Safety stock is a term used by inventory specialists to describe a level of extra stock that is maintained below the cycle stock to buffer against stockouts. Safety stock (also called buffer stock) exists to counter uncertainties in supply and demand. Safety stock is defined as extra units of inventory carried as protection against possible stockouts (shortfall in raw material or packaging). By having an adequate amount of safety stock on hand, a company can meet a sales demand which exceeds the demand they forecasted without altering their production plan. It is held when an organization cannot accurately predict demand and/or lead time for the product. It serves as an insurance against stockouts.

Reasons for safety stock

Safety stocks enable organizations to satisfy customer demand in the event of these possibilities:

  • Supplier may deliver their product late or not at all
  • The warehouse may be on strike
  • A number of items at the warehouse may be of poor quality and replacements are still on order
  • A competitor may be sold out on a product, which is increasing the demand for your products
  • Random demand (in reality, random events occur)
  • Machinery breakdown
  • Unexpected increase in demand

Economic order quantity is the level of inventory that minimizes the total inventory holding costs and ordering costs. It is one of the oldest classical production scheduling models. The framework used to determine this order quantity is also known as Wilson EOQ Model or Wilson Formula. The model was developed by F. W. Harris in 1913, but R. H. Wilson, a consultant who applied it extensively, is given credit for his early in-depth analysis it.

Variables

  • Q = order quantity
  • Q* = optimal order quantity
  • D = annual demand quantity of the product
  • P = purchase cost per unit
  • S = fixed cost per order (not per unit, in addition to unit cost)
  • H = annual holding cost per unit (also known as carrying cost or storage cost) (warehouse space, refrigeration, insurance, etc. usually not related to the unit cost)

The Total Cost function

The single-item EOQ formula finds the minimum point of the following cost function:

Total Cost = purchase cost + ordering cost + holding cost

- Purchase cost: This is the variable cost of goods: purchase unit price × annual demand quantity. This is P×D

- Ordering cost: This is the cost of placing orders: each order has a fixed cost S, and we need to order D/Q times per year. This is S × D/Q

- Holding cost: the average quantity in stock (between fully replenished and empty) is Q/2, so this cost is H × Q/2

.

To determine the minimum point of the total cost curve, set the ordering cost equal to the holding cost:

Solving for Q gives Q* (the optimal order quantity):

Therefore: .

Note that interestingly, Q* is independent of P; it is a function of only S, D, H.

Example

  • Suppose annual requirement (AR) = 10000 units
  • Cost per order (CO) = $2
  • Cost per unit (CU)= $8
  • Carrying costpercentage (percentage of CU) = 0.02
  • Carrying cost Per unit = $0.16

Economic order quantity =

Economic order quantity = 500 units

Number of order per year (based on EOQ)

Number of order per year (based on EOQ) = 20

Total cost = CU * AR + CO(AR / EOQ) + CC(EOQ / 2)

Total cost = 8 * 10000 + 2(10000 / 500) + 0.16(500 / 2)

Total cost = $80080

If we check the total cost for any order quantity other than 500(=EOQ), we will see that the cost is higher. For instance, supposing 600 units per order, then

Total cost = 8 * 10000 + 2(10000 / 600) + 0.16(600 / 2)

Total cost = $80081

Similarly, if we choose 300 for the order quantity then

Total cost = 8 * 10000 + 2(10000 / 300) + 0.16(300 / 2)

Total cost = $80091

This illustrates that the Economic Order Quantity is always in the best interests of the entity.

Reorder point ("ROP") is the level of inventory when a fresh order should be made with suppliers to bring the inventory up by the Economic order quantity ("EOQ").

The two factors that determine the appropriate order point are the delivery time stock which is the Inventory needed during the lead time (i.e., the difference between the order date and the receipt of the inventory ordered) and the safety stock which is the minimum level of inventory that is held as a protection against shortages due to fluctuations in demand.

Therefore:

Reorder Point = Normal consumption during lead-time + Safety Stock .

Another method of calculating reorder level involves the calculation of usage rate per day, lead time which is the amount of time between placing an order and receiving the goods and the safety stock level expressed in terms of several days' sales.

Reorder level = Average daily usage rate x lead-time in days .

