The demand forecast for a product has a mean of 400 units and a standard deviation of 100 units. The product is purchased at a unit cost of $15, and is sold at a regular price of $23. The unsold product at the end of the selling season is salvaged at a discounted price of $11. The Newsvendor model is applied to find the optimal stocking quantity. How many units should the company stock to maximize its profit?
Optimizing inventory management is a crucial task for any business. In particular, the Newsvendor model, derived from the field of operations research, can help companies strike the right balance between understocking and overstocking products, ultimately maximizing profit. In this scenario, we’ll apply the Newsvendor model to determine the optimal stocking quantity for a product with a mean demand of 400 units and a standard deviation of 100 units.
The Newsvendor model hinges on the idea of balancing the costs associated with understocking and overstocking. Understocking, or not having enough product to meet customer demand, leads to lost sales and potential reputation damage. On the other hand, overstocking, or carrying excess inventory, results in holding costs, including storage and obsolescence expenses.
In this case, the product in question is purchased at a unit cost of $15 and sold at a regular price of $23. Any unsold units at the end of the selling season can be salvaged at a discounted price of $11. The goal is to find the optimal stocking quantity that maximizes profit.
The Newsvendor model provides a simple formula to calculate the optimal stocking quantity (Q*), which is as follows:
Q* = μ + zσ
Where:
– Q* is the optimal stocking quantity.
– μ is the mean demand (400 units).
– σ is the standard deviation of demand (100 units).
– z represents the critical ratio, which can be calculated using the service level desired. The critical ratio is given by (P – Salvage) / (P – C), where P is the selling price, Salvage is the salvage price, and C is the unit cost.
In our case:
– P (selling price) = $23
– Salvage price = $11
– Unit cost = $15
Calculating the critical ratio:
Critical Ratio (CR) = (23 – 11) / (23 – 15) = 12 / 8 = 1.5
Now, we need to find the corresponding z value from a standard normal distribution table for a CR of 1.5. Typically, businesses target a service level, which corresponds to a specific z value, to balance the risk of understocking and overstocking. Common service levels are 90%, 95%, or 99%. Let’s assume a 95% service level, which corresponds to a z value of approximately 1.645.
Now, we can calculate the optimal stocking quantity:
Q* = 400 + 1.645 * 100 = 564.5
Since we can’t stock a fraction of a unit, we round up to 565 units.
Therefore, the company should stock approximately 565 units of the product to maximize its profit, considering the mean demand, standard deviation, unit cost, selling price, and salvage price. This stocking level balances the cost of understocking and overstocking, helping the company achieve the desired service level while optimizing profitability.
As a renowned provider of the best writing services, we have selected unique features which we offer to our customers as their guarantees that will make your user experience stress-free.
Unlike other companies, our money-back guarantee ensures the safety of our customers' money. For whatever reason, the customer may request a refund; our support team assesses the ground on which the refund is requested and processes it instantly. However, our customers are lucky as they have the least chances to experience this as we are always prepared to serve you with the best.
Plagiarism is the worst academic offense that is highly punishable by all educational institutions. It's for this reason that Peachy Tutors does not condone any plagiarism. We use advanced plagiarism detection software that ensures there are no chances of similarity on your papers.
Sometimes your professor may be a little bit stubborn and needs some changes made on your paper, or you might need some customization done. All at your service, we will work on your revision till you are satisfied with the quality of work. All for Free!
We take our client's confidentiality as our highest priority; thus, we never share our client's information with third parties. Our company uses the standard encryption technology to store data and only uses trusted payment gateways.
Anytime you order your paper with us, be assured of the paper quality. Our tutors are highly skilled in researching and writing quality content that is relevant to the paper instructions and presented professionally. This makes us the best in the industry as our tutors can handle any type of paper despite its complexity.
Recent Comments