A company that sells TVs has an inventory policy of 12/7 for quantity/reorder (Q/R), meaning that if their inventory falls below 7 at the end of the week, the team will place an order to bring inventory back to 12. It is my team's job to find analyze the Q and R values to recommend the best inventory policy. I need help in determining which Q and R values would best benefit the company.

The store is open on Wednesday through Sunday and each week has the following probability that up to 4 TVs will be sold:

0 TVs demanded 10% of the time

1 TVs demanded 20% of the time

2 TVs demanded 40% of the time

3 TVs demanded 25% of the time

4 TVs demanded 5% of the time

The store can only hold up to 12 TVs at a time, so the Q value can only get smaller in my recommendation. TVs can only be ordered on Sunday night arrive on Wednesday morning.

Every TV sells for $2000. The costs of ordering each TV is $700 and the fixed ordering cost is $500. The cost of holding each TV in inventory is $50 per TV and is calculated for the week on Sunday night. If a customer comes in and you don't have a TV in stock, then the TV is specially ordered and delivered to their house for $1,500.In addition, you estimate a penalty of $300 due to the likelihood of the customer not returning.

As a simplification of the model, Sers has agreed that the demand from week to week is constant and that the demand from week to week is memoryless.The memoryless property would be that a high/low demand this week does not change the demand for the following week.

Please use the Markov Chain Methodto determine the best inventory policy to replace Q=12 and R=7.

If you have a 100% chance of selling 4 or less TVs each week, why would you keep 12 in inventory? The R value wouldn't be less than 4, because we would want to avoid the exceptional cost of special delivery and losing a customer. The optimal quantity must be between 12 and 4 and the optimal R is probably between 4 and 7. Please guide me towards the best solution for the Q and R values.