NOTES PROBLEMS

NOTES

A. Demand Forecasting

1. A trucking company would like to determine the number of drivers and trucks to be available on a weekly basis. The standard schedule is to send drivers over the pick up and delivery route on Monday and return them to the originating point on Friday. The trucking requirements can be determined from the total volume to be moved for the week; however, they must be known a week in advance for planning purposes. The volume for the last ten weeks is given here:

Week Volume Week Volume

10 weeks ago 20,60,000 5 weeks ago 23,65,000 9 weeks ago 22,50,000 4 weeks ago 27,50,000 8 weeks ago 18,95,000 3 weeks ago 21,20,000 7 weeks ago 15,15,000 2 weeks ago 24,00,000 6 weeks ago 12,92,000 This week 25,10,000

(i) Using exponential smoothing model, predict the expected volume for the next week for á = 0.20.

(ii) Estimate the forecast error.

(iii) Find the range over which the actual volume is likely to vary.(Hint: Compute statistical confidence band. Assume 95% confidence level)

1. For the problem (1) if â = 0.2, what is the trend corrected forecast for the next week?

2. An electric company has a difficult in predicting the quarterly sales for its room air conditioner due to the substantial seasonality in product sales. Quarterly sales data for the last three years are shown as follows:

Last year Two years ago Three years ago Quarter Units Quarter Units Quarter Units

1 35000 1 30000 1 28000

2 80000 2 72000 2 68000

3 50000 3 45000 3 42000

4 18000 4 16000 4 12000

i) Determ ine the best straight line trend using simple regression analysis.

ii) Determine the seasonal indices for each quarter using the trend line values in your seasonal index computations.

iii) By means of decomposition, forecast the sales for the next four quarters.

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B. Inventory Management

1. An equipment manufacturer purchases lubricants at the rate of Rs 50 per unit from a vendor. The requirement of these lubricants is 2000 per year. What should be the order quantity per order, if the cost per placement of an order is Rs 20 and inventory carrying charge is 20% of the average inventory value?

2. An item is produced at the rate of 100 per day. The demand occurs at the rate of 75 per day. If the setup cost is Rs 125 and holding cost is Rs 0.05 per unit of item per day, find the economic lot size for one run, assuming that shortages are not permitted. Also, find the time of cycle and minimum total cost for one run.

3. .Find the optimum order quantity for the following

NOTES

Annual Demand = 4000 units

Ordering cost = Rs 100

Cost of carrying inventory = 20% of the unit cost.

Quantity range Price/Unit (Rs)

Upto 99 20.00

100 - 199 18.00

>=200 16.00

4. A shop keeper has uniform demand of an item at the rate of 100 per month. He buys from supplier at a cost of Rs 10 per unit and cost of ordering is Rs 18 each time. If the sock holding costs are 20% per year of stock value, how frequently should be replenish his stock? Now suppose the supplier offers a 5% discount on orders between 300 and 999 items, and a 10% discount on orders exceeding or equal to 1000. Can shop keeper reduce his costs by taking advantage of either of these discounts?

5. A firm uses Rs 40,000 worth of a raw material per year. The ordering cost per orders is Rs 120 and the carrying cost is 20% per year of the average inventory. If the company follows the EOQ purchasing policy, calculate the re-order point, the maximum inventory and the average inventory, given that the firm works for 300 days a year, the replenishment time is 12 days and the safety stock is worth Rs 500.

6. A newspaper boy buys paper for Rs 1.50 each and sells them for Rs 2.00 each. He cannot return unsold newspapers. Daily demand has following distribution:

Number sold 22 23 24 25 26 27 28 29 30 31

Probability 0.01 0.03 0.06 0.1 0.2 0.25 0.15 0.1 0.05 0.05 If each day‟s demand is independent of the previous day‟s demand, how many papers should be ordered each day?

NOTES

1. A company‟s marketing manager has estimated the following demand requirement for the forth coming periods:

Period Forecast Period Forecast

1 1600 5 2400

2 1800 6 2500

3 2000 7 2000

4 2100 8 1600

The operations manager is considering the following plans

Plan 1: maintain a stable workforce that is capable of producing 2000 units per period, and meet the demand by overtime at a premium of Rs 25 per unit. Idle time costs are equivalent to Rs 30 per unit. Do not build to inventory.

Plan 2: produce at a steady state of 1800 units per period, and a limited number of backorders during periods when demand exceeds 1800 units. The stock out cost of lost sales is Rs.100 per unit. Inventory costs per period are Rs.20 per unit.

Plan 3: produce at a steady rate equal to minimum requirements of 1600 units and subcontract the additional units at a Rs.75 per unit premium.

Plan 4: vary the workforce level, which is currently capable of producing 1600 units per period. The cost of additional workforce per 100 units is Rs.5000 and the cost of layoffs per 100 units is Rs.7500.

Plan 5: vary inventory levels, but maintain a stable workforce level by maintaining a constant production rate equal to the average requirements. The company can accumulate required inventory before period 1 at no additional cost. The inventory cost per period is Rs.20 per unit. Plot a histogram for the demand and show the average requirements on your graph.

Discuss the merits and demerits of these plans. Which plan would you recommend?

2. Refer Seetharaman

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NOTES

UNIT V