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Dr. Abedini

IME 326. Dr. Abedini. Inventory Control. Inventory analysis Space and money prevent companies from producing goods Total Cost = Pc+Cc+Oc Where Pc = Purchasing Cost per year Cc =Carrying or Holding Cost per year Oc = Ordering Cost per year. C = $Cost/unit D = Annual demand

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Dr. Abedini

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  1. IME 326 Dr. Abedini

  2. Inventory Control • Inventory analysis • Space and money prevent companies from producing goods • Total Cost= Pc+Cc+Oc • Where • Pc= Purchasing Cost per year • Cc=Carrying or Holding Cost per year • Oc= Ordering Cost per year

  3. C= $Cost/unit • D= Annual demand • H=$Holding cost/unit/year • (Based on Annual Demand) • Q= Order Quantity • P= $Ordering cost/order/year • R= Reorder Point (quantities) • Total Cost= (C)(D)+H(Q/2)+P(D/Q) • dTC/dQ = (0)+H/2 – PD/Q • Therefore Q*= √(2DP/H) • Q*= Economic Order Quantity

  4. R=Lead time • Q*= Economic ordering quantity • (How many to order) • T= Time

  5. Example #1 • C= $10/unit • D= 365,000 • H= $5/unit/year (based on demand) • P= $500 • Q*=√[2(365,000)(500)/5] = 8544 • (# of units per order) • 365,000/8544 = 42.7 • (times in year you order)

  6. Total cost of carrying inventory= • 10(365,000)+5(8544/2)+500(365,000/8544) • 3650000+21360+21360 • $3,692,720.02 • Under these conditions we assume that the demand is constant and the lead time is constant • This is known as Simple E.O.Q.

  7. Service Level • % of quantity ordered that can be supplied from the available stock • Ex.) • You want 100 parts but the company has only 90 • Service Level = 90%

  8. Service level when demand is distributed discretely 0<n<20 • More than 20 data points becomes continuous • S.L. =

  9. Stockout Probability • Probability that you run out of stock before you receive your new order

  10. E.O.Q. With uncertain demand (Continuous distribution) • Now you don’t know when you will run out

  11. Z = X- µ/ σ • µ= 1000/day • σ = 100/ day σ σ

  12. Remember • If you an 84 % service level then you would just add 1 standard deviation • If you want a 97 % service level then you add 2 standard deviations • 84% = 1000+100 = 1100 • 97% = 1000+2(100) = 1200

  13. Example #2 • Annual Demand = 365,000 • Daily Demand = 1000 units/day • P = $50 / order • H = $1.25 / unit / year • L = 9 days • C = $12.50 / unit • SL = 95 % • σ = 1000 units / day • Z = 1.64

  14. SS = Zσ√(L) • = 1.64(100) √(9) • = 492 Units • R = DL + SS • = (1000)9 + 492 • = 9492 Units • This is when you reorder • Q* = Q*= √(2DP/H) • = √[2(365,000)(50)]/ 1.25 • = 5,404 Units • This is the number of units you should order during reorder time

  15. Scheduling • Priority rules • 1.) First come first serve • 2.) Shortest processing time (SPT) • 3.) Earliest due dates (EDD) • Prioritize as what is due next

  16. Abbreviations • i = task • di = due date for task i • ti = processing time for i • Li = lateness for I = (Fi - di) • Negative values represent early times • Fi = flow time for i • Ti = tardiness for i (never negative) • SLi = slack time for I = (di - ti) • Ci = make span for i (time to complete all tasks) • Wi = weight for i

  17. Scheduling n tasks to 1 processor • Rule 1: minimize the average flow time by sequencing in the order of (SPT)

  18. Rule 1 : t2, t4, t7, t1, t8, t5, t3, t6

  19. Critical Path Method • List Activities • Set Precedence • Compute each crash time • Design network • Compute early start times • Compute late finish times • Design critical path • Compute project cost • Crash one activity • Iterate

  20. Critical path – • Occurs when early start times equal late finishes

  21. Pert • Project evaluation and review technique • Use expected values rather than estimated values

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