Ch 7 Assigned HW Solutions

Ch 7 Assigned HW Solutions - 7.4 =1: :1: a. .1509 =...

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Unformatted text preview: 7.4 =1: :1: a. .1509 = 1’2“) = W = 395 units. vr $8 * 0.16! yr b. Safety factor (k): Q 395 D(TBS) = 4000*6!12 satisfies p“2 (k) = 0.198 , that is k = 0.850. = 0.198 < 1. Hence, the safety factor is the value of k that- Safety stock (SS): SS = k 0}, =0.85 * 100 = 85 units. Reorder point (5) = lead-time demand (EL) + safety stock (SS): 3 = D*L + SS = 40001‘12 + 85 = 419 units. 0. EVSPY = 01 v Gu(k) D! Q. The table below shows the values of k and EVSPY for values of TBS between 3 months (0.25 year) and 21 months (1.75 years). Time Between Stockout TBS 0.25 0.50 0.75 1.00 1.25 1.50 1.75 (in ears)‘ stepl 0.40 0.20 0.13 0.10 0.08 0.07 0.06 [5 value in step] > I ? test FALSE FALSE FALSE FALSE FALSE FALSE FALSE safetyfactor k 0.27 0.85 1.12 1.29 1.41 1.51 1.59 G. (k) 0.28 0.11 0.07 0.05 0.04 0.03 0.02 - 0.40 0.20 0.13 0.10 0.03 0.07 0.06 R (k) 0.39 0.23 0.21 0.17 0.15 0.13 0.11 eercted value short Ber year EVSPY $2,268 $890 $536 $ 378 $ 289 $ 233 $ 195 156 7.11 a. Using the EOQ, the order quantity is 328 gallons corresponding to an estimated demand of two months. We follow the steps in section 7.10.2 to obtain the standard deviation of the lead time demand, given by the table below: 161 yearly demand D 2000 standard deviation demand 0' 400 variance demand ' var(D) 160000 lead time EU.) 0.0833 standard deviation lead 0.016? time variance lead time var(L) 0.0003 exp. lead time demand E(x) 166.67 variance lead time demand var(x) 14444 standard deviation It. 0'; 120 demand The present contract adopts a 33 = $0.325 shortage cost per day, that is $118.63 shortage cost per year. The proposed alternatives correspond to a B; = $1000 and a 32v = $65. The foIlOwing table gives their optimal policies and their total relevant costs: Chargefunit shortlunit time B; (present contract) $ 1 18.63 G"(k) 0.00460 (run Solver or check Normal table) I: 2.22 SS 266.40 s 16'? Purchasing and Holding COSt $ 3,865 Shortage Cost $ 251 . TRC . S 4,116 Costs'stockout occasion B; (first alternative) 35 1,000.00 step 1 3.1171 15 the value in "step I " < I ? test FALSE 1': l .5 1 SS 180.95 s 34% Purchasing and Holding Cost $ 3,309 Shortage Cost $ 401 TRC $ 3,710 Chmgdunit short B; (second alternative) . 2.00 step 1 0.0164 [5 the value in "step 1"> I ? test FALSE 1': 2.13 SS _ 256.12 3 423 Purchasing and Holding Cost $ 3,798 Shortage Cost $ 280 TRC $ 4,077 162 b. Both alternatives are more attractive than the present contract, providing lower total relevant cost. You should prefer the contract with the flat charge of $1000 per stockout occasion. 7.15. a. through c. The following table shows the a110cation of the 31200 for each service criterion. The allocation is the same in all cases, except Bl. a characteristic of the (R. g} £1152. Product XRL-l )ERL-Z XRI.»3 Total ufety factor k 1.29 1.29 1.29 acme! p..