Stephanie Robbins is attempting to perform an inventory analysis on one of her most popular products. Annual demand for this product is​ 5,000 units; carrying cost is​ $50 per unit per​ year; order costs for her company typically run nearly​ $30 per​ order; and lead time averages 10 days.​ (Assume 250 working days per​ year.) ​a) The economic order quantity is ​b) The average inventory is ​c) The optimal number of orders per year is ​d) The optimal number of working days between orders is ​e) The total annual inventory cost​ (carrying costordering ​cost) is ​ ​f) The reorder point is

Solution :

Given :

The annual demand, units

Ordering cost,

Carrying cost,

Lead time, L = 10 days

Number of days per year = 250 days

So, average demand is d = days

                                         =  = 20 units

a). The economic order quantity, Q =

                                                               = 77 units

b). Average inventory =

                                    ≈ 39 units

c). Number of orders per year =

                                                  = 65 units

d). Time between orders =  x number of days per year

                                        = 3.85

e). Annual ordering cost =

                                        = $ 1948.05

    Annual carrying cost =

                                          = $ 1925

    Total annual cost of inventory = $ 1948.05 + $ 1925

                                                       = $ 3873.05

f). Reorder point =

                            units

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