Question

James Sullivan, the firm’s general manager, is approached by a supplier of #3925 valves offering quantity discounts, ultimately forcing a ‘Make vs. Buy’ decision: continue in-house production/sourcing or contract with the supplier in question (i.e., outsource).   Accordingly, he must determine both the quantity and method of delivery (i.e., either orders received gradually or orders received all at once) for one material.      And, consequently, determine if the valves should continue to be made in-house or out-sourced.

Mike Wazowski develops the following estimates from accounting information:

Annual Demand = 10,000 valves per year

Cost per valve = $1.60

Annual Inventory Holding Rate = 25%

Ordering Cost (per order) = $5.50

Working Days per Year = 250

The supplier’s quantity discount schedule is:

                        Range of Order Quantities           Discount %              Unit Cost

                                1 to 399                                        0%                   $1.70

                            400 to 699                                       4%                       $1.632

                              700+                                             6.75%                  $1.585

Answer 1

Annual Demand, D = 10,000 valves per year

Cost per valve, C = $1.60

Annual Inventory Holding Rate = 25%

Holding cost, H = 1.6*0.25 = 0.4

Ordering Cost (per order), S = $5.50

Working Days per Year = 250

EOQ = SQRT(2DS/H) = SQRT(2*10000*5.5/0.4) = 524

Annual cost of EOQ policy = Ordering cost + Holding cost + Purchase cost = (D/Q)*S + (Q/2)*H + D*C

= (10000/524)*5.5 + (524/2)*0.4 + 10000*1.6

= $ 16,210

For next quantity slab, Q=700, Unit cost = 1.585

Holding cost, H = 1.585*0.25 = 0.3963

Annual cost = Ordering cost + Holding cost + Purchase cost = (D/Q)*S + (Q/2)*H + D*C

= (10000/700)*5.5 + (700/2)*0.3963 + 10000*1.585

= $ 16,067

Total cost of order policy of Q=700 is lower. Therefore, they should order in lots of 700