A famous department store must decide on the quantity of women’s handbags to procure. Type 2…

A famous department store must decide on the quantity of women’s handbags to procure.

Type 2 handbags are in the store’s ‘classic range’. They will always sell well. The monthly sales rate is fairly stable throughout the year but with some variation. The store estimates that the monthly sales of Type 2 handbags are normally distributed with mean 200 bags and standard deviation 40 bags. The Type 2 bags cost $20 each. The lead time between placing an order and receiving Type 2 handbags is 2 months. The department store estimates that the cost of placing an order is $50; that the inventory holding cost for Type 2 handbags is $1 per unit per month, and the cost of stock out is $40 per unit. [no specific word limits]

(a) What inventory model would you use to manage the stock of Type 2 handbags? Use this model to calculate the optimal inventory policy for Type 2 handbags and determine the expected annual cost of controlling Type 2 handbags according to this policy. Interpret your results and draw a visualization of the inventory evolution. In your drawing, show when and how stock-outs might occur?

(b) For type 2 handbags, if instead of the optimal policy, the managers decide to satisfy at least 95% of the demand, what policy they can take?
(c) For type 2 handbags, if the store orders 200 bags whenever the inventory level drops to 500 units, what percentage of the demand can be satisfied? What is the probability that the store faces a stock-out during lead time?

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