Question

production planning and inventory control’s exam

2-) A company has been buying a chemical water conditioner for its bait (to help keep its baitfish alive) in an optimal fashion. The supplier has now offered the firm a discount of kr.0.50 off all units if the firm will make its purchases monthly or TL 1.00 off if the firm will make its purchases quarterly. Current data for the problem are: annual demand equals to 720 units per year, ordering cost is TL6.00, holding cost is calculated as 20% per year over the selling price, selling price is TL 25. 25 Order quantity Unit price 0<Q< 59 60<Q< 179 24,5 180 <Q 24 a) What is the optimum order quantity at the current behavior? (8p) b) What is the annual total cost, including procurement cost, of continuing their current behavior? (7p) c) What are the annual total costs, if they accept either of the proposed discounts? (5p) d) At the cheapest of the total costs, are carrying costs equal to ordering costs? Explain. (5p)

Answer 1

Answer a= EOQ= (2*720*6/0.2*25)^0.5 =41.57 or 42 units

Answer b= Annual total cost = 720*25+(720/41.57)*6 +(41.57/2)*0.2*25=18207.85

Answer c= When the price is 25,

EOQ= (2*720*6/0.2*25)^0.5 =41.57 or 42 units

TC=720*25+(720/41.57)*6 +(41.57/2)*0.2*25=18207.85

When the price is 24.5

EOQ= (2*720*6/0.2*24.5)^0.5=41.99

Order quantity=60

TC=720*24.5+(720/60)*6+(60/2)*0.2*24.5= 17859

When the price is 24

EOQ= (2*720*6/0.2*24)^0.5=42.43

Order quantity=180

TC=720*24+(720/180)*6+(180/2)*0.2*24= 17736

Answer d= The cheapest cost is obtained for the Order quantity=180

At this cost, the carrying cost =(720/180)*6=24

ordering cost =(180/2)*0.2*24=432

So the carrying cost and ordering costs are not equal.

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