Inventory Systems $($SC$\_5\_3\_051\_$E$)$

Class Assignment Problem

Instructions

Everyone needs to submit their workings:

$($a$)$ Excel file

$($b$)$ Notes on your solution $-$ handwritten or typed.

Hint: The notes should contain all the assumptions that you have made and all the

formula that you have used for solving the problem.

Read the entire question carefully before answering

The assignment will start at $10$:$15$ am$.$ Subsequently you have $3$ hours to complete your

analysis.

Before $10$:$15$ am you can clear any doubts about the question paper.

You can use the internet for help.

Topic: Echelon Inventory Theory

Question: We consider a dyadic supply chain system consisting of one distribution centre

$($DC$)$ and one field location $($FL$)$ for this problem.

At the FL$,$ the following observations have been made by the inventory manager:

The annual demand at FL: $x$ units

The natural time period at FL is: $2$ days

The DC$\text{'}$s lead time to serve an order from FL is: $l=4$ days

The demand generated by the customers is poisson distributed

The maximum demand that has ever occurred $($at this FL$)$ is $6$

Annual holding cost at the FL: $25\%$ of product retail price

Per unit gross margin: $50\%$ of product retail price

Back ordering penalty: $90\%$ of product retail price

At the DC$,$ the following observations have been made by the inventory manager:

The annual mean demand at DC: Y units

The standard deviation of demand at DC; $250$ units

The natural time period at DC is: $1$ week

The manufacturer's lead time to serve an order from DC is: $l=7$ weeks

The demand generated by FL is considered normally distributed

Following additional information are also known about this dyadic system:

For both DC and FL$,$ the target in$-$stock probability is $95\%.$

The per unit retail price of the product is: $60$

Ordering cost at DC is: $300$ per order