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Q3. Discuss the various models of Inventory system. Give practical life examples.
Definition of Inventory
The term inventory includes materials- raw, in process, finished packaging, spares, and others stocked in order to meet an unexpected demand or distribution in the future.
Objectives of Inventory
- Ensures a continuous supply raw materials and supplies to facilitate uninterrupted production.
- Maintain sufficient finished goods for smooth sales operation and efficient customer service.
- Inventories permit the procurement of raw materials in economic lot sizes as well as processing of these raw materials into finished goods is the most economical quantity known as “economic lot size”.
- Reduce dependencies of one another and enable the organisations to schedule its operations independently of another.
- Inventory management helps to reduce material handling costs.
- It helps to utilise people and equipment reasonably.
- It facilitates product display and service to customers.
Inventories cost money. The cost factor must be considered while taking any decision regarding inventories. Inventory cost includes ordering cost, carrying cost, out of stock or shortage cost and capacity cost. Each of these comprises several elements as shown below:
- Ordering Costs
- Cost of placing an order with a vendor of materials:
Preparing a purchase order
Receiving and inspecting the material
- Ordering from the plant:
Start-up scrap generated from getting a production run started
- Carrying Costs
- Costs connected directly with materials:
- Financial Costs
- Set up(or production change) costs
To make each different product involves obtaining the necessary materials, arranging specifi c equipment setups, filling out the required papers, appropriately charging time and materials, and moving out the previous stock of material. If there were no costs or loss of time in changing from one product to another, many small lots would be produced. This would reduce inventory levels, with a resulting savings in cost. One challenge today is to try to reduce these setup costs to permit smaller lot sizes.
- Shortage Costs
When the stock of an item is depleted, an order for that item must
either wait until the stock is replenished or be cancelled. When the demand is not met
and the order is cancelled, this is referred to as a stock out. A backorder is when the
order is held and filled at a later date when the inventory for the item is replenished.
There is a trade-off between carrying stock to satisfy demand and the costs resulting
from stock outs and backorders. This balance is sometimes is sometimes difficult to obtain because it may not be possible to estimate lost profits, the effects of lost customers, or lateness penalties. Frequently, the assumed shortage cost is little more than a guess, although it is usually possible to specify a range of such costs.
An inventory system provides the organizational structure and the operating policies for
maintaining and controlling goods to be stocked. The system is responsible for ordering and
receipt of goods: timing the order placement and keeping track of what has been ordered,
how much, and from whom.
- Single Period Inventory Model
In a single-period model, the items unsold at the end of the period is not carried over to the next period. The unsold items, however, may have some salvage values. In the single-period model and in some of the multi-period models, there remains only one question to answer: how much to order.
A single period model includes:-
- Computer that will be obsolete before the next order.
- Perishable Product.
- Seasonal Products such as bathing suits, winter coats etc.
- Newspaper and magazine.
Trade offs in single period model
Loss resulting from the items unsold
ML= Purchase price- Salvage value
Profit resulting from the items sold
MP= Selling price - Purchase price
Given costs of overestimating/underestimating demand and the probabilities of various demand sizeshow many units will be ordered?
Consider an order quantity Q
Let P = probability of selling all the Q units
= probability (demandï‚³Q)
Then, (1-P) = probability of not selling all the Q units
We continue to increase the order size so long as
Order maximum quantity Q such that
where P = probability (demandï‚³Q)
Single-periodinventory models are useful for a wide variety of service and manufactur- ing applications. Consider the following:
1 .Overbooking of airline flights.It is common for customers to cancel flight res- ervations for a variety of reasons. Here the cost of underestimating the number of cancellations is the revenue lost due to an empty seat on a flight. The cost of over- estimating cancellations is the awards, such as free flights or cash payments, that are given to customers unable to board the flight.
- .Ordering of fashion items.A problem for a retailer selling fashion items is that often only a single order can be placed for the entire season. This is often caused by long lead times and limited life of the merchandise. The cost of underestimating demand is the lost profit due to sales not made. The cost of overestimating demand is the cost that results when it is discounted.
- Any type ofone-timeorder.For example, orderingT-shirtsfor a sporting event or printing maps that become obsolete after a certain period of time.
Consider the problem that the newsperson has in deciding how many newspapers to put in the sales outside in a hotel lobby each morning. If the person does not put enough newspapers in the stand, some customers will not be to purchase a paper and the newsperson will lose the profit associated with these sales. On the other hand, if too many papers are placed in the stand, the newsperson will have paid for papers that were not sold during the day.
