A manufacturer has to supply to his customer 600 units of his product per year. Storage is not allowed and the inventory carrying cost amounts to 0.60 per unit per year. The set up cost per run is 80. Find:
(i) The economic order quantity (i) The minimum average yearly cost
(iii) The optimum number of orders per year (iv) The optimum period of supply per optimum order.
Answers
Answer:
Introduction
In the last lesson we have seen that maintenance of proper Inventory Control System helps in keeping the investment in Inventories as low as possible and yet (i) ensures availability of materials by providing adequate protection against supply uncertainty and consumption of materials and (ii) allows full advantages of economies of bulk purchases and transportation costs. The basic Inventory Control problem therefore lies in determining firstly when should an order for materials be placed and secondly how much should be produced at the beginning of each time interval or what quantity of an item should be ordered each time. In this lesson we will learn how to develop inventory model.
11.2 Variables in Inventory Problem
The variables used in any inventory model are of two types: Controlled and Uncontrolled variables
11.2.1 Controlled variables
The following are the variables that may be considered separately or in combination:
� How much quantity acquired
� The frequency or timing of acquisition .How often or when to replenish the inventory?
� The completion stage of stocked items.
11.2.2 Uncontrolled variables
The following are the principal variables that may be controlled:
� The holding costs, shortage or penalty cost, set up costs.
� Demand: It is the number of units required per period and may be either known exactly or is known in terms of probabilities or is completely unknown. Further if the demand is known, it may be either fixed or variable per unit of time. The model which has fixed demand is known as deterministic model.
� Lead Time: This is the time of placing an order and its arrival in stock as shown in Fig. 11.1. If the lead time is known and not equal to zero and if demand is deterministic then one should order in advance by an amount of time equal to lead time. If the lead time is zero then there is no need to order in advance. If lead time is variable then it is known as probabilistically.
Fig. 11.1 Inventory with constant demand rate and constant lead time
� Amount delivered (supply of goods) : The supply of goods may be instantaneous or spread over a period of time .If a quantity q is ordered for purchase, the amount delivered may very around g with known probability density function .