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In the following a problem from Nahmias, Production and Operatons Analysis (sixth Edition, page 279). The particularity is that the reorder point s is greater than the max level of Inventories on Hand (EOQ+safety stocks).

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This is a re-elaborated version of the Original (Nahmias). A shop supply automotive components and in particular the one considered in the following: an oil filter. The cost of this component is 1.5 €/item. Order Setup cost A is 100 €/order (see Silver et al., 1998). Warehouse carrying costs are 28% €/€-y.

Monthly demand follow a normal distribution with average demand D=280 items/month and standard deviation σ=77 items/months.

Order Lead time is 5 months.

Unsatisfied demand is backordered with a backorder cost of 12.8 €/item.

Find the following:

 

a) the optimal level of order quantity and the reorder point

b) the yearly average carrying costs, setup costs and backorder, on the hypothesis to follow an optimal policy

c) Evaluate the cost of the uncertainty of this process, by comparing the cost obtained in  point b) with the one in the hypothesis of no variance.

d) What happen in the case of LT=6 months but A=50€?

e) What happen if LT reduce to 4 months but a standard deviation of 1 month?