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Aggregate Production Planning

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  • 1. Aggregate Planning
    • It is about translating demand forecasts into production and capacity levels over a fixed planning horizon
    • Assumes the demand forecast is fairly accurate.
    • It generally uses an aggregate unit of production
  • 2. Conflicting Objectives in AP
    • Objective 1 : React quickly to anticipated changes in demand
      • Called “chase” strategy
      • Involves frequent and large changes in the size of the labor force
      • May not be the best strategy in the long-run
      • Cost of firing and hiring
    • Objective 2 : Retaining a stable workforce
      • Leads in to inventory build-ups during low demand periods or to idle time increases.
    • Objective 3 : Plan that maximize profit s.t constraints on capacity
  • 3. Aggregate Unit of Production
    • Aggregate planning is usually based on an aggregate unit of production
    • If the products are similar, an “average” item can represent the aggregate unit
    • If there are variety of products then the aggregate unit may be
      • Weights (tons of steel)
      • Volume (gallons of gasoline)
      • Amount of work required (hours of labor)
      • Dollar value (value of the inventory in dollar)
  • 4. Aggregate Unit of Production : Example
    • Two products made of steel
    • It takes the same amount of time to produce a one $ worth of product.
    • Aggregate unit  1 $ worth of output
    • Forecasted demand in aggregate unit = (forecast for prod. A*500 + Forecast for prod. B*1250)
    • Example; (200 units*500 + 150 units*1250)=287500 $ worth of product is needed. 287500*2=575000 min. of production time is needed
    ½ ½ 500 1250 1000 min 2500 min Product A Product B Price/Prod. time Price ($) Production Time
  • 5. Aggregate Unit of Production : Example
    • Replace the price by volume in the above example. Now what is aggregate unit?
    ½ ½ 500 1250 1000 min 2500 min Product A Product B Volume/Prod. time Volume(cm 3 ) Produc. Time
  • 6. Aggregate Unit of Production : Example
    • A plant produces six models of washing machines
    • What aggregate unit the plant manager can use for planning?
    725 5.8 M38 525 5.4 M26 425 5.2 L38 395 5.1 L98 345 4.9 K42 285 4.2 A55 Selling Price ($) Total Production Time (hours) Model Number
  • 7. Aggregate Unit of Production : Example
    • Can we use one dollar of output as aggregate unit?
      • Selling values are not consistent with the worker hours required
      • The ratio of selling price to total worker hours required differs from one model to the other
    • Say that we have an almost constant percentage of sales in total sales across the models (32%, 21%, 17%, 14%, 10%, 6% respectively)
  • 8. Aggregate Unit of Production : Example
    • A valid aggregate unit is a weighed average of hours required, weighted by percent sales
      • Fictitious machine = .32(4.2)+.21(4.9)+.17(5.1)+.14(5.2)+.10(5.4)+ .06(5.8) = 4.856 hours of labor
    • An aggregate forecast can be obtained in the same way.
