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PERIODIC REVIEW MODEL WITH PROBABILISTIC DEMAND 443

The cycle time between production batches is given terms it will probably be easier to schedule produc-
by Equation (10.7): tion every three months (60 working days) and,
assuming a constant demand of 500 t-shirts per
240Q 240 1414 month, to produce batches of 1500. Although tech-
T ¼ ¼ ¼ 56:6 days
D 6000 nically this is not the minimum cost solution, in
practical terms it will be easier for the cooperative
In other words the t-shirts should be produced in
to plan and manage.
batches of 1414 every 56.6 working days. In practical

Problems

1 Suppose that the CBC has a soft drink product that shows a constant annual demand
rate of 3600 cases. A case of the soft drink costs CBC E3. Ordering costs are E20 per
order and holding costs are 25 per cent of the value of the inventory. CBC has 250
workingdaysper year,and theleadtimeisfivedays. Identify thefollowing aspectsof
the inventory policy.
a. Economic order quantity.
b. Reorder point.
c. Cycle time.
d. Total annual cost.
2 A general property of the EOQ inventory model is that total inventory holding and
total ordering costs are equal at the optimal solution. Use the data in Problem 1 to
show that this result is true. Use Equations (10.1), (10.2) and (10.3) to show that,
in general, total holding costs and total ordering costs are equal whenever Q*
is used.
3 The reorder point [see Equation (10.6)] is defined as the lead-time demand for an item. In
cases of long lead times, the lead-time demand and thus the reorder point may exceed the
economic order quantity Q*. In such cases, the inventory position will not equal the
inventory on hand when an order is placed, and the reorder point may be expressed in
terms of either the inventory position or the inventory on hand. Consider the economic
order quantity model with D ¼ 5000, C o ¼ E32, C h ¼ E2 and 250 working days per year.
Identify the reorder point in terms of the inventory position and in terms of the inventory on
hand for each of the following lead times.
a. 5 days.
b. 15 days.
c. 25 days.
d. 45 days.
4 Suyuti Auto purchases a component used in the manufacture of automobile generators
directly from the supplier. Suyuti’s generator production operation, which is operated at a
constant rate, will require 1000 components per month throughout the year (12 000 units
annually). Assume that the ordering costs are E25 per order, the unit cost is E2.50 per
component and annual holding costs are 20 per cent of the value of the inventory. Suyuti
has 250 working days per year and a lead time of five days. Answer the following inventory
policy questions.

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