A particular product has a weekly demand of 1000 (consider that there are 52 weeks in a year.
Demand does not experience seasonal fluctuations but there is a random variation in demand and this can be approximated with a normal distribution with a standard deviation equal to 100. It takes a week from ordering the product until it is available for sale.
The set up cost is $ 400 and the production rate is 4000 units per week when the product is being produced. The manufacturing cost excluding the set up cost is $20 per unit.
The cost of operating the warehouse $ 1 per unit per year. In addition the cost of investing money in inventory is 10% per year.
Design an inventory system for this product. Determine the point of reordering Such that there is only a 5% chance of running out of inventory during the lead time week. Derive an equation to determine the more economic quantity to be ordered. Calculate that amount.