EOQ Model with Backorders: Decision Variables and Cost Analysis

This assignment delves into the Economic Order Quantity (EOQ) model, examining the impact of backorders on optimal replenishment policies. It discusses how backordering can affect inventory levels and costs, exploring the decision variables involved, such as carrying costs, ordering costs, and warehouse costs. The assignment derives the expression of the total relevant cost as a function of these decision variables and analyzes the benefits of backordering, including increased customer satisfaction and reduced inventory handling costs. Furthermore, it provides a practical example of inventory reorder levels and analyzes a scenario where a newsstand owner, Fred, faces the challenge of determining the optimal order quantity for newspapers, considering potential losses from unsold copies and backorders. The analysis includes calculating expected demand, expected loss, and determining the optimal order quantity to minimize costs.

RUNNING HEAD: - Economic 0 | P a g e
Economnic
Module Number

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Table of Contents
Introduction.................................................................................................................................................2
Exercise A (Answerer)..................................................................................................................................2
(B) Determine decision variables of the EOQ model with backorders and derive the expression of the
total relevant cost as function of decision variables................................................................................4
Exercise- B...................................................................................................................................................4
ECONOMIC ORDER QUANTITY WITH BACK ORDERS................................................................................4
Average loss compared to optimal policy................................................................................................5
Conclusion...................................................................................................................................................6
References...................................................................................................................................................7

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Introduction
With the ramified economic changes, economic order quantity is imperative part for the business
economic project. In this report, various parts of the project has been taken into consideration
which reveals the EOQ model, expected cost and average loss compared to optimal policy has
been divulged.
Exercise A (Answerer)
(a) It is the optimum quantity of the a product which required to be purchased at one time in
order to minimize the ordering cost and carrying cost of product. In today’s world customer is
the king of market and the company who is selling the product has to provide the product to
customer on insistent demand that’s means customer do not accept waiting time before they
receive their orders. Therefore inventory management implement replenishment policy which
means inventory manager will order the product quantity when level of stock will reach to
optimum stock level. (Average daily usage multiply by the lead time in days. The backordering
means when company do not have the sufficient stock available to satisfy customer demand then
it has to take time to make the product available to customer.
Impact of Backordering over Optimal replenishment:-
The inventory level is affected by demands and replenishments, but the demand process is
variable. Sometimes the demand is high causing quickly declining inventory levels, for example
there would be some inventory level 100 quantity at which there would place an order for an
inventory replenishment. This is known as the reorder quantity level. When there is order is
placed then there must wait for some period which also known as the lead time, before the
inventory is replenished. Demand cannot be constant Because of the variable demand and the
lead time, there is a risk that shortages will occur. If the demand is high during the lead time then
there would not be able to satisfy all of our customer then there will have to backorder the
shortage. Eventually as supply becomes available the backordered demand is satisfied. It is
analyzed that that there could set the reorder point high to make shortages unlikely, but that will
increase the inventory levels.

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Benefit of backordering
By applying the backordering formula a company can save the customer base which it can lose
by not having product available at customer demand. It increase the product value as customer is
ready to wait for the product that means customer want the company’s product on priority basis.
In backordering System Company do not have to keep high stock which decrease the inventory
handling cost (Aguswahyudi, Cokrodewo, & Sin, 2018).
It increase the customer satisfaction and improve the customer relationship management.
Example of inventory reorder level
Opening stock Delivery Demand
Closing
inventory
Reorder
quantity
500 0 50 450 0
450 0 100 350 0
350 0 100 250 250
250 0 50 200 0
200 0 50 150 0
150 0 50 100 0
100 0 50 50 0

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50 250 50 250 0
250 0 50 200 0
(B) Determine decision variables of the EOQ model with backorders
and derive the expression of the total relevant cost as function of
decision variables
The order quantity affects both shortages and inventories as well as the cost of replenishment.
Therefor due to backordering our inventory level become high and our cost also increase
(Aguswahyudi, Cokrodewo, & Sin, 2018). There are several decision variable sof the EOQ
models with the backorders.
 Carrying cost
 Ordering cost
 Warehouse costing and handling cost
 Replenishment cost
 Cost of capital (As opportunity cost)
 Blockage of the resources
Decisions variables  Total relevant cost of decision
variables
Carrying cost- $ 300 Total revenant cost increased by $ 300
Ordering cost- $ 250 Total revenant cost increased by $ 250
Warehouse costing and handling cost- 300 Total revenant cost increased by $ 300
Blockage of the resources Total revenant cost increased by $ 280
Exercise- B
ECONOMIC ORDER QUANTITY WITH BACK ORDERS
Economic order quantity helps the company to reduce the cost in terms of ordering cost
and handling cost of the business inventory (Kazemi, et al. 2018). Backorder affects the EOQ
cost in negative way as it increase the carrying cost and ordering cost. To overcome from this
cost scenario company has to involve the backorder quantity estimation in EOQ calculation so
that backorder can be beneficial to customers (Sulak, et al. 2015).
EXPECTED DEMAND OF NEWS PAPER IN A DAY AS PER

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THE FRED ESTIMATION
Quantity Probability Demand
15 0.4 `
16 0.2 3.2
17 0.3 5.1
0 0.1 0
TOTAL 14.3
Average loss compared to optimal policy
As from part b, if Fred will take 15 order then he will not be able to sale 1 newspaper. Therefore
he will have to sold the unsold newspaper at 0.50$ resulting of which loss of $ 1 will arise to
Fred on a day (Öztürk, Eroglu, & Lee, 2015)
AVERAGE LOSS TO FRED :
PARTICULAR QUANTIT
Y
ORDER QUANTITY 15
NEWS PAPER SOLD 14
UNSOLD NEWSPAPER
EVERYDAY 1
PARTICULAR AMOUNT
$
COST OF UNSOLD NEWSPAPER 1.5
REFUND 0.5
EXPECTED LOSS 1
As from above calculation, if Fred will only have order of 14 newspaper then he must take order
quantity of 14 only to minimize the expected cost (Taleizadeh, Stojkovska, & Pentico, (2015).

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Conclusion
After assessing all the details, it has been inferred that expected economic order quantity need to
be computed which shows the order placed quantity for Fred. However, different situations, Fred
might place various orders at the different quantity.

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References
Aguswahyudi, F. D., Cokrodewo, A., & Sin, L. G. (2018, December). Analysis of the
Effectiveness of Probabilistic Economic Order Quantity (Eoq) Method Using Model (Q,
r) in Medication Industry (Case Study: Apotek Griya Medika Malang). In Journal of
International Conference Proceedings (Vol. 1, No. 1).
Kazemi, N., Abdul-Rashid, S. H., Ghazilla, R. A. R., Shekarian, E., & Zanoni, S. (2018).
Economic order quantity models for items with imperfect quality and emission
considerations. International Journal of Systems Science: Operations & Logistics, 5(2),
99-1
Öztürk, H., Eroglu, A., & Lee, G. M. (2015). AN ECONOMIC ORDER QUANTITY MODEL
FOR LOTS CONTAINING DEFECTIVE ITEMS WITH REWORK
OPTION. International Journal of Industrial Engineering, 22(6).
Sulak, H., Eroglu, A., Bayhan, M., & Avci, M. A. (2015). An economic order quantity model for
defective items under permissible delay in payments and shortage. International Journal
of Academic Research in Business and Social Sciences, 5(1), 302.
Taleizadeh, A. A., Stojkovska, I., & Pentico, D. W. (2015). An economic order quantity model
with partial backordering and incremental discount. Computers & Industrial
Engineering, 82, 21-32.