Reference no: EM13179040

Inventory control:
Suppose that you are employed by a local department store, and you are placed in charge of ordering vacuum cleaners. Based on the past experience, you know that the store will sell 500 vacuum cleaners per year. You must decide how many times a year to order vacuum cleaners and how many to get with each order. You could order all 500 at the beginning of the year, but there will be cost (the holding cost) for storing the unsold vacuum cleaners. You could order 5 at a time and place 100 orders over the course of the year, but there are cost for paper work and shipping for each order you place. Perhaps there is an amount to order somewhere between 5 and 500 that minimizes the total cost: The holding cost plus the reorder costs. This number is called the lot size.
To simplify the mathematics, we make two assumptions:
a. Demand for vacuum cleaners remains constant through the year.
b. Stock is immediately replenished exactly when the inventory level of vacuum cleaners reaches zero.
Here x is the lot size, the amount ordered each time inventory reaches zero. The graph signifies that the inventory is decreasing at a constant rate (lines with negative slope). The average number of items in the stock is x/2
Let D be the annual demand for the item. [for the vacuum cleaners, D = 500] Our goal is to find a function C = C(x), where C represents the holding costs plus the reorder costs and x is the lot size. We seek the value of x that minimizes C.