2. Fixed Order Quantity System or ‘Q’ System
A fixed quantity of material is ordered whenever the stock on hand reaches the reorder point. The fixed quantity of material ordered each time is the economic order quantity (EOQ). Fixed–orderquantity models attempt to determine the specific point,R, at which an order
will be placed and the size of that order,Q. The order point,R, is always a specified numberof units. An order of sizeQis placed when the inventory available (currently in stock and on order) reaches the point R.
When the new consignment arrives, the total stock shall be within the maximum and the minimum limits.
Advantages of ‘Q’ system
- Each material can be procured in the most economical quantity.
- Purchasing and inventory control personnel automatically devote attention to the items that are needed only when required.
- Positive control can easily be exertedto maintain total inventory investmentat the desired level simply by manipulatingthe planned maximum and minimum values.
Disadvantages Of ‘Q’ System
- The orders are raised at irregular intervals which may not be convenient to the suppliers.
- In case the lead time is very high, say three months, and the ordering quantity happens to be material supplies for one month, there would be two or three pending orders with the supplier each time and there is every likelihood that he may supply all orders at a time.
- The items cannot be grouped or ordered at a time since the reorder points occur irregularly.
- EOQ may give you an order quantity which is much below the supplier minimum, and there is always a chance that the ordering level for an item has been reached but not noticed in which case a stock-out may occur.
- Further, the system assumes stable usage and definite lead time. When these change significantly, a new order quantity and a new order point should be fixed, which is quite cumbersome.
Now, the following points must be considered
- An order quantity of EOQ works well
- If demand is constant, reorder point is the same as the demand during the lead time.
- If demand is uncertain, reorder point is usually set above the expected demand during the lead time
- Reorder point = Expected demand + Safety stock
The EOQ model can be applied to any quantity decision that is repeated over time, where there is a trade-off between a fixed cost (i.e., EOQ’s order cost K) and a variable cost associated with that decision (i.e., EOQ’s inventory-holding cost), and where the choice is based on minimizing the cost/time associated with that decision. The most popular such application involves the management of cash. The simplest version of a cash-management scenario corresponds to the basic EOQ scenario, but with its inputs reinterpreted. In particular: (1) D is the rate at which cash is being accumulated from some business activity into a noninterest bearing account (e.g., checking account); (2) h is the interest being paid in an interest-bearing account (e.g., money-market account), and is measured in dollars/(dollar x time); and (3) K is the fixed cost incurred in transferring any amount of money, Q, from the non-interest to the interest-bearing account. Hence, Q* from (4) is the optimal transfer quantity.
Fixed-Order Period System or ‘P’ System
In this, the stock position of each item of material is regularly reviewed. When the stock level of a given item is not sufficient to sustain the production operation until the next scheduled review, an order is placed replenishing the supply. The frequency of reviewsvary from firm to firm. It also varies among materials within the same firm, depending upon the importance of the material, specific production schedules, market conditionsand so forth, likewise, vary for different materials.
Advantages of ‘P’ System
- The ordering and inventory costs are low. The ordering cost is considerably reduced through follow-up work for each delivery may be necessary.
- The suppliers will also offer attractive discounts as sales are guaranteed.
- The system works well for materials which exhibit an irregular or seasonal usage and whose purchases must be planned in advance on the basis of sales estimates.
Disadvantages of ‘P’ System
- It compels a periodic review of all items, this in itself makes the system somewhat inefficient. Because of differences in usage rates, supplies may not have to be ordered until the succeeding review. Conversely, the usage of some items during the period may have increased to the point where they should have been ordered before the review date. Consequently, this system must be augmentedwith a minimum balance figure which signals the need for an early reorder in the case of a sharp usage increase.
- Equally important, the system demands the establishment of rather inflexible order quantities in the interest of administrative efficiency. Theoritically, there exists an optimum economic order quantity for each item, depending upon its price structure, its rate of usage and attendant internal costs. However, because all items must fit reasonably well into a limited number of ordering cycles. Under this system, actual order quantities may deviate substantially from the optimum.
- The periodic review system tends to peak purchasing work around the review dates.
Example Placing orders on a periodic basis is desirable in situations where vendors make routine visit to customers and take orders for their complete line of products, or when buyers combine orders to save transportation costs.