From the above formula it can be easily deduced that an order for replenishment of materials be made when the level of inventory is just adequate to meet the needs of production during lead-time.

Example

If the average daily usage rate of a material is 50 units and the lead-time is seven days, then:

Reorder level = Average daily usage rate x Lead time in days = 50 units x 7 days = 350 units

When the inventory level reaches 350 units an order should be placed for material. By the time the inventory level reaches zero towards the end of the seventh day from placing the order materials will reach and there is no cause for concern.

Re-order point = Average Lead Time*Average Demand + Z*SQRT(Avg. Lead Time*Standard Deviation of Demand^2 + Avg. Demand^2*Standard Deviation of Lead Time^2)

Reorder point = S x L + J ( S x R x L) Where

  • S = Usage in units
  • L = Lead time in days
  • R = Average number of units per order
  • J = Stock out acceptance factor
  • The stock-out acceptance factor, `F', depends on the stock-out percentage rate specified and the probability distribution of usage (which is assumed to follow a Poisson distribution— probability theory and statistics).

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Basic inventory decisions and EOQ

At the very basic level any firm faces two main decisions concerning the management of inventory: When should new stock be ordered and in what quantities? With regard to the order quantity, which minimises inventory related costs, we are familiar with the classical EOQ (economic order quantity) model. This remains the basic inventory model even when it is not applicable in real life business situations in most cases.

In inventory related literature, the answer to the question of when to order is given with reference to the ROP (reorder point), the point at which the replenishment order should be initiated so that the facility receives the inventory in time to maintain its target level of service. The ROP can be defined in terms of units of days or in units of inventory. In the static and deterministic model, the ROP is the simple multiplication of the number of lead days and the daily demand. It means that every time the inventory falls to the ROP level, an order must be initiated. And the order quantity is given by the EOQ model which is based on cost minimisation.

Above Figure: A simple deterministic inventory model based on fixed demand and fixed lead time

You are aware that the EOQ quantity is the balance between order and holding costs attached with the inventory. The order cost is made up of fixed and variable costs, whereas the holding cost consist of costs of insurance, taxes, maintenance and handling, opportunity costs and costs of obsolescence.

The formula for EOQ or economic order quantity is well known:

Q is the order quantity per order.
K is the fixed set up cost which the warehouse incurs every time it places an order.
D is the demand per day.
h is the inventory carrying or holding cost per unit per day.

You will notice that your text highlights two important insights regarding the EOQ model. These are:

  • Optimum order size is a good balance between the holding cost and the fixed order cost.
  • Total inventory cost is related with order size, but the relationship is not very significant.

A discussion of the EOQ model would remain incomplete if the inherent assumptions on which the model is based are ignored. Bowersox (2001) explains that these major assumptions are:

  • All demand is satisfied.
  • The rate of demand is continuous, constant and known.
  • Replenishment lead time is constant and known.
  • There is a constant price of product that is independent of order quantity or time.
  • There is an infinite planning horizon.
  • There is no interaction between multiple items of inventory.
  • There is no inventory in transit.
  • There are no limits on capital availability.

Problem 1

Cal Automotive Products
Cal Automotive Products manufactures components used in the automotive industry. The company purchases parts for use in its manufacturing operation from a variety of different suppliers. One supplier provides a part where the assumptions of the EOQ model are realistic. The annual demand is 5000 units, the ordering cost is $85 per order, and the annual holding cost rate is 20%.
a. Determine the economic order quantity if the cost of the part is $25 per unit.
b. Determine the reorder point if the lead time for an order is 12 days. Assume 250 days of operation per year.
c. Determine the reorder point if the lead time for the part is seven weeks (35 days).
d. Determine the reorder point for part (c) if the reorder point is expressed in terms of the inventory on hand rather than the inventory position.

Problem 2

Satou Saitou is the purchasing agent for West Valve Company. West Valve sells industrial valves and fluid control devices. one of the most popular valves is the western, which has a annual demand of 4000 units the cost of each valve is $90 and the inventory carrying cost is estimated to be 10% of the cost of each valve. Satou has made a study of the cost involved in placing an order for any of the valves that west valve stocks, and she has concluded that the average ordering cost is $25 per order. Furthermore, it takes about two weeks for an order to arrive from the supplier and during this time the demand per week for west valves is approximately 80.
What is the EOQ?
What is the ROP?
what is the average inventory? What is the annual holding cost?
How many orders per year would be placed? What is the annual ordering cost?

