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THE BRINKAMN MEDICAL SUPPLY COMPANY WISHES TO DETERMINE AN APPROPRIATE INVENTORY POLICY FOR ITS KIDNEY DIALYSIS FILTERS. BASED ON RECORDS FOR THE LAST FEW YEARS, THE OPERATINS MANAGER FOR THE COMPANY ESTIMATES ANNUAL SALES OF KIDNEY DIALYSIS FILTERS TO BE 8,000. THE COST IF PLACING AN ORDER FOR THE FILTERS WITH THE MANUFACTURER IS exist300. IN ADDITION, THE COST OF STOCKING AND MAINTAINING THE FILTER. THIS COST INCLUDES THE COST OF PHYAICAL STORAGE, MAINTENANCE, INSURANCE, ETC. IT IS DESIRED TO DETERMINE AN OPTIMAL ORDERING POLICY WHICH WILL MINIMIZE TOTAL ANNUAL COST TO THE BRINKMAN CORPORATION. THE FORMULAS FOR THE INVEMTORY MODEL TO BE USED ARE SHOWN AT THE END OF THIS PROBLEM. CALCULATE THE ECONOMIC ORDER QUANTITY (Q*) FROM THE FORMULAS. ALSO CALCULATE THE TOTAL ANNUAL COST FOR THIS POLICY, ALSO FROM THE FORMULAS. TC = TOTAL ANNUAL COST D = ANNUAL DEMAND FOR DIALYSIS FILTERS Q = NUMBER OF DIALYSIS FILTERS PER ORDER CO = THE FIXED COST OF PLACING AN ORDER CC = CARRYING (HOLDING) COST PER FILTER PER YEAR A) WHAT IS THE SIZE OF THE ORDER QUANTITY TO BE PLACED WITH THE MANUFACTURER WHENEVER AN ORDER IS PLACED (E. O. Q.) VALUE? SHOW YOUR CALCULATION BELOW. ______________ B) WHAT IS THE TOTAL ANNUAL COST OF THIS NVENTORY POLICY? SHOW YOUR CALCULATION BELOW._______________ C) BRINKMAN CURRENTLY PURCHASES ITS DIALYSIS FILTERS FROM THE JASMINE CO. FOR exist10 A FILTER. DETERMINE HOW MUCH BRINKMAN PAYS FOR THE FILTERS ANNUALLY. (THIS IS JUST exist10 times ANNUAL DEMAND.) FINALLY, CALCULATE THE TOTAL COST AS THE SUM OF ANNUAL INVENTORY COST (YOUR ANSWER TO PART (B)) AND THE ANNUAL COST OF THE FILTERS. (SHOW YOUR CALCUALTION.) __________________
Expert Answer
Ordering cost(Co) = $300
Carrying cost(Cc) = $20
A) Economic Order Quantity(EOQ) = Sqrt of [(2 X D X Co) / Cc]
= Sqrt of [(2 X 8000 X 300) / 20]
= Sqrt of 240000
= 489.89 or rounded to 490 filters
So,the size of the order quantity to be placed is 490 filters.
B) In this inventory policy Q = 490 filters
Annual holding cost = (Q/2)Cc = (490/2)20 = 245X20 = $4900
Annual ordering cost = (D/Q)Co = (8000/490)300 = 16.3X300 = $4890
Total annual cost = Annual holding cost + Annual ordering cost
= $4900 + $4890
= $9790
C) Brankman purchases its filter for $10 a filter.
Amount Brankman pays for the filter annually = Annual demand of filter X cost per filter
= 8000 X $10
= $80000
The total cost as the sum of annual inventory cost = Total annual cost of inventory+ Annual cost of the filters
= $9790 + $80000
= $89790
