Example: Inventory System with Lost Sales and Backorders

It is described in different sources [1, 2]. So, this is chapter 11 of [2] and section 6.7 of [1].

A large discount house is planning to install a system to control the inventory of
a particular radio. The time between demands for a radio is exponentially distributed
with a mean time of 0.2 weeks. In the case where customers demand the radio when it
is not in stock, 80 percent will go to another nearby discount house to find it, thereby
representing lost sales, while the other 20 percent will backorder the radio and wait
for the next shipment arrival. The store employs a periodic review-reorder point
inventory system where the inventory status is reviewed every four weeks to decide if
an order should be placed. The company policy is to order up to the stock control level
of 72 radios whenever the inventory position, consisting of the radios in stock plus
the radios on order minus the radios on backorder, is found to be less than or equal to
the reorder point of 18 radios. The procurement lead time (the time from the placement
of an order to its receipt) is constant and requires three weeks.

The objective of this example is to simulate the inventory system for a period of six
years (312 weeks) to obtain statistics on the following quantities:

  1) number of radios in stock;
  2) inventory position;
  3) safety stock (radios in stock at order receipt times); and
  4) time between lost sales.

The initial conditions for the simulation are an inventory position of 72 and no
initial backorders. In order to reduce the bias in the statistics due to the initial
starting conditions, all the statistics are to be cleared at the end of the first year
of the six year simulation period.

[1] A. Alan B. Pritsker, Simulation with Visual SLAM and AweSim, 2nd ed.
[2] Труб И.И., Объектно-ориентированное моделирование на C++: Учебный курс. - СПб.: Питер, 2006