Question

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

Answer 1

Solution :

Given :

The annual demand, $D=5000$ units

Ordering cost, $S=\ 30$

Carrying cost, $H=\ 50$

Lead time, L = 10 days

Number of days per year = 250 days

So, average demand is d = $\frac{D}{250}$ days

                                         = $\frac{5000}{250}$  = 20 units

a). The economic order quantity, Q = $\sqrt{\frac{2DS}{H}}$

                                                               $=\sqrt{\frac{2\times 5000 \times 30}{50}}$

                                                               = 77 units

b). Average inventory = $\frac{Q}{2}$

                                    $=\frac{77}{2}$

                                    ≈ 39 units

c). Number of orders per year = $\frac{D}{Q}$

                                                  $=\frac{5000}{77}$

                                                  = 65 units

d). Time between orders = $\frac{Q}{D}$  x number of days per year

                                         $=\frac{77}{5000} \times250$

                                        = 3.85

e). Annual ordering cost = $\frac{D}{Q} \times S$

                                        $=\frac{5000}{77} \times 30$

                                        = $ 1948.05

    Annual carrying cost = $\frac{Q}{2} \times H$

                                        $=\frac{77}{2} \times 50$

                                          = $ 1925

    Total annual cost of inventory = $ 1948.05 + $ 1925

                                                       = $ 3873.05

f). Reorder point = $d \times L$

                           $=20 \times 10$

                           $=200$ units