Question

Osprey Sports stocks everything that a musky fisherman could want in the Great North Woods. A particular musky lure has been very popular with local fishermen as well as those who buy lures on the Internet from Osprey Sports. The cost to place orders with the supplier is ​$40 per order; the demand averages 5 lures per​ day, with a standard deviation of 1 ​lure; and the inventory holding cost is

​$1.00​/lure/year. The lead time form the supplier is 9 ​days, with a standard deviation of 3 days. It is important to maintain a 97 percent​ cycle-service level to properly balance service with inventory holding costs. Osprey Sports is open 350 days a year to allow the owners the opportunity to fish for muskies during the prime season. The owners want to use a continuous review inventory system for this item. Refer to the standard normal table for​ z-values.

c. What is the total annual cost for this inventory​ system?

​$Enter your response rounded to two decimal​ places.)

The table below shows the total area under the normal curve for a point that is Z standard deviations to the right of the mean.

Z	0.00	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
0.0	0.5000	0.5040	0.5080	0.5120	0.5160	0.5199	0.5239	0.5279	0.5319	0.5359
0.1	0.5398	0.5438	0.5478	0.5517	0.5557	0.5596	0.5636	0.5675	0.5714	0.5754
0.2	0.5793	0.5832	0.5871	0.5910	0.5948	0.5987	0.6026	0.6064	0.6103	0.6141
0.3	0.6179	0.6217	0.6255	0.6293	0.6331	0.6368	0.6406	0.6443	0.6480	0.6517
0.4	0.6554	0.6591	0.6628	0.6664	0.6700	0.6736	0.6772	0.6808	0.6844	0.6879
0.5	0.6915	0.6950	0.6985	0.7019	0.7054	0.7088	0.7123	0.7157	0.7190	0.7224
0.6	0.7258	0.7291	0.7324	0.7357	0.7389	0.7422	0.7454	0.7486	0.7518	0.7549
0.7	0.7580	0.7612	0.7642	0.7673	0.7704	0.7734	0.7764	0.7794	0.7823	0.7852
0.8	0.7881	0.7910	0.7939	0.7967	0.7996	0.8023	0.8051	0.8079	0.8106	0.8133
0.9	0.8159	0.8186	0.8212	0.8238	0.8264	0.8289	0.8315	0.8340	0.8365	0.8389
1.0	0.8413	0.8438	0.8461	0.8485	0.8508	0.8531	0.8554	0.8577	0.8599	0.8621
1.1	0.8643	0.8665	0.8686	0.8708	0.8729	0.8749	0.8770	0.8790	0.8810	0.8830
1.2	0.8849	0.8869	0.8888	0.8907	0.8925	0.8944	0.8962	0.8980	0.8997	0.9015
1.3	0.9032	0.9049	0.9066	0.9082	0.9099	0.9115	0.9131	0.9147	0.9162	0.9177
1.4	0.9192	0.9207	0.9222	0.9236	0.9251	0.9265	0.9279	0.9292	0.9306	0.9319
1.5	0.9332	0.9345	0.9357	0.9370	0.9382	0.9394	0.9406	0.9418	0.9430	0.9441
1.6	0.9452	0.9463	0.9474	0.9485	0.9495	0.9505	0.9515	0.9525	0.9535	0.9545
1.7	0.9554	0.9564	0.9573	0.9582	0.9591	0.9599	0.9608	0.9616	0.9625	0.9633
1.8	0.9641	0.9649	0.9656	0.9664	0.9671	0.9678	0.9686	0.9693	0.9700	0.9706
1.9	0.9713	0.9719	0.9726	0.9732	0.9738	0.9744	0.9750	0.9756	0.9762	0.9767
2.0	0.9773	0.9778	0.9783	0.9788	0.9793	0.9798	0.9803	0.9808	0.9812	0.9817
2.1	0.9821	0.9826	0.9830	0.9834	0.9838	0.9842	0.9846	0.9850	0.9854	0.9857
2.2	0.9861	0.9865	0.9868	0.9871	0.9875	0.9878	0.9881	0.9884	0.9887	0.9890
2.3	0.9893	0.9896	0.9898	0.9901	0.9904	0.9906	0.9909	0.9911	0.9913	0.9916
2.4	0.9918	0.9920	0.9922	0.9925	0.9927	0.9929	0.9931	0.9932	0.9934	0.9936
2.5	0.9938	0.9940	0.9941	0.9943	0.9945	0.9946	0.9948	0.9949	0.9951	0.9952
2.6	0.9953	0.9955	0.9956	0.9957	0.9959	0.9960	0.9961	0.9962	0.9963	0.9964
2.7	0.9965	0.9966	0.9967	0.9968	0.9969	0.9970	0.9971	0.9972	0.9973	0.9974
2.8	0.9974	0.9975	0.9976	0.9977	0.9977	0.9978	0.9979	0.9980	0.9980	0.9981
2.9	0.9981	0.9982	0.9983	0.9983	0.9984	0.9984	0.9985	0.9985	0.9986	0.9986
3.0	0.9987	0.9987	0.9987	0.9988	0.9988	0.9989	0.9989	0.9989	0.9990	0.9990
3.1	0.9990	0.9991	0.9991	0.9991	0.9992	0.9992	0.9992	0.9992	0.9993	0.9993
3.2	0.9993	0.9993	0.9994	0.9994	0.9994	0.9994	0.9994	0.9995	0.9995	0.9995
3.3	0.9995	0.9995	0.9995	0.9995	0.9996	0.9996	0.9996	0.9996	0.9996	0.9997

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Osprey Sports stocks everything that a musky fisherman could want in the Great North Woods. A particular musky lure has been very popular with local fishermen as well as those who buy lures on the Internet from Osprey Sports. The cost to place orders with the supplier is $40/order, the demand averages 5 lures per day, with a standard deviation of 1 lure; and the inventory holding cost is $1.00/lure/year. The lead time form the supplier is 9 days, with a standard deviation of 3 days. It is important to maintain a 97 percent cycle-service level to properly balance service with inventory holding costs. Osprey Sports is open 350 days a year to allow the owners the opportunity to fish for muskies during the prime season. The owners want to use a continuous review inventory system for this item. Refer to the standard normal table for z-values. a. What order quantity should be used? 374 lures. (Enter your response rounded to the nearest whole number.) b. What reorder point should be used? 75 lures. (Enter your response rounded to the nearest whole number.) c. What is the total annual cost for this inventory systern? $ (Enter your response rounded to two decimal places.)

Answer 1

Average daily demand (d) = 5 units

Number of days per year = 350

Annual demand (D) = d × number of days per year = 5 × 350 = 1750 units

Ordering cost (S) = $40

Holding cost (H) = $1

Economic order quantity (Q) = √(2DS/H)

= √[(2 × 1750 × 40)/1]

= √(140000/1)

= √140000

= 374 units

C) Annual ordering cost = (D/Q)S = (1750/374)40 = $187.17

Annual holding cost = (Q/2)H = (374/2)1 = $187

Total annual cost = Annual ordering cost + Annual holding cost = $187.17 + $187 = $374.17