A manufacturer buys cardboard boxes from a supplier. the annual demand is 36000
ID: 443025 • Letter: A
Question
A manufacturer buys cardboard boxes from a supplier. the annual demand is 36000 boxes and is uniformly distributed.the boxes cost $4 each. the estimated order cost is $6, and the carrying cost rate is 30% per year.
a. what are the EOQ, and the annual order and carrying cost?
b. how many times a year are orders placed, and what is the average time, in weeks, between orders?
c. Using the answer from (b), if you round the average time between orders to the nearest week, what should the order quantity be? Would you recommend using this order quantity and time interval
Referring to the problem above, again, suppose the box supplier is located close to the manufacturer's plant. For any quantity ordered from the manufacturer, the supplier fills it by making daily deliveries of up to 200 boxes per day, for as many days as it takes to fill the order. Both the supplier and the manufacturer use a 5-day workweek.
d. what are the economic order quantity and the annual order and carrying cost?(hint: use EMQ)
e. what is the manufacturer's annual savings in carrying cost by using this system instead of the one in problem above?
f. what is the average time, in weeks, between orders?
g. suppose the manufacturer places orders at 2-week intervals. What should the order quantity be? How many days will it take the supplier to fill the order?
Explanation / Answer
a.
Annual Demand = 36,000 boxes
K = ordering/setup cost = $ 6 per order
F = holding cost = unit cost * holding cost% = 4*30% = $ 1.2 per unit per year
EOQ = SQRT(2*(Annual demand*Ordering cost))/Carrying cost per unit year
= SQRT (2* (3600* 6) / 1.2 = 600
Annual order = 36000/600 =60 orders per year
Carrying cost =( 600/2 )*1.2 *4 = $1440 per year
b. The order has to be placed 60 times in a year and the avergae time in weeks between orders is 6 days.
c. Rounding off the order days, the order has to be placed every week in the year. In this cse the order quantity will become 500 boxes per order. The order quantity is not recommended since it carries a higher ordering cost and a higher carrying cost.
d. In this problem , we need to find the economic order quantity. We will use Economic Production quantity (EPQ or EMQ) to arrive at a solution. Here, production will be the supply rate from the supplier which is 200 boxes per day As given, Annual Demand = 36,000 boxes
No. of days = 5*52 = 260
K = ordering/setup cost = $ 6 per order
D = demand rate = 36000/260 = 138.5 boxes per day
F = holding cost = unit cost * holding cost% = 4*30% = $ 1.2 per unit per year
P = production rate = 200 boxes per day x = D/P = 138.5/200 = 0.69
EPQ formula where, Q* = SQRT(2*6*36000/1.2*0.69) = 600
e. annual order = 60 per order
Ordering cost = 60*6 = 360 per order
f. Time bewteen order = 4.33 days or 5 days
g. If order time is 2 weeks then manufacture will save 360 per order and ordering quantity would be 1200 instead of 600.
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