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Math Help - Economic Order Quantity Problem

  1. #1
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    Economic Order Quantity Problem

    Hello Everyone,

    I need some help with this problem. It is giving me a migraine. Can anyone help? Thank you in advance!

    A flower shop uses 800 clay pots a month. The pots are purchased at $2 each. Annual carrying costs are estimated at $0.60 per pot per year and ordering costs are $20 per order. The manager has been currently using an order size of 1600 flower pots per order.

    • What additional cost is the shop incurring by using this current order size rather than the economic order quantity?
    • Other than potential cost savings, what benefit(s) would using the optimal order quantity yield?
    • What is the number of orders per year if the manager uses the current order quantity of 1600?
    • What is the number of orders per year if the manager uses the Economic Order Quantity?
    • What is the maximum number of flower pots that are held in inventory in a given ordering cycle?
    • How long will each order last (in months) if the manager uses the Economic Order Quantity?
    • Assume that the lead time for the pots is 1 month. What is the Reorder Point?
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  2. #2
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    Exactly what are you stuck on. Can you find the economic order amount?

    if not, Can you formulate the problem you would solve to find the economic order amount?



    Consider reading Economic order quantity - Wikipedia, the free encyclopedia
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  3. #3
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    I don't even know where to begin with this entire problem........it is so confusing to me......



    Quote Originally Posted by SpringFan25 View Post
    Exactly what are you stuck on. Can you find the economic order amount?

    if not, Can you formulate the problem you would solve to find the economic order amount?



    Consider reading Economic order quantity - Wikipedia, the free encyclopedia
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  4. #4
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    The three sections in bold are what I am having trouble with. Can anyone help me?

    Thank you in advance!

    A flower shop uses 800 clay pots a month. The pots are purchased at $2 each. Annual carrying costs are estimated at $0.60 per pot per year and ordering costs are $20 per order. The manager has been currently using an order size of 1600 flower pots per order.
    • What additional cost is the shop incurring by using this current order size rather than the economic order quantity?
    EOQ = 2(AR * CO) = 2(9,600 * $20) = 384,000 = 800 units
    CU * CC% $2 * .3 0.6
    Total Cost = CU * AR + CO(AR/EOQ) + CC(EOQ/2)
    = $2 * 9,600 + $20(9,600/800) + $.60(800/2)
    = $19,200 + $20(12) + $.60(400)
    = $19,200 + $240 + $240
    = $19,680

    = $2 * 9,600 + $20(9,600/1600) + $.60(1,600/2)
    = $19,200 + $20(6) + $.60(800)
    = $19,200 + $120 + $480
    = $19,800
    Additional Costs = $19,800 - $19,680 = $120 in additional costs

    • Other than potential cost savings, what benefit(s) would using the optimal order quantity yield?
    • What is the number of orders per year if the manager uses the current order quantity of 1600?
    Annual Requirements / Order Quantity
    9,600 / 1,600 = 6 orders per year


    • What is the number of orders per year if the manager uses the Economic Order Quantity?
    Annual Requirement / EOQ
    9,600 / 800 = 12 orders per year
    • What is the maximum number of flower pots that are held in inventory in a given ordering cycle?

    • How long will each order last (in months) if the manager uses the Economic Order Quantity?
    Annual Requirements / 12 months in a year
    9,600 / 12 = 800 required per month
    EOQ = 800, therefore each order will last around 1 month
    • Assume that the lead time for the pots is 1 month. What is the Reorder Point? Verbally, interpret the meaning of this Reorder Point.
    ROP = Demand Rate x Lead Time
    ROP = (800/30) x 30
    ROP = 800 units
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  5. #5
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    This answer comes with the caveat that i have never seen this topic before (but i do have a postgraduate degree in economics)

    The first questions are conceptual and do not require calculation. The firm knows it will have to buy 800 units over the year. It must choose between placing 1 large order for 800 units, or 800 small orders for 1 unit, or anywhere in between. In general:
    If you place a small number of large orders you will save on the order fees
    If you place lots of little orders you will save on storage costs


    (a) What additional costs is the store incurring by not using the economic order amount.
    The economic order amount is the order amount that minimises the total inventory cost for the year. This is equal to the cost of stock + cost of storage.

    If the firm orders less than the economic order amount they will place more than the optimal number of orders and incur unnecessary order fees
    If the firm orders more than the economic order amount they will place fewer than the optimal number of orders and incur unecessary storage fees

    (b) Other than potential cost savings, what benefits are there tousing the economic order amount.
    I do not understand this question. I dont see any non-financial benefits that would be relevent to the decision

    (c) How many orders are placed per year if the manager porders in batches of 1600.
    800*12 units are needed per year, so an order of 1600 will last 2 months

    800*12/1600 = 6 orders per year


    d) how many orders per year if you use the economic order quantity?

    Define:
    N = orders per year
    X = Number of units in each order

    so,
    Time between orders = 1/N
    Cost of storage between orders=0.6*0.5*X*(1/N)
    Cost of storage per year = 0.6*0.5*(1/N)*N = 0.6*0.5X

    Cost of orders per year: 20N + 2XN

    Total Cost if you have N orders per year:
    0.6*0.5X + 20N +2XN

    But, you must order 4800 units per year in total
    XN = 4800
    X=4800/N

    Total Cost
    0.3 * \frac{4800}{n} +20N + 2*4800

    You should be able to minimise this function by choosing n (differentiate). This gives you the economic number of orders per year. The economic order quantity is X. You already know that X=4800/N



    •What is the maximum number of flower pots that are held in inventory in a given ordering cycle?
    Just after the order arrives, you have X units in storage

    •How long will each order last (in months) if the manager uses the Economic Order Quantity?
    If there are N order per year, then each order lasts 1/N years

    •Assume that the lead time for the pots is 1 month. What is the Reorder Point?
    Ive neverheard of the re-order point. Presumably it is 1 month before the order must arrive.
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  6. #6
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    Well that is sucky timing. You posted your solution at the same time as mine.

    You can ignore my earlier post since you already have the answers. Responding to your comments in bold:

    What are the other benefits
    If the EOQ is lower than the current order quantity then changing to the EOQ will mean less inventory is held. This makes the business less vulnerable to a collapse in demand (if demand is uncertain).

    What is the maximum inventory level
    This is the EOQ. Immediately after the order arrives, you must place the whole thing in storage



    What is the reorder point
    ROP is the inventory level at which you place a new order. If there are is an order ever K months, and you must place the order at K-1 months, the the Proportionate inventory level is 1- \frac{K-1}{K} = 1/K

    So the total inventory when you place the order is EOQ / K
    Last edited by SpringFan25; June 18th 2010 at 01:09 PM.
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  7. #7
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    Re: Economic Order Quantity Problem

    this topic is so hard im struggling with it too the question im trying to figure out is;

    A local supermarket sells Beauty Bar Soaps which are ordered from a manufacturer. Annual demand for Beauty Bar Soaps is 5000. The supermarket incurs an annual holding cost of 20 percent of purchase price and incurs a fixed order placement, transportation and receiving cost of £49 each time an order for the soaps is placed, regardless of the order quantity. The price charged by the manufacturer varies according to the following discount pricing:

    Order quantity Unit Price
    0 – 999 £5.00
    1000 – 2499 £4.85
    2500 and over £4.75

    Determine the quantity of Beauty Bar Soaps that the supermarket should order each time it makes an order.

    my head hurts xxx
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