Report

Dr. Abedini 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= $Cost/unit D= Annual demand H=$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 R=Lead time Q*= Economic ordering quantity • (How many to order) T= Time 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) 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. % 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% Service level when demand is distributed discretely 0<n<20 • More than 20 data points becomes continuous S.L. = D P 1 .01 2 .04 3 .10 4 .20 5 .30 Reorder 5 .20 6 .10 7 .04 8 .01 9 6 7 8 9 SS 0 SL .30 .35 .2(1)+.1 1 2 3 .20 .10 .04 .15 .05 .01 4 .01 0 88.8% Probability that you run out of stock before you receive your new order With uncertain demand (Continuous distribution) Now you don’t know when you will run out σ Z = X- µ/ σ µ= 1000/day σ = 100/ day σ 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 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 SS = Zσ√(L) R = DL + SS = (1000)9 + 492 = 9492 Units This is when you reorder Q* = Q*= √(2DP/H) = 1.64(100) √(9) = 492 Units = √[2(365,000)(50)]/ 1.25 = 5,404 Units This is the number of units you should order during reorder time Priority rules 1.) First come first serve 2.) Shortest processing time (SPT) 3.) Earliest due dates (EDD) • Prioritize as what is due next 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 Scheduling n tasks to 1 processor Rule 1: minimize the average flow time by sequencing in the order of (SPT) Task i ti di Li Fi Li 1 10 15 .1 31 16 100 40 25 15 0 2 5 15 .2 5 -10 25 12 -3 5 -10 3 18 20 .3 78 58 10 33 13 4 7 30 .05 12 -18 23 7 -23 49 19 5 17 50 .05 60 10 340 78 28 98 48 6 20 40 .05 98 58 400 98 58 69 29 7 9 29 .05 21 -8 180 49 20 42 13 8 12 42 .05 43 1 240 61 19 81 39 16.75 49 18.88 µ wi Fi 100 % 43.5 Li 13.4 Ti/wi Fi 90 30 46.9 Rule 1 : t2, t4, t7, t1, t8, t5, t3, t6 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 Critical path – Occurs when early start times equal late finishes Project evaluation and review technique Use expected values rather than estimated values