1. Chapter 4/1 Chapter 4 Planning the Production Program

2. 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 years capacities 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. 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, …Synchronisation Always produce average yearly demand (high utilization) „Emancipation“ (level workforce plan)  inventory holding cost „Emancipation Goal: Trade-off between these costs  minimize total costs Solution by column minimum procedurecolumn minimum procedure

4. Chapter 4/4 Synchronisation Synchronisation: No active planning, just reaction on demand (forecasts) Always produce the demand (forecast) overview

5. 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

6. 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 TP In each cell (row t … production period, half row k … capacity type, and column  … demand period) the unit extra cost are: c tk  = u k + h(  - t) where :u k... 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. 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: u 1 = 1,5 € for each unit produced in overtime k = 1 Determine optimal production plan

8. Chapter 4/8 Example I - Table Period 1 2 3 4 5 6capacity 1 0,01,02,03,04,05,0 100 1,52,53,54,55,56,5 10 2 0,01,02,03,04,0 100 1,52,53,54,55,5 10 3 0,01,02,03,0 100 1,52,53,54,5 10 4 0,01,02,0 100 1,52,53,5 10 5 0,01,0 100 1,52,5 10 6 0,0 100 1,5 10 Demand9011050110100130 production in period for period No extra cost Advance production: holding cost h*(# periods) h = 1 Extra capacity extra cost u in 2 nd half row u = 1,5 formula No shortages permitted (otherwise shortage cost) Normal Extra Normal Extra Normal Extra Normal Extra Normal Extra Normal Extra

9. Chapter 4/9 Example I – Column Minimum Procedure 90 10 100 10 50 10 50 40 10 30 2010 Prod 100 0 0 70 0 100 0 110 10 100 110 10 total cost Column Minimum Procedure

10. 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. Normal100 70100 Extra000010 table

11. Chapter 4/11 Example II 2 sources of extra capacity k = 1 overtime & k = 2 subcontracing table

12. 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 = 2780 Total demand = 2550 unused capacity = 2780 - 2550 = 230 Initial inventory can be treated in 2 ways: Variant 1: treat as additional (artificial) production row 0 oder Variant 2: subtract from demand of first period data

13. Chapter 4/13 Example II – Variant 2 data 700 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 = 2780 Total demand = 2550 unused capacity = 2780 - 2550 = 230 Initial inventory can be treated in 2 ways: Variant 1: treat as additional (artificial) production row 0 oder Variant 2: subtract from demand of first period

14. 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