Managing inventory

Case Analysis Guidelines
1-Summary of the case (the more concise the better)
2-General analysis and comments: (not related to the questions of the case)
3-Answers to the questions
THE CASE IS RELATED TO PRODUCTION COURSE . THERE ARE SPECIFIC EQUITTIONS FOR THIS CASE AND THE NAME FOR THE CHAPTER (Managing inventory through supply chain)
**The Case Study**
The Qatar General Electricity & Water Corporation KAHRA-MAA provides Qatar’s need of electricity and water services. KAHRA-MAA delivers electricity and water to
the city of Doha. The total amount (in Qatari Riyals) of each electricity invoice sent by KAHRA-MAA to the customers is based on the reading (the consumption of
electricity per period of 30 days) of that customer’s meter. The invoice preparation takes time and the customer will receive it 10 days after the reading of the
meter. The cost of the meter reading and sending the invoice to the customers is 5 Riyals.
A recent study shows that the monthly consumption of electricity within Doha is uniformly distributed with an average of 120 Riyals per customer. The KAHRA-MAA can
invest its capital at the bank with an annual rate of 6%. In other words, each Riyal of electricity consumed and not billed to the consumer costs 0.005 Riyals per
month to KAHRA-MAA.
The actual policy of KAHRA-MAA is to produce and send monthly (there are 30 days per month) invoices to the customers. We assume also that the invoices are paid as
soon as they are received by the consumers.
First Question:
Based on this policy:
a. How much does a customer owe KAHRA-MAA just before paying his bill?
b. How much does a customer owe KAHRA-MAA just after paying his bill?
c. Plot a graphic representing the amount of money that each consumer owes to
KAHRA-MAA.
d. Show that the monthly cost related to the current billing system is 5.5 Riyals.
e. Can we conclude that this policy is not optimal?
Second Question
2. KAHRA-MAA has decided to use inventory management models to optimize its billing system. Compute the following quantities:
a. The optimal amount to be billed each month per consumer that minimizes the monthly billing cost.
b. The optimal cycle of billing. c. The optimal number of invoices to be sent to each consumer per year. d. The monthly optimal cost related to the billing system
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