John is the manager at a grocery store. The average demand for a brand of cereal

Question

John is the manager at a grocery store. The average demand for a brand of cereal is 5 boxes per week. Each box costs $6. The replenishment lead time of the supplier is 3 weeks and the demand during that time has a Poisson distribution. It costs $20 to place a replenishment order and John has decided to place orders to guarantee a service level of 99% and incur an annual ordering cost of $400. Holding costs are based on a 20% annual rate and the cost a back order is $35 per unit-year. Assume 52 weeks/year.

a) What is the total inventory holding cost?

b) what is the total back order cost per year?

c) What is the safety stock?

Explanation / Answer

Weekly demands 5 Units D Annual Demand 260 Units K Ordering cost 20 $ h Holding cost/unit 1.200 $ P Cost per unit 6 $ W Working Weeks 52 week LT Lead time 3 week Q Economic lot size 93.09493363 Units Optimal Prod quantity Sqtr((2*Annual Demand*order cost)/Annual inventory carrying cost) (sqrt(2*KD/h) Avg S Avg Stock (Q/2) 46.54746681 47 Avg Stock N Optimal no of orders 2.792848009 (Demand/EOQ) 3 No of Orders DBO Week between order (W/N) 18.61898673 18.62 Days Cycle time TC Total cost ((KD/Q)+(hQ/2)) 111.71 $ Total cost OC Ordering cost (KD/Q) 55.86 $ HC Holding cost (hQ/2)) 55.86 $ Ans A PC Production cost (P*D) 1560.00 $ GTC 1671.71 $ LTD Lead time mean 15.00 Units Service level 99% SS Safety stock 49.8952 Poisson distribution for 99% and M=15 Ans C 50.0 Units B Back order 10.0000 Poisson distribution for 01% and M=15 Back order cost 1050.0000 $ ($35*3 orders *B units per order) Ans B

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