Unit: Advanced Management Accounting
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Login to Access| Data for Part No. H 24 | |
| Lead times (Days) | Probabbility |
| 15 | 0.2 |
| 20 | 0.5 |
| 25 | 0.3 |
| Daily demand (Units) | Probability |
| 5,000 | 0.4 |
| 7,000 | 0.6 |
| Order policy | Units of product “X” ordered |
| Order twice monthly | 500 units per order |
| Order monthly | 1,000 units per order |
| Order quarterly | 3,000 units per order |
| Order semi-annually | 6,000 units per order |
| Order annually | 12,000 units per order |
| Daily demand (units) | Probability | Lead time days | Probability |
| 3,000 | 0.2 | 20 | 0.4 |
| 5,000 | 0.5 | 25 | 0.6 |
| 6,000 | 0.3 |
| 1. | Annual demand is 15,000 pairs of Sola. |
| 2. | The cost price of Sola averages Sh.200 per pair. |
| 3. | The fixed ordering cost of requisition is estimated to be Sh.80. |
| 4. | For each pair of Sola, annual inventory holding opportunity cost of capital is 13.33% of its cost price. |
| 5. | The management has determined economic order quantity based on data given above which should be used as reorder quantity. |
| 6. | The initial inventory available is 180 pairs of Sola while the reorder level is set at 50 pairs of Sola. |
| 7. | The out of stock costs amount to Sh.100 per pair of Sola units that are out of stock. |
| 8. | The customer demand is unknown. However, the total usage of Sola over the four days lead time is expected to be as follows: |
| 8. | Annual demand (Pairs of Sola) | Probability | Lead time (Days) | Probability |
| 30 | 0.2 | 1 | 0.15 | |
| 60 | 0.3 | 2 | 0.30 | |
| 90 | 0.4 | 3 | 0.45 | |
| 120 | 0.1 | 4 | 0.10 |
| 9. | The random numbers generated by the computer software are as follows: | ||||||||||
| Annual demand: | 4 | 8 | 6 | 1 | 7 | 1 | 9 | 0 | 3 | 8 | |
| Lead time: | 28 | 10 | 56 | ||||||||
Required: | |||||||||||
| (i) | The economic order quantity (EOQ). | ||||||||||
| (ii) | Simulate the inventory operation for a period of 10 days. | ||||||||||
| (iii) | Using the information in (b) (ii) above, estimate the average daily stockholding costs. | ||||||||||
| Invoice cost per unit | Sh.1,200 |
| Shipping charges | Sh.25 per unit plus Sh.140,000 per shipment |
| Inventory insurance | Sh.10 per unit per year |
| Annual handling and inspection cost of the raw material: | |
| Warehouse utilities | |
| Warehouse rental | Sh.26 per unit plus Sh.150,000 per year |
| Unloading costs for units received (paid to shipper) | Sh.9,800 per month |
| Receiving supervisor’s salary: | Sh.115,000 per month |
| Processing invoices and other purchase documents | |
| Sh.8 per unit | |
| Sh.176,000 per month | |
| Sh.1,860 per order. |
| Safety stock (units) | Probability for stock-out |
| 500 | 0.25 |
| 1,000 | 0.08 |
| 1,500 | 0.02 |
| 2,000 | 0.01 |
| Usage during past re-order period Number of bags | Number of times this quantity was used |
| 225 | 9 |
| 300 | 15 |
| 375 | 20 |
| 450 | 3 |
| 525 | 2 |
| 600 | 1 |
| (a) | There is a recommendation by the Managing Director (MD) that applying the economic order quantity (EOQ) model is the only optimal way of improving the stock holding policy. The company’s annual demand is estimated to be 432,000 litres which the MD assumes to be evenly distributed over 330 working days in a year. The cost of delivery is estimated to be Sh. 6,000 per order and the annual variable holding cost per litre at Sh. 2.4 plus 1% of the purchase price. The company’s policy is to order 20,000 litres each time and the lead time for an order is 3 working days. |
| (a) | Required: | |
| (i) | Calculate the EOQ, frequency of ordering and any annual cost savings if the company abandons the present inventory policy for the EOQ model. | |
| (ii) | The supplier has intimated that he will offer quantity discounts on purchases of quantities above 20,000 as follows: | |
| (a) | (ii) | 20,001 – 37,000 litres | Sh.150 per liter |
| 37,001 litres and above | Sh.140 per litre | ||
| Advice the distributor on the most optimal inventory policy. | |||
| (b) | The company’s finance director (FD points out that demand within the ten days’ lead time has not been entirely even over the past year causing stock outs. In case of a stock-out, it would be necessary to obtain the detergent by a special courier service at an additional cost of Sh.10 per litre. In this regard, he has given the frequency of the lead time demand over the last year as follows: |
| (b) | Lead time demand per day (No. of litres) | Frequency | Probability |
| 1,700 | 2 | 0.02 | |
| 1,500 | 10 | 0.10 | |
| 1,400 | 20 | 0.20 | |
| 1,300 | 30 | 0.30 | |
| 1,100 | 25 | 0.25 | |
| 1,000 | 13 | 0.13 |
| (b) | Required: | |
