Sathya Industries has the following demand forecasted for the next 12 months.

Month 1 2 3 4 5 6 7 8 9 10 11 12 Demand

(units)

900 700 800 400 500 800 900 300 200 800 700 700 The firm can have the strategies of overtime, sub-contracting, and inventory in its aggregate planning of production.

Given the following details, develop an optimal production plan for the firm. (The demands of the customer are always met.)

(a) Regular-time production capacity : 600 units per month, maximum

(at a work force level of 24 persons)

(b) Overtime production capacity : 100 units per month, maximum

(c) Beginning inventory : 50 units

(d) Desired inventory at the end of 12 months : 150 units

(e) Cost of regular production : Rs. 100 per unit

(f) Cost of overtime production : Rs. 160 per unit

(g) Cost of sub-contracting : Rs. 180 per unit

(h) Inventory Carrying Cost : Rs. 36 per unit per annum