Question

Please answer all parts in detail. Thank you.

Q2. A toy manufacturer started a new production plant. The plant manager wishes to optimize the inventory costs of the company’s best-selling doll. The monthly demand for the doll is 1000 and the plant works 240 days per year. The plant can produce the doll at a rate of 100 dolls per day. The cost to prepare the equipment to start a production run is $160 and the annual inventory carrying cost is $3 per year.

(a) What is the optimum quantity of dolls to produce?

(b) What is the maximum inventory achieved during a production run?

(c) How many production runs are needed to meet the annual demand?

(d) What is the length of a production run?

(e) What is the average inventory of the doll?

(f) What is the total annual cost of producing and storing the company’s best-selling doll?

Answer 1

Monthly demand = 1000

Annual demand (D) = 1000*12 = 12000

Number of work days in an year = 240

Usage rate (u) = Annual demand/Number of work days in an year = 12000/240 = 50 per day

Production rate (p) = 100 per day

Set up cost (S) = 160

Holding cost (H) = 3

a) Optimum quantity (Q) = sqrt(2*D*S/H)*sqrt(p/(p-u)) = sqrt(2*12000*160/3)*sqrt(100/(100-50)) = 1600

b) Maximum inventory (Imax) = Q*(p-u)/p = 1600*(100-50)/100 = 800

c) Number of production runs = D/p = 12000/100 = 120 runs

d) Length of production run = Q/p = 1600/100 = 16 days

e) Average inventory = Imax/2 = 800/2 = 400

f) Total cost = Carrying cost + Setup cost = Average inventory*H + D/Q*S = 400*3 + 12000/1600*160 = 2400