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Chapter 4

Chapter 4. Planning the Production Program. Planning the Production Program. Based on demand forecasts and orders plan the production quantities for the (main) products for the „next“ periods 2 variants:

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Chapter 4

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  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“ cost of hiring/firing, overtime, subcontracting, idle time, … • Always produce average yearly demand (high utilization)„Emancipation“ 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

  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: 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

  8. Example I - Table forperiod No extra cost 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)

  9. Example I – Column Minimum Procedure 90 10 10 Column Minimum Procedure 100 30 50 10 10 50 40 100 100 10 100 total cost 10 10 30 20 10 10

  10. 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

  11. 2 sources of extra capacity k = 1 overtime & k = 2 subcontracing Example II 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 ways:Variant 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 ways:Variant 1: treat as additional (artificial) production row 0oderVariant 2: subtract from demand of first period data 700

  14. Example II – Solution • Column minimum procedure • Total cost =100*0+(700+700+700)*40+(50+50)*50+50*52+150*70+50*72= 105700 100 50 150

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