Question

1. Emily Larson is in charge of purchasing surgical supplies for a county hospital. Emily is evaluating two suppliers (suppliers A and B) to purchase forceps for the hospital's surgical use. The quantity-price schedules of both suppliers are given in the following table. The annual demand for forceps is 10,000 units. The ordering cost is US$150 per order, and the carrying cost is 20% of the item's purchase price per unit Supplier A Suppler B Quantity Price per unit in U.S dollars) Price per unit n U.S dollars) Ordered 0 to 2999 2000 to 4,999 5,000 to 7,999 .000+ Ordered 10.00 0 to 3,999 50 4,000 to 7,999 10.50 800 8000 to 11,999 9.00 7.00 12000 11.00 7.00 a. What is the economic order quantity for each supplier? b. What quantity should be ordered, and from which supplier? c. What is the total cost for the quantity ordered in "b"? d. What additional factors should Emily consider besides total cost?

Answer 1

Given Data, For Supplier A, [ Ch] Holding Cost = 20% of the Unit Cost per unit per Year, [Co ]Ordering Cost = USD 150 Per Order, [ D ]Annual Demand = 10,000 Units Item cost could vary as per the table data, Considering each Item cost, if we calculate Optimal order quantity, then the result will fall in between 0 to 2,999, thus let me consider, for any order in between 0 to 2,999, Price will come USD10 per unit,

For Supplier A, Formula for Optimal Order Quantity = Square Root of [( 2 X D X Co)/ Ch], Or, Optimal Order Quantity = Square Root of [ ( 2 X 10,000 X 150 )/ (0.20 X 10)] Or, Optimal Order Quantity = Square Root of [ 15,000,00] = 1224.74 = 1225 Units, So, for the Optimal order quantity 1225 Units, Firm should pay the price per unit = USD 10 per unit, Number of Order = Annual Demand / Optimal Order Quantity Or, Number of Order = 10,000 / 1225 = 8.16 Orders Total Annual Ordering Cost = Number of Order X Ordering Cost per Order = 8.16 X USD 150= USD 1224.489 = USD 1224.50 Total Annual Holding Cost = Average Units X Holding Cost per unit per Year Or, Total Annual Holding Cost = (1225/2) X USD (0.20 X 10) = USD 1225 Total Annual Purchasing Cost = Order Quantity X Number of Order X Purchase cost per Unit = 1225 * 8.16* USD 10 = USD 132,486.624 Total Annual Cost = Total Annual Ordering Cost + Total Annual Holding Cost + Total Annual Purchasing Cost = USD 1,00,000 Or, Total Annual Cost at the Optimal Behavior = USD 1224.50 + USD 1225 + USD 1,00,000= USD 102449.5

Given Data, For Supplier B, [ Ch] Holding Cost = 20% of the Unit Cost per unit per Year, [Co ]Ordering Cost = USD 150 Per Order, [ D ]Annual Demand = 10,000 Units Item cost could vary as per the table data, Considering each Item cost, if we calculate Optimal order quantity, then the result will fall in between 0 to 3,999, thus let me consider, for any order in between 0 to 3,999, Price will come USD11 per unit,

For Supplier B, Formula for Optimal Order Quantity = Square Root of [( 2 X D X Co)/ Ch], Or, Optimal Order Quantity = Square Root of [ ( 2 X 10,000 X 150 )/ (0.20 X 11)] Or, Optimal Order Quantity = Square Root of [ 1363636] = 1167.748 = 1168 Units, So, for the Optimal order quantity 1168 Units, Firm should pay the price per unit = USD 11 per unit, Number of Order = Annual Demand / Optimal Order Quantity Or, Number of Order = 10,000 / 1168 = 8.56 Orders Total Annual Ordering Cost = Number of Order X Ordering Cost per Order = 8.56 X USD 150= USD 1224.489 = USD 1284.247 = USD 1284.25 Total Annual Holding Cost = Average Units X Holding Cost per unit per Year Or, Total Annual Holding Cost = (1168/2) X USD (0.20 X 11) = USD 1284.8 Total Annual Purchasing Cost = Order Quantity X Number of Order X Purchase cost per Unit = 1168 * 8.56* USD 11 = USD 11,0000 Total Annual Cost = Total Annual Ordering Cost + Total Annual Holding Cost + Total Annual Purchasing Cost Or, Total Annual Cost at the Optimal Behavior = USD 1284.25 + USD 1284.8 + USD 110000= USD 112569,

Answer for a) Given Above,

Answer for b)

as, total cost for supplier A is lower than that of Supplier B, thus, we will choose Supplier A and Economic Order quantity with supplier A is 1225 Units,

Answer for c)

Total Cost for the quantity order in "b" USD 102449.50, calculation shown above,

Answer for d)

Factors like Quality of the purchased Item, External impacts like Currency risk and currency fluctuations, Accidental Risk, Return or Reverse logistics issues and cost, all such should be considered besides the total cost,