1. Dr. Abedini

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

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

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

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

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

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

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

9. DP1.01 2.04 3.10 4.20 5.30 6.20 7.10 8.04 9.01 ReorderSSSL50.30.35.2(1)+.188.8% 61.20.15 72.10.05 83.04.01 94.010

10. Probability that you run out of stock before you receive your new order Probability that you run out of stock before you receive your new order

11. With uncertain demand (Continuous distribution) Now you don’t know when you will run out Now you don’t know when you will run out

12. Z = X- µ/ σ Z = X- µ/ σ µ= 1000/day µ= 1000/day σ = 100/ day σ = 100/ day σσ

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

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

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

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

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

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

19. Rule 1 : t2, t4, t7, t1, t8, t5, t3, t6 Rule 1 : t2, t4, t7, t1, t8, t5, t3, t6 Task i tidiwiFiLiTi/wiFiLiFiLi 11015.131161004025150 2515.25-102512-35-10 31820.378589030103313 4730.0512-18237-234919 51750.05601034078289848 62040.05985840098586929 7929.0521-818049204213 81242.0543124061198139 µ 100 % 43.513.446.916.754918.88

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

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

22. Project evaluation and review technique Project evaluation and review technique Use expected values rather than estimated values Use expected values rather than estimated values