Inventory Modeling
Operations Management
What is inventory management?
Inventory is working capital and therefore the control of inventories is an important aspect of operations management.
The basic questions in the management of inventory are:
What is inventory management?
Purposes of Inventory
Purposes of Inventory
All firms (including JIT operations) keep a supply of inventory for the following reasons:
Purposes of Inventory
All firms (including JIT operations) keep a supply of inventory for the following reasons:
Purposes of Inventory
All firms (including JIT operations) keep a supply of inventory for the following reasons:
What is inventory management?
The principal functions of inventory
Basic Function
Inventory is needed for the definite consumption demand of materials, and to take care of the uncertainty involved in the usage or availability of the materials.
The inventory taking care of the first aspect of normal consumption is called the normal inventory and the inventory taking care of the second aspect of uncertainty is called the safety stock or buffer stock of inventory.
There are various other categories of inventories, anticipation inventory, transit inventory and pipeline inventory.
These are modified versions of the two concepts
Lot for Lot (L4L) as a technique…..
Lot-for-lot (L4L)
A common technique used to avoid differences between needed or used.
Inventory Costs
Relevant Costs
The relevant costs for the “how much” and “when” decisions of normal inventory keeping are:
Costs | Description |
Cost of capital | This is the opportunity cost of investing in inventory. |
Space Cost | This cost may be the rent paid for the space needed for the inventory. |
Material Handling Cost | The inventory needs to be moved within the warehouse and the factory. |
Insurance Costs | The firm might have taken insurance against a risk of fire, theft or pilferage of materials. |
Costs of General Administration | Inventory keeping will involve the use of various staff. |
Inventory Procurement Costs | When an order for procurement is to be placed to an external agency supplying the materials, there is a cost associated with activities such as tendering, evaluation of bids, ordering, etc. |
Models of Inventory
Optimal Order Quantity
The total relevant costs would show a minimum at a certain value of the order quantity. The latter is the desired optimal order quantity.
Optimal Order Quantity
Considering the cost that we have managing the inventory, it is important to analyze and calculate the quantity necessary to order to our supplier, this, with the minimum cost.
Optimal Order Quantity
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.
The Economic Order Quantity is 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.
Optimal Order Quantity
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
Optimal Order Quantity
The average inventory level (also called order-size or lot-size inventory) is inventory resulting from the acquisition or production of lots larger than those needed for immediate consumption or sale.
Average inventory level= Q / 2
The inventory carrying cost can be calculated by multiplying the average inventory by the cost of holding an item in inventory during the stated period.
Optimal Order Quantity
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.
Optimal Order Quantity
Finally, it is possible to know the minimum / total cost necessary to expend having managed our inventory.
Considerations of uncertainties
In the actual practice, there are always uncertainties stemming from two basic reasons:
The buffer stock can be used to cover the risk in inventory.
Approaches to determine buffer stock
There are two approaches to determine the buffer stock to kept in order to cover demand rate variations
1. Explicit consideration of shortage costs. |
Since inventory control basically involves the trade-offs between different costs, we may consider
The former cost per unit of the material is called as the understocking cost or the shortage cost; the latter cost per unit of the material is called as the overstocking cost. |
2. Implicit consideration of shortage costs. |
Instead of speaking in terms of explicit values of the understocking and overstocking costs, of which the former is not very easy to obtain, one may gauge the uncertain demand rates in terms of a risk factor o risk-level. The buffer stock is then computed based on the risk which the organization is willing to undertake. |
Fixed Order Period Models
In many organizations, the purchasing policy is to place and order for materials at definite periodic intervals, such as monthly, quarterly, etc.
In the Fixed order period models or P-system of inventory control, the ordering period if fixed but the order size (quantity) may be varying.
Fixed Order Period Models
The procedure consists of:
Fixed Order Period Models
The two quantities which need to be determined in a P-system are:
Fixed Order Period Models
The Quantity order using this model, once the period is defined and known.
Q = d(T+L) +zσ(T+L) – I
Q= Quantity.
d = Demand
T = The ordering period.
L = Lead time.
z = Policy of satisfying.
σ = Standard deviation.
I = inventory.
Fixed Order Period Models
The EOQ model provides the best "economic time interval" to establish an optimal policy that can be used also in fixed periods.
Economic time interval = (Q / D) * Working days in a year.
Is important to clarify that the result of this form, is used to consider to know when will be checked the inventory.
Don’t forget to consider the days of working time you have in a year. If a specific time is not mentioned, consider 365 days.
Annual inventory rotation
Inventory turnover, also called "turnover rate", is an indicator of an operational and financial nature, which allows to know on average how many times the company sells and replaces its stocks during a determined period of time (generally one year).
It can be given by:
Annual inventory rotation = Annual Demand / Cycle time