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home / study / math / statistics and probability / statistics and probability questions and answers / marly bird cosmetics company allows independent sales consultants to sell cosmetics to their ... Question: Marly Bird Cosmetics Company allows independent sales consultants to sell cosmetics to their own ... Marly Bird Cosmetics Company allows independent sales consultants to sell cosmetics to their own clients via a network-and-sell scheme. They manufacture their own lipsticks and supply them to the Sales Consultants in their network. They need to identify what the optimal production lot size would be and how often to run their production cycle. They provide you with the following information so that you can help them by identifying the Optimal Inventory Policy for lipsticks in terms of the production lot size, total annual cost, average inventory level and reorder points along with the number of production runs per year and the cycle time in days.

-The annual production capacity of the facility is 300,000 units of lipsticks.

-The annual demand is estimated at 250,000 lipsticks with the demand rate expected to be constant throughout the year. -The cost of setting up the production line is expected to be around $1000 for raw materials and production requires a lead time of 10 days. -The manufacturing cost per lipstick is $15.00, which includes the wages, shipping costs, and the costs of raw materials. -The annual holding cost is figured at a 20% rate. -The number of working days per year are 250.

Solution

Annual Demand (D) = 250,000 Lipsticks

Set up Cost (S) = $1,000

Manunfacturing Cost per unit = $15

Annual Holding Cost (H) = 20% = $15 x 20% = $3

No. of Working days per year = 250 days

Lead Time = 10 days

Daily Production Rate (p) = 300,000 units / 250 days = 1200 units

Demand per day (u) = 250,000 units / 250 days = 1000 units

Reorder Point = Demand during lead time = (250,000 units / 250 days ) x 10 days

Reorder Point = 10,000 units