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Inventory Management

It is important to visualize inventory as stacks of money sitting on forklifts, on shelves, and in trucks and planes while in transit .

That’s what inventory is – Money.

For many businesses, inventory is the largest asset on the balance sheet at any given time.

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Inventory Management

The following techniques described are most appropriate when demand is difficult to predict with great precision.

The single-period model. This is used when we are making a one-time purchase of an item.
Fixed-order quantity model. This is used when we want to maintain an item “in-stock”, and when we resupply the item, a certain number of units must be ordered each time.
Fixed-time period model. This is similar to the fixed-order quantity model and is used when the item should be in-stock and ready to use.

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Inventory Management

Inventory is the stock of any item or resource used in an organization.

An inventory system is the set of policies and controls that monitor levels of inventory and determine what levels should be maintained, when stock should be replenished, and how large orders should be.

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Purposes of Inventory

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Purposes of Inventory

All firms (including JIT operations) keep a supply of inventory for the following reasons:

To maintain independence of operations. A supply of materials at a work center allows center flexibility in operations.

To meet variation in product demand. If the demand for the product is know precisely, it may be possible to produce the product to exactly meet the demand.

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Purposes of Inventory

All firms (including JIT operations) keep a supply of inventory for the following reasons:

To allow flexibility in production scheduling. A stock of inventory relieves the pressure on the production system to get the goods out.

To provide a safeguard for variation in raw material delivery time. When material is ordered from a vender, delays can occur for a variety of reasons.

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Purposes of Inventory

All firms (including JIT operations) keep a supply of inventory for the following reasons:

To take advantage of economic purchase order size. There are costs to place an order: labor, phone calls, typing, postage, and so on.

Many other domain-specific reasons. Depending on the situation, inventory may need to be carried.

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Inventory Costs

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Inventory Costs

In making any decision that affects inventory size, the following cost must be considered:

Holding (or carrying) costs. This broad category includes the costs for storage facilities, handling, insurance, pilferage, breakage, obsolescence, depreciation, taxes, and the opportunity cost of capital.

Setup (or production change) costs. To make each different product involves obtaining the necessary materials, arranging specific equipment setups, filling out the required papers, appropriately charging time and materials, and moving out the previous stock of material.

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Inventory Costs

In making any decision that affects inventory size, the following cost must be considered:

Ordering costs. These costs refer to the managerial and clerical costs to prepare the purchase or production order.

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 canceled.

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Independent versus Dependent Demand

In inventory management, it is important to understand the trade-offs involved in using different types of inventory control logic.

The following framework shows how characteristics of demand, transaction cost, and the risk of obsolete inventory map into different types of systems.

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Independent versus Dependent Demand

Transaction cost is dependent on the level of integration and automation incorporated in the system.

The risk of obsolescence is also an important consideration. If an item used infrequently or only for a very specific purpose, there is a considerable risk in using inventory control logic that does not track the specific source of demand for the item.

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Independent versus Dependent Demand

An important characteristic of demand relates to whether demand is derived from an end item or is related to the item itself.

Dependent demand

The need for an item is a direct result of the need for some other item usually an item of which it is a part.

Also, when the demand for the item can be predicted with accuracy due to a Schedule of specific activity.

Independent demand

The demands for these items are unrelated to each other, or to activities that can be predicted with certainty.

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Inventory control systems

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Inventory control systems

An inventory system provides the organizational structure and the operating policies for maintaining and controlling goods to be stocked.

We can divide systems into:

Single-period systems.
Multiple-period systems.

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A Single-Period Inventory Model

Answer the question of how much to order when an item is purchased only one time and it is expected that it will be used and then not reordered.

This model is useful for a wide variety of service and manufacturing applications:

Overbooking of airline flights.
Ordering of fashion items.
Any type of one-time order.

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Multi-period Inventory System

There are two general types of multiperiod inventory system:

Fixed-order quantity model. EOQ.
Fixed-time period model. P-Model.

Multiperiod inventory systems are designed to ensure that an item will be available on an ongoing basis throughout the year.

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Multi-period Inventory System

The basic distinction is that fixed-order quantity model are “event triggered” and fixed-time period models are “time triggered”.

Fixed-order quantity model. Initiates and order when the event of reaching a specified reorder level occurs.

Fixed-time period model is limited to placing orders at the end of a predetermined time period.

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Multi-period Inventory System

Fixed-time period model (P-model)

An inventory control model that specifies inventory is ordered at the end of a predetermined period. The interval of time between orders is fixed and the order quantity varies.

