# Demand Management Problems

Question 1:

A San Antonio stockyard uses about 200 bales of hay per month and pays a broker $80 per order to locate a supplier who handles the ordering and delivery arrangements. Its own storage and handling costs are estimated at 30 per cent per year. If each bale costs $3, what is the most economical order quantity and how many times a year broker's services should be used?

Question 2:

Far West Freeze-Dry company purchases 1200 tins of tea annually in economic order quantity lots of 100 tins and pays $9.85 per tin. If processing costs for each order are $10, what is the implied carrying cost of this policy?

Question 3:

A manufacturer requires 6000 printed circuit boards per year and estimates an ordering cost of $20 per order. Inventory is financed by short term loans at approximately 10%, which work out to a interest carrying charge of $0.10 per unit per year. Storage and housing costs are $0.25 per unit per year, and the purchase price is $1 per unit.

a) Find the most economic order quantity.

b) Find total annual cost of inventory, and

c) The number of orders placed per year.

Question 4:

A producer of photo equipment buys lenses from a supplier at $100 each. The producer requires 125 lenses per year, and ordering costs is $18 per order. Carrying costs per unit per year are estimated to be 20% of purchase price. The supplier offers a per unit discount of six percent for purchases of 50 or more lenses and an 8% discount for purchases 100 or more at one time. What is the most economical amount to order at a time?

Question 5:

Golden Valley cannery uses 64000 size 7-X cans annually and can purchases any quantity up to 10,000 cans at $0.40 per can. At 10,000 cans the unit cost drops to $0.32 per can, and for purchases of 30,000, it is $0.30 per can. The cost of ordering are $24 per order and interests costs are 20% of the price per can and apply to the average inventory.

a) What is the EOQ, disregarding the quantity discounts.

b) What is the most economical order quantity , considering quantity discounts

Question 6:

A store sells car batteries. The monthly sales are as follows:

Month Jan Feb Mar Apr May Jun July Aug Sep Oct Nov Dec

Sales 20 21 15 14 13 16 17 18 20 20 21 23

Forecast next month (i.e. next Jan) demand using each of the following methods:

a) Naïve approach

b) 3-month moving average

c) 6-month weighted moving average using 0.1, 0.1, 0.1, 0.2, 0.2 and 0.3 with heaviest weight applied to the most recent months.

d) Exponential smoothing using an alpha= 0.3 and Sept forecast of 18.

e) A trend projection method

f) At this point in time, which method allows you to forecast next March's sales?

Question 7:

HP uses X63 chip in their computers and prices for these chips for last 12 months are:

Month Jan Feb Mar Apr May Jun July Aug Sep Oct Nov Dec

Price ($) 1.80 1.67 1.70 1.85 1.90 1.87 1.80 1.83 1.70 1.65 1.70 1.75

Forecast next month (i.e. next Jan) sales price using each of the following:

a) First use 2-month and then 3-month moving average method to forecast sales price. Using MAD approach, which average is better?

b) If the initial Jan forecasts were also $1.80; in an exponential smoothing method, first use alpha= 0.1 and then alpha= 0.5; Using MSE approach, which value of alpha is better to predict sales price?

c) In practice, both MAD and MSE can be used to find forecast accuracy giving the same decisions. Why would you choose one over the other?

Question 8:

Sales for a product are as follows:

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

Sales 7 9 5 9 13 8 12 13 9 11 7

Forecast demand using each of the following:

a) From month 4 to month 12, forecast demand using a 3-month moving average.

b) From month 4 to month 12, forecast demand using a 3-month weighted moving average with weights of 0.1, 0.3, 0.6 using 0.6 for most recent month.

c) Using MSE approach, which method (MA or WMA) gives better results?

Question 9:

A company sells vacuum cleaners. Monthly sales for last seven-months are:

Month Feb Mar Apr May Jun July Aug

Sales (1000) 19 18 15 20 18 22 20

Forecast Sept sales using each of the following:

a) A trend-projection method.

b) A 5-month MA.

c) Exponential smoothing with alpha = 0.20 and a March forecast of 19(1000).

d) A weighted average using weights 0.6 for August; 0.30 for July and 0.10 for June.

Question 10:

Room occupancy (in thousand rooms) at the Sheraton Vancouver hotel has been recorded for the last 9 years. The management wants to use trend projection method to evaluate if they need to plan for future expansion. Forecast the occupancy for 2011.

Year 2001 2002 2003 2004 2005 2006 2007 2008 2009

Occupancy (1000) 17 16 16 21 20 20 23 25 24

#### Solution Summary

There are 10 problems. Solutions to given problems explain the methodology to calculate economic order quantity, carrying costs, order costs. Solutions also explain the steps to make a forecast by using moving and weighted average, exponential smoothing and trend projection methods.