forecasting and inventory calculation

Exercise Problems for Chapter 4

Problem 4.4

A manufacturing firm located in Calgary produces an item in a 3-month time supply. An analyst, attempting to introduce a more logical approach to selecting run quantities, has obtained the following estimates of the characteristics of the item. Assume that the production rate is much larger than D.

D = 4,000 units/year A = $5 v = $4 per 100 units r = $0.25/year

a. What is the EOQ of the item?

b. What is the time between consecutive replenishment of the item when EOQ is used?

c. The production manager insists that the A = $5 figure is only a guess. Therefore, he insists on using his simple 3-month supply rule. Indicate how you would find the range of A values for which the EOQ (based on A = 5) would be preferable (in terms of a lower total replenishment and carrying costs) to the 3-month supply.

Problem 4.9

A mining company routinely replaces a specific part on a certain type of equipment. The usage rate is 40 per week and there is no significant seasonality. The supplier of the part offers the following all-units discount structure. Orders less than 300 units have a cost of $10.00 per unit. Orders equal to or larger than 300 units cost $9.70 per unit. The fixed cost of a replenishment is estimated to be $25 and a carrying charge of $0.26/yr is used by the company.

a. What replenishment size should be used?

b. If the supplier was interested in having the mining company acquire at least 500 units at a time, what is the largest unit price they could charge for an order of 500 units?

Problem 4.11

A particular product is produced on a fabrication line. Using the finite replenishment EOQ models, the suggested run quantity is 1,000 units. On a particular day of production, this item is being run near the end of a shift and the supervisor, instead of stopping at 1,000 units and having to set up for a new item (which would make her performance look bad in terms of the total output), continues to produce the item to the end of the shift, resulting in a total production quantity of 2,000 units. Discuss how you would analyze whether or not she made a decision that was attractive from a company standpoint. Include comments on the possible intangible factors.

Problem 4.17

Monopack is a manufacturer of a single product. The company has been concerned about the rising inflation rate in the economy for sometime. Currently, Monopack does not incorporate the effects of inflation into its calculation of its EOQ. The company is interested in finding out if inflation will impact its choice of replenishment sizes. Characteristics of the product were found to be

D = 3,000 units/yr A = $5.45 v = $0.60 / unit r = 20%

Assume that the product price is established independent of the ordering policy and that inflation affects A and v in the same manner.

a. Calculate the EOQ in units.

b. Calculate the optimum replenishment quantities when the inflation rate is i = 0.2%, 4%, 9%, and 15%.

c. Calculate the PCP associated with using the EOQ (ignoring inflation) for all values of i.

d. What is the limiting value of the PCP?