Basic Inventory Models
We introduce a simple single period inventory problem where a newsvendor has to decide on the amount of newspaper to order at the start of each day. When goods are not perishable, inventory can be kept across periods. Here, we introduce a simple multi-period inventory problem commonly referred to as the Economic Order Quantity (EOQ) model.
Newsvendor problem (6 questions)
Suppose the cost price of each newspaper is $0.30 and each newspaper is sold at a retail price of $1.00. Newspapers that are unsold by the end of the day are discarded. The newsvendor is equally likely to sell 20, 21, 22, 23 or 24 newspapers each day.
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Newsvendor solution (6 questions)
For the newsvendor problem, the optimal number of newspapers to order Q* is simply the largest order quantity such that the probability of demand being greater than or equals to that amount is at least as large as the ratio of cost to price:
As before, suppose the cost price of each newspaper is $0.30 and each newspaper is sold at a retail price of $1.00. In addition, the newsvendor is equally likely to sell 20, 21, 22, 23 or 24 newspapers each day.
EOQ model (9 questions)
Suppose we operate a retail shop that sells exactly one bag each day, 365 days a year. The cost price for each bag is $12.50. The annual inventory holding cost (e.g., storage space cost) for each bag is $2.30 per year. The cost of placing an order with the supplier is $50 per order (regardless of order quantity).
EOQ solution (2 questions)
For the EOQ model, the optimal order quantity Q* can be computed using the following formula:
Q* = (2DS ÷ H)0.5
where D is demand, Q is order quantity, S is order cost and H is holding cost.
As before, suppose the retail shop sells exactly one bag each day, 365 days a year, cost price for each bag is $12.50, annual inventory holding cost for each bag is $2.30 per year and cost of placing an order with the supplier is $50 per order.