2) A manufacturer is sourcing a component for a new product. Expected monthly de

Question

2) A manufacturer is sourcing a component for a new product. Expected monthly demand is 705 units. The component can be purchased from either supplier A or supplier B, with the following price breaks: SUPPLIER A SUPPLIER B Quantity Unit Price Quantity Unit Price 1–199 $14.00 1–149 $14.10 200–499 13.80 150–349 13.90 500 + 13.6 350 + 13.5 Ordering cost is $31 and annual holding cost is 25 percent of unit price per unit. a. Which supplier should be used? b. What order quantity is optimal if the intent is to minimize total annual costs? c. What is the minimum annual inventory cost?

Explanation / Answer

Supplier A Annual Demand (705 * 12) 8460 Ordering Cost $         31.00 Carrying Cost - 25% of price i.e. 25% * $14 $           3.50 EOQ = 2AO / C where A = Annual Demand O = Ordering Cost per order C = Carrying Cost per unit per annum Initial EOQ at base price EOQ = 2AO / C = (2 * 8460 * 31) / 3.50 = 387.1212 units or, 387 units This is not feasible solution as qty ordered has to be within 199 units Since supplier gives discount when qty ordered is more than 199, hence EOQ needs to be calculated at each price range Supplier gives disount offer if qty purchased is between 200-499 units When Price is $13.80, Carrying cost = $3.45 EOQ = 2AO / C = (2 * 8460 * 31) / 3.45 = 389.9164 units or 390 units Supplier gives disount offer if qty purchased is 500 or more When Price is $13.60, Carrying cost = $3.40 EOQ = 2AO / C = (2 * 8460 * 31) / 3.40 = 392.7729 units or 393 units This is not feasible solution as qty ordered has to be 500 or more. Hence optimal order qty will occur at lowest of range that is 300 units and for 0-199 units at higher end of range, i.e 199 units Optimal Order Quanity 1 - 199: 199 200 - 499: 390 500 or more: 500 Inventory Order Size (A) 199 390 500 Price (B) 14.00 13.80 13.60 Direct Cost (Price * Annual Demand = B* 8460) (C) $118,440.00 $116,748.00 $115,056.00 No of orders (Annual Demand/Order Quantity per order = 8460 / A) (D) 43 22 17 Ordering Cost (No orders * $31 = D *$31) ( E) $1,317.89 $672.46 $524.52 Carrying Cost per unit (25% * B) (F) $3.50 $3.45 $3.40 Carrying Cost (Order Size / 2 * Carrying Cost per unit per annum = A/2 * F) (G) $348.25 $672.75 $850.00 Total Cost (B+E+G) $120,106.14 $118,093.21 $116,430.52 Since the total cost is lowest at 500 units, this is the optimal order quantity. Total Cost of Ordering Optimal Order quanity = $116,430.52 Supplier B Annual Demand (705 * 12) 8460 Ordering Cost $         31.00 Carrying Cost - 25% of price i.e. 25% * $14.10 $           3.53 EOQ = 2AO / C where A = Annual Demand O = Ordering Cost per order C = Carrying Cost per unit per annum Initial EOQ at base price EOQ = 2AO / C = (2 * 8460 * 31) / 3.53 = 385.7460 units or, 386 units This is not feasible solution as qty ordered has to be within 149 units Since supplier gives discount when qty ordered is more than 149, hence EOQ needs to be calculated at each price range Supplier gives disount offer if qty purchased is between 150-349 units When Price is $13.90, Carrying cost = $3.475 EOQ = 2AO / C = (2 * 8460 * 31) / 3.475 = 388.5113 or 389 units This is not feasible solution as qty ordered has to be within 349 units Supplier gives disount offer if qty purchased is 350 or more When Price is $13.50, Carrying cost = $3.375 EOQ = 2AO / C = (2 * 8460 * 31) / 3.375 = 394.225 or 394 units Optimal Order Quanity 1 - 149: 149 150 - 349: 349 350 or more: 394 Inventory Order Size (A) 149 349 394 Price (B) 14.10 13.90 13.50 Direct Cost (Price * Annual Demand = B* 8460) (C) $119,286.00 $117,594.00 $114,210.00 No of orders (Annual Demand/Order Quantity per order = 8460 / A) (D) 57 24 21 Ordering Cost (No orders * $31 = D *$31) ( E) $1,760.13 $751.46 $665.63 Carrying Cost per unit (25% * B) (F) $3.53 $3.48 $3.38 Carrying Cost (Order Size / 2 * Carrying Cost per unit per annum = A/2 * F) (G) $262.61 $606.39 $664.88 Total Cost (B+E+G) $121,308.75 $118,951.85 $115,540.51 Since the total cost is lowest at 350 units, this is the optimal order quantity. Total Cost of Ordering Optimal Order quanity = $115,540.51 a. Supplier B should be used as Total Cost is lowest at 394 units EOQ for Supplier B b. Optimal Order Quantity - 394 units c. Minimum Annual Inventory Cost = $115,540.51

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