Fixed-order quantity model (Q-model)

An inventory control model where the amount requisitioned is fixed and the actual ordering is triggered by inventory dropping to a specified level of inventory.

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Multi-period Inventory System

Fixed-Order Quantity and Fixed-Time Period Differences

Feature	Q-Model�Fixed-Order Quantity Model	P-Model Fixed-Time Period Model
Order quantity	Q-Constant (the same amount ordered each time).	Q-Variable (varies each time order is placed).
When to place order	R-When the inventory position drops to the reorder level.	T-when the Review period arrives.
Recordkeeping	Each time a withdrawal or addition is made.	Counted only at Review period.
Size of inventory	Less tan fixed-time period model.	Larger than fixed-order quantity model.
Time to maintain	Higher due to perpetual recordkeeping.	Efficient, because multiple ítems can be ordered at the same time.
Type of ítems	Higher-priced, critical, or important ítems.	Typically used with lower-cost items.

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Multi-period Inventory System

Fixed-Order Quantity Models

This models attempt to determine the specific point, R, at which and order will be placed and the size of that order, Q. The order point, R, is always a specified number of units. An order of size Q is placed when the inventory available (currently in stock and on order) reaches the point R.

Inventory position

The amount on hand plus on-order minus backordered quantities

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Multi-period Inventory System

The first step is to develop a functional relationship between the variables of interest and the measure of effectiveness.

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Multi-period Inventory System

TC = Total annual cost.

D = Demand (annual).

C = Cost per unit.

Q = Quantity to be ordered.

S = Setup cost or cost of placing an order.

R = Reorder point.

L = Lead time.

H = Annual holding and storage cost per unit of average inventory.

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Multi-period Inventory System

The second step in model Development is to find that optimal order quantity Qopt at which total cost is a minimum.

Because the simple model assumes constant demand and lead time, neither safety stock nor stockout cost is necessary, and the reorder point, R, is simply:

d = Average daily demand (constant).

L = Lead time in days (constant).

R = dL

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Multi-period Inventory System

The Fixed-Order Quantity Model assumed that the demand was constant and known. In the majority of cases, though, demand is not constant but varies from day to day. Safety stock must therefore be maintained to provide some level of protection against stock outs.

Safety Stock. The amount of inventory carried in addition to the expected demand.

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Multi-period Inventory System

Fixed-Order Quantity Model with Safety Stock. A fixed-order quantity system perpetually monitor the inventory level and places a new order when stock reaches some level, R.

The danger of stockout in this model occurs only during the lead time, between the time and order is placed and the time it is received.

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Multi-period Inventory System

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Multi-period Inventory System

Fixed-Time period System

In a fixed-time period system, inventory is counted only at a particular times, such as every week or every month.

Counting inventory and placing order periodically are desirable in situations such as when vendors make routine visits to customers and take orders for their complete line of products, or when buyers want to combine orders to save transportation costs.

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Multi-period Inventory System

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Multi-period Inventory System

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Multi-period Inventory System

q = Quantity to be ordered.

T = The number of days between reviews.

L = Lead time in days (time between placing and order and receiving it).

d = Forecast average daily demand.

z = Number of standard deviations for a specified service probability.

= Standard deviation of demand over the review and lead time.

I = Current inventory level (includes items on order).

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Multi-period Inventory System

Inventory Turn Calculation

It is important for managers to realize that how they run items using inventory control logic relates directly to the financial performance of the firm.

Inventory turn = Cost of goods sold

Average inventory value

The inventory turn is a measure of the expected number of times inventory is replaces over a year.

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Multi-period Inventory System

Price-Break Model

The price-break model deals with the fact that, generally, the selling price of an item varies with the order size.

This model is useful for finding the order quantity of an item when the price of the item varies with the order size.

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Multi-period Inventory System

Price-Break Model

The calculations can be simplified in the following two-step procedure:

Sort the prices from lowest to highest and then, beginning with the lowest price, calculate the economic order quantity for each price level until a feasible economic order quantity is found.

If the first feasible economic order quantity is for the lowest price, this quantity is best and your finished. Otherwise, calculate the total cost for the first feasible economic order quantity and also calculate the total cost at each price break lower then the prices associated with the first feasible economic order quantity. This is the lowest order quantity at which you can take advantage of the price break. The optimal Q is the one with the lowest cost.

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Multi-period Inventory System

ABC Inventory Classification

This schemes divides inventory items into three grouping: high dollar volume:

High dollar volume.
Moderate dollar volume
Low dollar volume

Dollar volume is a measure of importance; an item low in cost but high in volume can be more important that a high-cost item with low volume.

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