Question

Please answer part e,f,g,h and bonus.

Thank you.

Q1. Betty bakes and sells bagels all year round. Betty plans and manages inventories of paper take-out bags with her logo printed on them. Daily demand for take-out bags is normally distributed with a mean of 90 bags and a standard deviation of 30 bags. Betty’s printer charges her $10 per order for print setup independent of order size. Bags are printed at 5 cents ($0.05) each bag. It takes 4 days for an order to be printed and delivered. Betty has a storage room big enough to hold all reasonable quantities of bags. The holding cost is estimated to be 25% per year. Assume 360 days per year. (Use the H= i × C formula to compute the annual holding cost).

(a) What is the optimal order quantity per order for Betty?

(b) How many times per year does Betty need to order?

(c) How many days will elapse between two consecutive orders?

(d) What is Betty’s total annual inventory-related cost (cost of placing orders and carrying inventory)?  

(e) What is the total cost per bag?

(f) What is Betty’s monthly inventory turns?

(g) If Betty wants to make sure the bags do not run out with 99% probability during the order lead time, what is her optimal reorder point? (Use z=2.33 for 99% service level)

(h) If Betty’s printer charges her $12 per order irrespective of order size, what is the total annual inventory-related costs per bag?

(i) (Bonus) Assume that the print cost can be reduced to 3 cents per bag if Betty prints 9000 bags or more at a time. If Betty is interested in minimizing her total cost (i.e., purchase and inventory-related costs), should she begin printing 9000 or more bags at a time?

Answer 1

Average demand, d = 90 bags per day
Stdev of daily demand, σ = 30 bags
Ordering cost, K = $10 per order
Unit cost, C = $0.05 per unit
Lead time, L = 4 days
Unit holding cost, h = 0.25 of C = $0.0125

(a)

Annual demand, D = 90*360 = 32400 units

Q = (2.D.K/h)^1/2 = SQRT(2*32400*10/0.0125) = 7200 units

(d)

Total cost = (Q/2)*h + (D/Q)*K = (7200/2)*0.0125 + (32400/7200)*10 = $90

(e)

The total cost per unit = 90/32400 = $0.0028

(f)

Monthly inventory turns = Monthly demand / Q = (90*30)/7200 = 0.375

(g)

ROP = d.L + z.σ.√L = 90*4 + 2.33*30*√4 = 500 units

(h)

K = $12

Q = (2.D.K/h)^1/2 = SQRT(2*32400*12/0.0125) = 7887 units

Total annual inventory cost = (Q/2)*h + (D/Q)*K = (7887/2)*0.0125 + (32400/7887)*12 = $98.60

So, inventory cost per unit = 98.60 / 32400 = $0.0030

(i)

The total annual inventory cost for the EOQ-based policy was $90.

Total cost including the printing cost = 90 + 0.05*32400 = $1,710 per annum ----------------1

For Q=9000, C=$0.03, h = 0.25*0.03 = $0.0075

Total annual inventory cost = (Q/2)*h + (D/Q)*K = (9000/2)*0.0075 + (32400/9000)*10 = $69.75

Total cost including the printing cost = 69.75 + 0.03*32400 = $1,042 per annum -------------2

From 1 and 2, it's obvious that printing 9000 bags is more economical.