I need a detailed explanation on how to solve this problem: A paint shop implements an inventory policy on its stock of white paint, which costs the store $6 per can.  Monthly demand for cans of white paint is normal with mean 28 and standard deviation 8.  The replenishment lead time is 14 weeks.  Excess demand is backordered, but costs $10 per back ordered can in labor and loss of goodwill.  There is a fixed cost of $15 per order, and the holding cost is based on 30% interest rate per annum.  In your computations, assume 4 weeks per month. - Write down the model name and parameters. - What are the optimal lot size and reorder points for white paint (include the formulas)? - What is the optimal safety stock (include the formula)?   *** Suppose the paint shop from the above problem adopts a service level policy. - What are the optimal lot size and reorder points for white paint, such that 90% of the cycles are filled without backordering (include all formulas)? - What is the fill rate corresponding to the reorder policy computed in the previous part (include all formulas)?

Question

I need a detailed explanation on how to solve this problem:

A paint shop implements an inventory policy on its stock of white paint, which costs the store $6 per can.  Monthly demand for cans of white paint is normal with mean 28 and standard deviation 8.  The replenishment lead time is 14 weeks.  Excess demand is backordered, but costs $10 per back ordered can in labor and loss of goodwill.  There is a fixed cost of $15 per order, and the holding cost is based on 30% interest rate per annum.  In your computations, assume 4 weeks per month.

- Write down the model name and parameters.

- What are the optimal lot size and reorder points for white paint (include the formulas)?

- What is the optimal safety stock (include the formula)?  

*** Suppose the paint shop from the above problem adopts a service level policy.

- What are the optimal lot size and reorder points for white paint, such that 90% of the cycles are filled without backordering (include all formulas)?

- What is the fill rate corresponding to the reorder policy computed in the previous part (include all formulas)? 

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