| (i) | Assuming that the stock out cost is reliable and that the order quantity will be constant for all the orders in a year, calculate the safety stock level the company should maintain throughout. | |
| (ii) | Assuming that stock out cost is unreliable but the management have established a service level of 90% that stock will always be available, calculate the optimal safety stock level. | |
| NB: Ignore the supplier’s quantity discount offer. | ||
| 1. | Stock item X The weekly demand for the item is 200 units, with a normally distributed demand with a standard deviation of 30 units and a lead time of 16 weeks. |
| 2. | Stock item Y It has a daily demand of 50 units with a lead time that is normally distributed with a mean of 20 days and a standard deviation of 2 days. The re-order level of the stock item has been set at 1,100 units. |
| 3. | Stock item Z The item is ordered every 6 months. The lead time is 3 months and demand is normally distributed with a mean of 1,000 units per month and a standard deviation of 80 units. The cost of stock-out is Sh.80 and the cost of holding one unit of buffer stock is Sh.20 per annum. |
Required: | |
| (i) | The re-order level of stock item X that would restrict the probability of a stock out at 5% during a single re-order period. |
| (ii) | The probability of a stock out of item Y during a single re-order period. |
| (iii) | The total annual cost of holding safety stock and stock out cost if re-order level is set at 3,600 units. |
| Usage in units | 1,800 | 1,900 | 2,000 | 2,100 | 2,200 | 2,300 | 2,400 | 2,500 |
| Probability | 0.06 | 0.14 | 0.30 | 0.16 | 0.13 | 0.10 | 0.07 | 0.04 |
| Sales (units) | Probability |
| 270 280 290 300 310 320 | 0.10 0.15 0.20 0.35 0.15 0.05 |
| Usage during the re-order period (units) | Number of times the quantity is used |
| 1,800 1,900 2,000 2,100 2,200 2,300 | 34 40 90 20 10 6 |
| 1 | Daily demand is probabilistic and follows the following distribution: |
| Demand (Units) | Probability | |
| 10 14 18 22 | 0.22 0.30 0.40 0.08 |
| 2 | Lead time is also probabilistic and follows the following distribution: |
| Lead time (days) | Probability | |
| 2 3 4 5 | 0.1 0.3 0.2 0.4 |
| 3 | Ordering cost is Sh.1,000 per order. |
| 4 | Holding cost is Sh.50 per day while stock out cost is Sh.200 per unit. |
| 5 | The policy of the company is to order 55 books whenever stocks fall below 15 books. |
| 6 | The opening inventory on the first day was 55 books. |
| 7 | The following random numbers are provided: 94562406423947955223705699163168744270003 |
| Demand (units) | Probability |
| 3 4 5 6 7 8 9 10 11 12 | 0.02 0.08 0.11 0.16 0.19 0.13 0.10 0.08 0.07 0.06 |
| Lead time (days) | Probability |
| 2 3 4 5 | 0.20 0.30 0.35 0.15 |
| 1 | The ordering cost per order is Sh.80. |
| 2 | The holding cost per unit per day is estimated at Sh.2 while the unit shortage cost is Sh.20 per unit per day. |
| 3 | The re-order quantity is 40 units and the re-order level is 20 units with a beginning inventory balance of 30 units |
| Demand | 68 | 13 | 09 | 20 | 73 | 07 | 92 | 99 | 93 | 18 |
| Lead time | 30 | 22 | 17 | 13 | 08 | 39 | 32 | 24 | 12 | 34 |
| Demand during lead time | Probability |
| 600 650 700 750 800 850 900 950 1,000 1,050 1,100 | 0.25 0.23 0.12 0.10 0.08 0.05 0.05 0.04 0.03 0.03 0.02 |
| 1 | Trans Ltd. places 5 orders annually. |
| 2 | The ordering cost per order amounts to Sh.6,000. |
| 3 | The carrying cost amounts to Sh.1,000 per unit. |
| 4 | The estimated stock-out cost is Sh.5,000 per unit. |
| 5 | The re-order point is 850 units. |
| 6 | The lead time is 12 working days. |
| Daily sale | 100 | 101 | 102 | 103 | 104 | 105 | 106 | 107 | 108 | 109 | 110 |
| Probability | 0.01 | 0.03 | 0.04 | 0.07 | 0.09 | 0.11 | 0.15 | 0.21 | 0.18 | 0.09 | 0.02 |
| Daily sale | 0 | 1 | 2 | 3 |
| Probability | 0.70 | 0.20 | 0.08 | 0.02 |
| 1 | The vendor adopts the rule that, if there is no stock of pizza at the end of the previous day, an order of 110 pieces is placed, otherwise an order of 100 or 105 pieces is placed whichever is nearest to the actual fresh pizza sale on the previous day. |
| 2 | Use the following set of random numbers: |
| Fresh pizza | 37 | 73 | 14 | 17 | 24 | 35 | 29 | 37 | 33 | 68 | |
| One day old pizza | 17 | 28 | 69 | 38 | 50 | 57 | 82 | 44 | 89 | 60 |
| Selling price per unit Sh. | Probability | Variable cost per unit Sh. | Probability | Sales volume (Units) | Probability |
| 700 875 900 | 0.20 0.50 0.30 | 350 550 600 | 0.10 0.50 0.40 | 20,000 30,000 40,000 | 0.20 0.40 0.40 |
| Actual demand (units) | Frequency |
| 300-399 400-499 500-599 600-699 700-799 800-899 900-999 | 0 16 20 25 14 8 3 |
| Demand (packets) | Probability of demand |
| 1,800 | 0.05 |
| 2,000 | 0.10 |
| 2,200 | 0.20 |
| 2,400 | 0.30 |
| 2,600 | 0.20 |
| 2,800 | 0.10 |
| 3,000 | 0.05 |