIn 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
Chapter 4/7
Example I
Given• 6 Periods• Normal capacity in each Period: 100 units• Just 1 type of extra capacity: k = 1
max. 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
Chapter 4/8
Example I - Table
Period 1 2 3 4 5 6 capacity
10,0 1,0 2,0 3,0 4,0 5,0 100
1,5 2,5 3,5 4,5 5,5 6,5 10
20,0 1,0 2,0 3,0 4,0 100
1,5 2,5 3,5 4,5 5,5 10
30,0 1,0 2,0 3,0 100
1,5 2,5 3,5 4,5 10
40,0 1,0 2,0 100
1,5 2,5 3,5 10
50,0 1,0 100
1,5 2,5 10
60,0 100
1,5 10
Demand 90 110 50 110 100 130
production in period
for period
No extra cost
Advance production: holding cost h*(# periods)h = 1
Extra capacity extra cost uin 2nd half rowu = 1,5
formula
No shortages permitted (otherwise shortage cost)
Normal
Extra
Normal
Extra
Normal
Extra
Normal
Extra
Normal
Extra
Normal
Extra
Chapter 4/9
Example I – Column Minimum Procedure
90 10
10
10
10
100
100
100
100
1050
10
50 40
10
30
30 20 10
10
Prod Prod
100100
0
100100
0
7070
0
100100
0
100110
10
100110
10total cost
Column Minimum Procedure
Chapter 4/10
Example I – Cost & Production Plan
Total cost = 590 * C
Production cost
+ 10 * 1 + 10 * 1 + 10 * 3 + 10 * 2,5 + 10 * 1,5
Holding cost Cost of production using extra capacity
= 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
table
Chapter 4/11
Example II
2 sources of extra capacity• k = 1 overtime &• k = 2 subcontracing
table
Chapter 4/12
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 ways:Variant 1: treat as additional (artificial) production row 0oder Variant 2: subtract from demand of first period
data
Chapter 4/13
Example II – Variant 2
data700
• 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 ways:Variant 1: treat as additional (artificial) production row 0oder Variant 2: subtract from demand of first period
Chapter 4/14
Example II – Solution
• Column minimum procedure
50
150
100
• Total cost =100*0+(700+700+700)*40+(50+50)*50+50*52+150*70+50*72= 105700