1. avatar says

    Hi ACCA Tutors
    I would like to thank you and open tuition for all your help in my studies of ACCA. Your notes, videos & help makes it easy to study.

    I watched the video of example 4 where workings under square root of 2x50000x200 over 3×0.9 = 2722 units (order quantity) however when I checked it my calculator gives the following answer 2449 units.
    Could you please tell me how you got 2722 units?

  2. avatar says

    A company is able to manufacture its own components for inventory at the rate of 4,000 units a week. Demand for the company is at the rate of 2,000 units a week. Set up costs for each production run is $ 50. The cost of holding one unit of inventory is $ 0.001 a week.
    Calculate the economic production run .

    Q = ?((2 ???? 50 ???? 2,000)/0.001(1?2,000/4,000) ) = 20,000 units (giving an inventory cycle of 10 weeks)

    What makes the production run “economic”? How is it ‘economical’ at 10 weeks and not 9 weeks for example? Please use a TABULAR form to explain.
    For example
    OPEN INV 0 2000 4000 6000 8000 10000 12000 14000 16000 18000
    ORDER ?
    DEMAND -2000 -2000 -2000 -2000 -2000 -2000 -2000 -2000 -2000 -2000
    PRODN RATE 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000
    CLOS INV 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
    I do not understand how (My Question 1) Holding cost and Ordering cost fit in this table and why ( My Question 2) the Q = 20 000 units and is a 10 week cycle and not a 5 week cycle for example. Why is 10 weeks used? Please explain

    • Avatar of johnmoffat says

      Your table is wrong in that they will not be producing 4,000 units a week – that would be ridiculous since they are only selling 2,000 a week.
      The question says that they are able to manufacture 4,000 a week – not that they do manufacture 4,000 a week. That is simply telling you how fast they are capable of producing (and therefore how long it will take for them to make the 2,000 that are ordered each time).

      Assuming 52 weeks in a year:

      The total order cost per year will always be the number of orders x set-up cost each time.
      This is: (Demand per year)/(order quantity) x (cost each time)
      At an order quantity of 20,000, this comes to ((52 x 2,000) / 20,000 ) x $50 = $260 per year

      The total holding cost per year will always be average inventory x cost of holding 1 unit for 1 year
      This is: ((order quantity) / 2) x (1 – Demand/Production rate) x holding cost per unit per year
      At an order quantity of 20,000, this comes to (20,000 / 2) x (1 – 2,000/4,000) x (52 x 0.001) = $260 per year

      So the total cost per year is $260 + $260 = $520 per annum

      Try any other order quantity you like and the total cost will be great than $520 – that is why 20,000 is the economic batch quantity (i.e. the cheapest total cost per year).

      Since best is to order 20,000 each time and they are selling 2,000 each week, it means that they will be placing an order every 10 weeks. (If they placed an order every 5 weeks then they would be ordering far more than they were selling which would be stupid – in total they are only selling 2,000 every week (i.e. 104,000 a year) and so they will only be ordering 104,000 a year in total.

      I have no intention of producing a table – I told you before that it cannot be asked for and is wasting time.

      If you want to then fine. On Day 1, an order will be placed for 20,000 units. It will take 5 weeks for all 20,000 to arrive (because the rate of production is 4,000 a week). During those 5 weeks, they will have sold 10,000 units (because they sell 2,000 a week and they are continuing to sell while the order is being delivered). So the maximum inventory level is 20,000 – 10,000 = 10,000. After a further 5 weeks the inventory will have fallen to zero (again because they are selling 2,000 a week). Then a new order is placed and the cycle repeats itself.
      So…..the level of inventory is fluctuating between 10000 (maximum) and 0 (minimum) and is therefore on average 5,000 units throughout the year. At $0.001 per unit per week, this means that the holding cost over the year is 5,000 x 52 x $0.001 = $260 per year (as above).

      Since the total demand is 52 x 2,000 = 104,000 per year, and since they are ordering 20,000 each time, they will place 104,000 / 20,000 = 5.2 orders a year and so the total set-up cost is 5.2 x $50 per year = $260 per year (as above).

      ( Before you ask (although this is also dealt with in my lecture), they will actually place 6 order in the first year, but have inventory remaining and so only need 5 orders the second year, and so on. We always assume it to be a long-term policy and therefore on average there will be 5.2 orders a year.)

    • avatar says

      Thank you so much. The 4000 being able to manufacture, but doesn’t manufacture, answers my questions. Only thing though, the reason I’ve asked for a table is because I’m trying to understand the logic of the EQB formula. If you didn’t have the formula, how would you calculate (get to) 20 000 being the economic order qty? Sorry if this is a stupid question, but I’m obviously missing something somewhere.

      • Avatar of johnmoffat says

        In the exam, you will have the formula :-)

        However, the only other way you could do it (apart from deriving the formula – but that involves differentiating which is not in the syllabus for any ACCA exams), would be to calculate the total cost per year for several different order quantities. (In exactly the same way as in my previous answer – doing it (for example) for order quantities of 5,000, 10,000, 15,000, 20,000, 25000, etc.). Then you could plot them on a graph – total cost on the vertical axis and order quantity on the horizontal axis. You would find that you got a curve and you could then read off from the graph the order quantity that gave minimum total cost.

        But… cannot be asked to do this in the exam. You will be given the formula.

      • avatar says

        I was hoping you would say that lol Thank you so much. It was in one of the EOQ tables where I couldn’t understand where the different Order quantities had suddenly come from / have been calculated that confused me which you have now cleared up. I also understand the EQB better now. Thank you so much.

      • avatar says

        A last question on EBQ please – if the rate of production is 50 units a day and the order quantity is a 100. Is the production run 50 or 100? I’m assuming the ‘inventory cycle’ would be the qty ordered?

      • Avatar of johnmoffat says

        The production run is 100 units. Every time an order is placed for 100 units, a production run takes place and that many will be produced (and at the rate of 50 a day, it will take 2 days to produce them).

        The inventory cycle depends on how many they are selling per day. For example, if they order 100 each time and they are selling 10 units a day, then the inventory cycle is 100/10 = 10 days. (They will place an order every 10 days)

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