Q1.

A producer is considering either producing or procuring a certain part. The relevant data are as follows:

Initial inventory is 20 units and holding cost is Rs 5 per unit per period. Develop an aggregate production plan. Backordering not permitted.

Q2.

A manufacturer has the following information on its major product:

Regular time production capacity = 2600 units/period.

Regular time production cost = Rs 8 / unit.

Inventory carrying cost = Rs 2 /unit/period (based on ending inventory)

Backlog cost = Rs 5/unit/period.

Beginning inventory = 400 units

The demand forecast for the next 4 periods are 4000, 3200, 2000, 2800. Develop a production plan assuming uniform level of production that yields zero inventory at the end of period 4. What is the total cost of this plan?

Q3.

A manufacturing firm is trying to schedule for the coming three months. The product demands are 300, 250, 325 units respectively. Current Inventory is 95 units. At the end of the 3 months period, the finished inventory must be 120 units. Regular time production capacity is 200 units/month at a cost of Rs 10/unit. Overtime capacity is 200 units/month at a cost of Rs 10/unit. Overtime capacity is 100 units/month at a cost of Rs 15/unit. The inventory carrying cost is Rs 2.unit/month.

Structure the problem in a transportation LP format. Determine the master schedule or aggregate plan.

Q4.

Determine the optimum production plan.

Q5.

Two products A and B are manufactured on the same machine. Demand for each product over the next 6 weeks is as follows:

The machine is operated for 40 regular time hours per week maximum and overtime is limited to 20% of the scheduled regular time. The production rates of the machine for product A&B are 9800 units/hr and 6900 units/hr. and overtime cost is Rs 400/hr. The inventory carrying rate is Rs 1/machine-hr/week.

Suggest the optimal aggregate production plan in terms of machine hours for these products.

Q6.

The forecast of the demand (in units) for a product for the next 6 months s as follows:

Manufacturing cost: Rs 200/unit, Inventory carrying cost: Rs 5/month/unit; Shortage cost: Rs 20/month/unit.

Initial inventory is 200 units. Ten man hours are required to produce a unit of the product. The work day consists of 8 hours. Develop an appropriate LP model for the aggregate production plan assuming constant workforce and assume 22 working days/month except in June where only 7 working days are available.