Question

Surved Help Sove & Exit Given the following information, formulate an inventory management system. The item is demanded 50 weeks a year. PARAMETER Item cost Order cost Annual holding cost Annual deland Average Keekly demand VALUE $ 7.00 $283.ee 32% of item cost 22,100 442 per week PARAMETER Standard deviation of weekly demand Lead time Service probability VALUE 20 per week 1 week 95% a. Determine the order quantity and reorder point (Use Excel's NORM.S.INV() function to find the z value. Round z value to 2 decimal places and final answer to the nearest whole number.) Optimal order quantity Reorder point units units b. Determine the annual holding and order costs. (Round intermediate calculations to 2 decimal places. Round your answers Herimal places. < Prev 10 of 15 Next > о е 9 70%

Answer 1

Note: In case of any decimal rounding off issues, please mention it in the comment so that I can rectify it for you. Thank you.

(A)

Annual Demand (D) = 22,100

Weekly demand (d) = 442

Item cost (C) = $ 7

Annual Holding cost percent (h) = 32%

Order cost (S) = $ 283

Standard deviation of lead time (s) = 20

Lead time (LT) = 1 week

Service Probability = 95%

Value of Z corresponding to 95% service = 1.64

$EOQ=\sqrt{\frac{2.D.S}{C.h}}$

$EOQ=\sqrt{\frac{2X22100X283}{7X0.32}}$

EOQ = 2363 (rounded off)

Optimal Order Quantity = 2363 units

$Re-OrderPoint=d.L+Z.s.\sqrt{L}$

Re-order point = (442 × 1) + (1.64 × 20 ×1)

Re-Order Point = 475 (rounded off)

Therefore, re-order point = 475 units

(B)

Number of orders = D/Q

Number of orders = 22100/2363

Number of orders = 9.35

Ordering cost = Number of orders × S

Ordering cost = 9.35 × 283

Ordering cost = $ 2,646.05

Holding cost = (Q/2) × C × h

Holding cost = (2363/2) × 7 × 0.32

Holding cost = $ 2646.56

(C)

Discount on ordering cost (S') = $ 50

Quantity (Q) = 2200

Savings = (D/Q) × S'

Savings = (22100/2200) × 50

Savings = $ 502.27