Problem 3

12-19 Annual demand for the Doll two-drawer filing cabinet is 50,000 units. Bill Doll, president of Doll Office Suppliers, controls one of the largest office supply stores in Nevada. He estimates that the ordering cost is $10 per order. The carrying cost is $4 per unit per
year. It takes 25 days between the time that Bill places an order for the two-drawer filing cabinets and the time when they are received at his warehouse. During this time, the daily demand is estimated to be 250 units.
(a) Compute the EOQ, ROP, and optimal number of orders per year.
(b) Bill Doll now believes that the carrying cost may be as high as $16 per unit per year. Furthermore, Bill estimates that the lead time may be 35 days instead of 25 days. Redo part (a), using these revised estimates.

Problem 4

The Super Discount store (open 24 hours a day, every day) sells 8-packs of paper towels, at the rate of approximately 420 packs per week. Because the towels are so bulky, the annual cost to carry them in inventory is estimated at $.50 per pack. The cost to place an order for more is $20 and it takes four days for an order to arrive.
Find the optimal order quantity.
What is the reorder point?
How often should an order be placed?

Problem 5

Assume you have a product with the following parameters:
Annual Demand = 360 units
Holding cost per year = $1.00 per unit
Order cost = $100 per order
What is the EOQ for this product?

Problem 6

Inventory Model

#1
Cooper Automotive Products manufactures components used in the automotive industry. The company purchases parts for use in its manufacturing operation from a variety of different suppliers. One supplier provides a part where the assumptions of the EOQ model are realistic. The annual demand is 5000 units, the ordering cost is $85 per order, and the annual holding cost rate is 20%.
a. Determine the economic order quantity if the cost of the part is $25 per unit.
b. Determine the reorder point if the lead time for an order is 12 days. Assume 250 days of operation per year.
c. Determine the reorder point if the lead time for the part is seven weeks (35 days).
d. Determine the reorder point for part (c) if the reorder point is expressed in terms of the inventory on hand rather than the inventory position.
#2
Western Valve Company has a stable demand for 6000 of its WM-4 industrial valves each year.The valve is manufactured by Northern manufacturing Company which supplies the valve to Western for $150.00 per unit.it costs Western $68.00 to place an order, and the carrying cost is 20% of the unit cost per year.Northern Manufacturing will provide a 5% discount on order quantities of 200 units or more and a 10% discount on order quantities of 500 or more units.
Determine the optimal order quantity, cycle time, and total cost for the year.

Problem 7

Economic order quantity model

Background:
Jan Michael started a small grocery store in Florida. The store is open for three hundred and sixty days a year.He sells five thousand four hundred cases of cases of candy bars at a constant daily rate every year. He purchases the candy from a certain wholesaler in Ohio, who then charges approx. $1.50 per case plus an additional $0.50 per case to cover the shipping cost in another state. The delivery happens the day after an order is placed by Jan Michael. The purchasing department calls the wholesaler at the start of each week to place an order for one hundred cases of candy. The cost is ten dollars per order and it doesn't matter how many are ordered. Monies(capital) have been borrowed from USA bank at an annual interest rate of ten percent. Also, Jan has to pay tax of five percent of the annual inventory value and another five percent for insurance purposes. Jan makes the determination that operating costs are either fixed in nature or don't depend on the amount of candy that is ordered.
The following questions are asked using the economic order quantity model:
1) What is the total annual relevant cost of the company's current inventory policy?
2) What are the optimal order quantity and its cost? Will ordering that amount provide significant savings?
3) Joe Blow wants to apply the EOQ model to a product with lower sales, with a different variety of candy bars that sells 1,080 cases annually. The cost is twenty dollars per case. The order is placed and the order cost $100.00, independent of the number of cases ordered which now arrive seven days later. The holding cost allocation are the same as the regular candy. (A) What are the optimal order quantity and the total annual relevant cost of the special variety candy?

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