Capacities of production of an item over 3 consecutive months in regul...
Given:- Capacities of production in regular time: 100, 100, 80
- Capacities of production in overtime: 20, 20, 40
- Demands over 3 months: 90, 130, 110
- Cost of production in regular time: Rs. 20 per item
- Cost of production in overtime: Rs. 24 per item
- Inventory carrying cost: Rs. 2 per item per month
- Starting and final inventory levels: nil
- Backorder not permitted
Objective:To determine the level of planned production in overtime in the third month for minimum cost of plan.
Step-by-step Solution:
1. Calculate the regular time production needed:
- Regular time production = Demand - Inventory
- Month 1: Regular time production = 90 - 0 = 90
- Month 2: Regular time production = 130 - 0 = 130
- Month 3: Regular time production = 110 - 0 = 110
2. Calculate the overtime production needed:
- Overtime production = Demand - Regular time production
- Month 1: Overtime production = 90 - 90 = 0
- Month 2: Overtime production = 130 - 130 = 0
- Month 3: Overtime production = 110 - 110 = 0
3. Calculate the cost of regular time production:
- Month 1: Cost of regular time production = Regular time production * Cost per item = 90 * 20 = Rs. 1800
- Month 2: Cost of regular time production = 130 * 20 = Rs. 2600
- Month 3: Cost of regular time production = 110 * 20 = Rs. 2200
4. Calculate the cost of overtime production:
- Month 1: Cost of overtime production = Overtime production * Cost per item = 0 * 24 = Rs. 0
- Month 2: Cost of overtime production = 0 * 24 = Rs. 0
- Month 3: Cost of overtime production = 0 * 24 = Rs. 0
5. Calculate the carrying cost of inventory:
- Carrying cost of inventory = Inventory * Carrying cost per item per month
- Month 1: Carrying cost of inventory = 0 * 2 = Rs. 0
- Month 2: Carrying cost of inventory = 0 * 2 = Rs. 0
- Month 3: Carrying cost of inventory = 0 * 2 = Rs. 0
6. Calculate the total cost:
- Total cost = Cost of regular time production + Cost of overtime production + Carrying cost of inventory
- Month 1: Total cost = 1800 + 0 + 0 = Rs. 1800
- Month 2: Total cost = 2600 + 0 + 0 = Rs. 2600
- Month 3: Total cost = 2200 + 0 + 0 = Rs. 2200
7. Determine the level