Question

A chemical firm produces sodium bisulfate. Demand for this product is 400 bags per day. The capacity for producing the product is 1,000 bags per day. Setup costs 100 SR, and storage and handling costs are 0.25 SR per bag per year. The firm operates 200 days a year. Note: Round Qp to an integer value, but round any other values to a maximum of two decimals.

a. How many bags per run are optimal?

b. What would the average inventory be for this lot size?

c. Determine the approximate length of a production run, in days.

d. About how many runs per year would there be?

e. How much could the company save annually if the setup cost could be reduced to 25 SR per run?

Answer 1

Annual demand, D = 200 days *400 = 80000

Daily demand, d = 400

Production capacity, p =1000

Setup cost, S = 100 SR

Handling costm, H = 0.25 SR

a) Economic production quantity, EPQ, Qp = sqrt ((2*D*S) / (H * (1-d/p)))

= SQRT((2*200*400*100)/(0.25*(1-400/1000))) = 10327.96 or 10328 (Rounded off to integer value)

b) Average inventory = EPQ * (1-d/p) / 2= 10328 * (1-400/1000) / 2 = 3098.37

c & d) Length of production runs = Epq /p = 10328 / 1000 = 10.33 days

Total number of production runs = Demand / EPQ = 80000/10328 = 7.75 (Note - If you round this up to 8 runs then subsequent answers will change as well)

e) If the cost is reduced to 25 SR per run.

New EPQ. Qn = SQRT((2*200*400*25)/(0.25*(1-400/1000))) = 5164

Cost of setup and holding cost for Qp (10328) = (D/ Qp) * S + (EPQ/2) *(1-d/p) *H

= (80000/10328)*100 + (3098.37*0.25) = = 7.75*100 + (3098.37*0.25) = ~1549.59 SR

Cost of setup and holding cost for Qn (5164) = (D/ Qp) * S-new + (EPQ/2) *(1-d/p) *H

= (80000/5164)*25 + 5164 * (1-400/1000) / 2 * 0.25= 15.5*25 + 5164 * (1-400/1000) / 2 * 0.25 = ~774.80

Savings = 1549.59 - 774.80 = 774.80 SR