Chapter 4/1 Chapter 4 Planning the Production Program.

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