    • # of fictitious machines demanded = .32*fore. for A55+.21*fore. for (K42) +…. + .06* fore. for M38
    • If variety of products, sales dollars is good approximation as an aggregate unit
  • 9. Planning Steps hierarchy Forecast of aggregate demand for t period Planning horizon Aggregate production Plan : Production and Workforce levels for each period Master Production Schedule : Production levels by item by period Material Requirements Planning : Detailed Time table for production and assembly of Components and subassemblies
  • 10. Aggregate Production Plan
    • D 1 , D 2 , …, D T demand forecasts for next T planning periods
    • A period is usually a month
    • Demands are known constants
    • Goal of APP: determine aggregate production quantities and the levels of resources required to achieve these production goals
  • 11. Issues in Aggregate Planning
    • Smoothing ; refers to the cost of changing production and workforce level between periods
      • Firing and hiring costs
        • Hard to find the real costs
      • Trade-off between cost of changing workforce and saving in inventory costs
    • Bottleneck problems ; Inability to respond to sudden changes in demand as a result of capacity restrictions
      • High demand in one period
      • Breakdown of a vital piece of equipment
  • 12. Issues in Aggregate Planning
    • Planning Horizon ; number of periods for which the demand forecast and aggregate planning are done
      • If it is too small ; current aggregate plan may lead into not meeting the demand beyond planning horizon
      • If it is too large ; forecasts into far future will be less accurate
      • End-of-horizon effect
      • Rolling schedules are used in practice
  • 13. Costs in Aggregate Planning
    • Smoothing cost
      • Hiring cost ; advertising, interviewing, training
      • Firing cost ; severance penalty, decline in worker morale, lack of labor force in future
      • Mostly assumed to be a linear function of the number of workers
    • Holding cost
      • Major part is the opportunity cost of tied up money in inventories
      • Assumed to be linear in the level of inventory (end-of period or average inventory
      • It is in $/item/planning period
  • 14. Costs in Aggregate Planning
    • Shortage costs
      • Cost of not meeting demand on time (from inventory). Backlogging or lost sale
      • Usually assumed to be linear in number of items
    • Regular time costs
      • Cost of producing one unit in regular time
    • Overtime or subcontracting costs
      • Cost of producing one unit item in over time or through subcontracting production to an outside supplier
    • Idle time costs
  • 15. Aggregate Planning: Example
    • Example 3.2 (Nahmias’ Book) Densepack ; a disk drive producer
    • Has 300 workers employed at the moment
    • Ending inventory in December 500 units
    • Would like to have 600 unit at the end of June
    • Inventory requirements and on-hand inventories are dealt with by adding/ subtracting them to expected demand
  • 16. Aggregate Planning: Example
    • Demand data
    7520 2000 1400 June 5520 2000 2000 May 3520 1200 1200 April 2320 900 900 March 1420 640 640 February 780 780 1280 January Net cumulative demand Net predicted demand Predicted demand
  • 17. Aggregate Planning: Example Inventory
  • 18. Aggregate Planning: Example
    • Cost data
      • C H : cost of hiring one worker = $ 500
      • C F : cost of firing one worker = $ 1000
      • C I : cost of holding one unit of inventory one month = $ 80
    • K ; Number of aggregate units produced by one worker in one day
      • It was observed that 76 workers produced 245 disk drives in 22 days
      • K = 245/(76x22) = .14653
  • 19. Aggregate Planning: Example Strategy 1 : Chase the demand by changing work force levels Month Number of Working days Number of Units produced Per worker (Bx.14653) Forecast Net demand Min. # of Worker required (D/C) Initial Calculations Table D C B A
  • 20. Aggregate Planning: Example Total cost = 755(500)+145(1000)+30(80) = 524,900 Month # of Workers # of units per workers # fired # hired Cum. Product. Produc Tion (BxE) Cum. Demand. Inven tory. A B D C F E G H I Aggregate Production/capacity plan
  • 21. Aggregate Planning: Example Min. Number Of Workers required 411 Strategy 2: Constant work force : Keep the work force level constant throughout the planning horizon Month Cumulative net demand Cumulative # of units produced per worker Ratio (B/C) Required workforce for strategy 2
  • 22. Aggregate Planning: Example Total cost = (411-300)(500)+5963(80) = 532,540 Month Production Per worker Monthly Production (Bx411) Cumulative production Cumulative Net demand Inven tory Aggregate Production/capacity plan
  • 23. Are we missing anything?? :P
  • 24. Aggregate Planning: Example
    • What are the total cost of salary paid to workers in each strategy (assuming 2500 per month for each worker)
      • 6,598,924 for strategy 1 + 524,900 = 7,124,824
      • 6,165,000 for strategy 2 + 532,540 = 6,697,540
    • Strategy 2 costs about 425,000 less and also avoids some hard-to-determine costs of changing workforce levels frequently
  • 25. Aggregate Planning: Example Mixed Strategies
    • Instead of pure strategies (chase and constant workforce), we can have mixed strategies.
    • Any mixed strategy can be represented by combination of lines on the plot.
    • Lines represent constant work force
    • Any line combination not going below the cumulative demand curve is a feasible aggregate plan
  • 26. Aggregate Planning: Example Red strategy Blue strategy
  • 27. Aggregate Planning: Assignment
    • Figure out the costs of blue and red mixed strategies. What strategy should be used?

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