(k) 0.10 0.10 0.10 3 148 60 95 safety stock in 5 SS $151.08 3 755.40 $293.53 31.200 expected stoclwut occasions per year ESOPY 1.17 1.17 1.17 3.52 expected valueshonEyear EVSPY S 64 S 322 S 125 S 512 cycle service level P; 0.902 0.902 0.902 peat) 0.098 0.098 0.098. k 1.29 1.29 1.29 3 149 61 96 safety stock in 3 SSS 3151.08 5 755.40 $293.53 $1.200 expected stockout occasions per year ESOPY 1.17 1.17 1.17 3.52 expected value shonper leg EVSPY 3 64.42 5 322.12 $125.17 5 512 time betwem stockout TBS 0.85 0.85 0.85 k 1.29 1.29 1.29 s 148 ' 60 95 safety stockin S SSS $151.08 5 755.40 $293.53 $1.200 expected stockout occasions per year ESOPY 1.17 1.17 1.17 3.52 expected value short E year EVSPY 3 64.42 3 322.12 $125.17 5 512 fixed cost per stoekom occasion B; 3 23.85 3 23.85 3 23.85 1: 2.05 0.99 1.69 .r 157 55 100 safety stock in S SSS 3239.02 3 577.04 $383.94 51.200 expected stockmt occasions per year ESOPY 0.24 1.94 0.54 2.72 M value short per year ~ ~ EVSPY 3 10.42 3 595.29 3 50.49 3 656 Mondchargepuunitshort B: 0.10 0.10 0.10 k 1.29 1.29 1.29 s 148 60 95 safety stock in 5 853 $151.08 3 755.40 $293.53 $1.200 expected stoekout occasion per year ESOPY 1.17 1.17 1.17 3.52 cm value strung year EVSPY 3 64.42 3 322.12 $125.17 3 512 A 7.16 =$5 The table below show that (R, S) and the (s, Q) policies that are most appropriate for the XRL product line. ' 350 700 35 50 40 $ 5.00 $ 5.00 S 5.00 $ 10.00 $ 35.00 5 17.00 yearly demand std. dev. yearly demand fixed ordering cost unit price carrying costs 12% 12% 12% replenishments per year lot size 100 29 59 lead time 0.04 0 04 0 04 50.0 14.6 29.2 7.1 10.2 8.2 lead time demand std. dev. lead time demand fractional charge per unit short 0.15 0.15 0.15 0.15 0.15 0.15 k 1.50 . 1.50 1.50 1.50 1.51 1.50 (3,,(k) 0.03 0.03 0.03 0.03 0.03 0.03 s 151 64 98 61 30 - 4i safety stock in $ SSS $175.13 $ 875.63 $340.25 $ 107.24 $ 538.11 $ 208.06 expected value short per year EVSPY $ 40.93 3 204.64 5 79.52 5 25.06 $ 125.09 3 48.23 TRC $ 87.15 $ 197.02 $112.26 $ 76.63 $ 143.96 $ 92.03 Total cost $396.43 $ 312.61 a. through c. Notice that, although the reorder interval remains the same (because of the same reorder quantities), there is a significant reduction in the total relevant costs, due to the reduction in the uncertain period, from 40 days to 15 days. d. Cost savings in the XRL line due to switching from (R, S) to (s, Q) policy: savings = $396.43 - $312.61 = $83.821year. If the XRL represents 1% of the inventory at Safety Films, the pay back period is: pay-back = $30000!(100*83.82) = 3.6 years. Management has to decide whether this investment is compatible with the future of the firm, whether this is a growing market or a mature one, it may decide that the future savings could be larger than evaluated, and the new policy is valid. 165 = Joe +(I.q:n(lx%.'fl = 55:51 7.24 . Method 1 2 Q 2000.00 2000.00 0'; 1000.0 2300.0 P2 0.95 0.95 Gm?) 0. 100 0.043 k 0.900 1.322 SS 900.38 3041.67 r‘SS$ $ 360.15 $ 1,216.67 Forecasting Cost $ 200.00 $ 35.00 TRC $ 560.15 $ 1,251.67 Notice that the holding cost of the safety stock and the forecasting cost are the only relevant costs in this problem. The first forecasting method clearly dominates, allowing a small investment in safety stock. 174 ...
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This note was uploaded on 11/03/2008 for the course IE 251 taught by Professor Wilson during the Spring '08 term at Lehigh University .

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Ch 7 Assigned HW Solutions - 7.4 =1: :1: a. .1509 =...

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