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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 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: • 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
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
Synchronisation Synchronisation: No active planning, just reaction on demand (forecasts) Always produce the demand (forecast) overview
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
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
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
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)
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
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
2 sources of extra capacity k = 1 overtime & k = 2 subcontracing Example II table
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
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
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