Question

A company producing personal computers supplies various components from its suppliers and operates 52 weeks per year. A particular component is needed at the rate of 100 items per week. The company's inventory holding rate for this component is 20%. The administrative rate to place an order of any size to the manufacturer costs $50. The manufacturer, however, tries to have orders of larger size and comes up with the following discount policy Quantity purchased Price per unit 1 to 99 Discount category $100 100 to 199 $95 3. 200 to 499 $90 Note that the price in each category applies to every unit purchased (for example, the price of pur- chasing 130 units is equal to 130 x 95). (a) Determine the optimal order quantity according to the EOQ model with discounts. (b) With this order quantity, how many orders will be placed annually? What will be the time. interval between orders?

Answer 1

Step by step solution with explanation is given below:

1.

Aus Annual demand = Semand per week & No. of weeks in a year - (D) = 100x58 = 5200 units Holding cost (h) = 20%. Of cost per unit ordering cast (0) = $50 il tor wat will of mobil (a) Determine the EOQ with discounts: so yo Discount category quantity Price per unit Ilito qq 8100 2 100 100 10199 st &.95 200t0499 $90 JR 1) first we will calculate Eog using different price in # I of each category: (25-003 EOQ = 2xDxO r ! sperol www posts time top oli su For Price per unit = $90 (Category 3) eat at won ew 50 = 2X 5200x50 520,000 170 ( appuox.) 0,2X90 ww, & white wote EoQ for price per unit = $95 (Category 2). EOQ2 = 2x5200x50 = 520,000 = 165 (approx.) is 0.2x95 + 19 = EoQ for price per unit = $100 (Category 1 oos - 500,= 2x5200x50 - 529000 1660 lappers.) 20 0.2X100

2.

a) Now, we will compare the top at different prices with the range of quantities governs. sexol: → for Category 3 (price = $90), EO Q=170... . But Range = 200 to 499 " Thus it does not lies in the range puhul We have to order atleast 200 units to #getprice of $90. For category 2 (Price = $95), ...Eod= 165 Range = 100 to 199 Thus, if we want to avail do Price of $95, the Optimal quanlity to be ordered will be 165 units → Foxe category 1 (Price = 9:00), 800=16) po domy Range = 1 to 99 thus of we want to get price = 4100, noininaun we have to take & ad q9 units 1 8 timu mog sing mot 3) Calculate total cost po each coulegaery: → Feu Categouy 3, Quantity to be ordered = 200=0,1 TC - Purchasing cost + Ordering cost + Holding cost = Vall Qx pecice + bxo +9 xhxprice per unit 0 0 - 200x190 + 5200 x 50 + 200x0.2x90 200 DEXJOBS 1203 ( 18,000 + 1300 + 1800 = $21,100

3.

for category 2, Quantity to be ordered = 165=62 TC = Ozx Poice + e tot a xh x price = 165895 + 5200 x 50+ 165x0.2495 =415675 & 15,757.57 115 215675 + 1575.75 + 1515.75 = $18,826.5 (approx) > fou Category 3, Puantity to be ordered = 161+Q, TL= 161Xl@0 + 5209 x 50 + 16) X0.2xico = 16100+ 1614.9 + 1610 = $19,324.9 161 :. Lowest total cost is in category 2. i. Optimal quanlity to be ordered = 165 units arred at a price of $95. (b) orden to be placed = Demand (Annual) Budur Quantity > 5200 = 31.5 = 3d ouders (approx)

For calculating time between two orders given in part b, the following is to be done:

Time between two orders = Weeks in a year / Number of orders in a year

= 52/32

= 1.625 weeks i.e. 1.625*7 = 11.375 days

Therefore time between two orders will be approximately 12 days