EFIM20005 Management Science
Questions for Inventory Models Covered in Week 15
Question 1
A company examines one inventory item and decides that holding costs are about 25% of value a year, while shortage cost for back-orders is 150% of value a year. Unit cost is £400 and reorder cost is £100. Demand is constant at 300 units a year and all shortages are met by back- orders. What is the optimal policy for this item? What proportion of time is demand met by back-orders?
Question 2
Demand for an item is constant at 100 units a year. Unit cost is £50, reorder cost is £40, shortage cost is £30 per year and holding cost is 40% of value a year. Any demand which occurs when no stock remains is lost. What is the minimum selling price which makes it profitable to stock the item (answer will be expressed in terms of the shortage cost)?
Question 3
A perishable dairy product is ordered daily at a particular supermarket. The product, which costs £1.19 per unit, sells for £1.65 per unit. If units are unsold at the end of the day, the supplier takes them back at a rebate of £1 per unit. Assume that daily demand can be reasonably approximated by the following table:
|
Demand
|
10
|
20
|
30
|
40
|
50
|
60
|
70
|
|
Probability
|
0.05
|
0.15
|
0.4
|
0.2
|
0.1
|
0.05
|
0.05
|
a) What is your recommended daily order quantity for the supermarket?
b) What is the probability the supermarket will sell all the units it orders, if it adopts your recommendation from (a)?
c) In problems such as these, why would the supplier offer arebate as high as £1? For example, why not offer a nominal rebate of, say, 25p per unit? What happens to the supermarket order quantity as the rebate is reduced?
Question 4
The Bridgeport city manager and the chief of police agreed on the size of the police force necessary for normal daily operations. However, they need assistance in determining the number of additional police officers needed to cover daily absences due to injuries, sickness, vacations, and personal leave. Records over the past three years show that the daily demand for additional police officers is uniformly distributed between 30 and 70. The cost of an additional police officer is based on the average pay rate of $150 per day. If the daily demand for additional police officers exceeds the number of additional officers available, the excess demand will be covered by overtime at the pay rate of $240 per day for each overtime officer.
(a) If the number of additional police officers available is greater than demand, the city will have to pay for more additional police officers than needed. What is the cost of overestimating demand?
b) If the number of additional police officers available is less than demand, the city will have to use overtime to meet the demand. What is the cost of underestimating demand?
c) What is the optimal number of additional police officers that should be included in the police force?
d) On a typical day, what is the probability that overtime will be necessary?
Question 5
Floyd Distributors Inc provides a variety of auto parts to small local garages. Floyd purchases parts from a manufacturer according to the EOQ model and then ships the parts from a regional warehouse direct to its customers. For a particular type of muffler, Floyd’s EOQ analysis recommends orders with Q = 25 to satisfy an annual demand of 200 mufflers. Floyd has 250 working days per year and the lead time averages 15 days.
a. What is the reorder point if Floyd assumes a constant demand rate?
b. Suppose lead time demand follows a normal distribution with mean = 12 and standard deviation = 2.5. If Floyd’s management can tolerate one stock-out per year, what is the revised reorder point?
c. What is the safety stock for (b). If H = $5 / unit / year, what is the extra cost due to the uncertainty of demand?