Numerical Questions for OM

**Layout Problems**

# Exercise

- What is the percentage change in EOQ when the annual demand is doubled?
- What will be the percentage change in EOQ if 50% decreases in the ordering cost and the Holding cost?
- What will be the % change in EOQ if 40% decrease in the Holding cost and 60% decreases in the ordering cost?
- What will be the % change in EOQ if 40% decrease in the Holding cost and 60% increase in the ordering cost?
- Compute total annual cost of inventory if number of order is 5 @Rs. 20 per order and optimum order quantity is 400 units with holding cost Rs. 2 per unit.
- A manufactures has to supply his customers with 2400 units of his product per year. Shortages are not allowed and storage cost amounts to 1.20 Rs. per unit per year. The setup cost per run is Rs. 160. Find the optimal order quantity, optimum number of orders in a year, and cycle time in days.
- A manufacturing company with stable demand for its product is managing its inventory system for EOQ 320 units. No of order per year are 12 and set up or order preparation cost is Rs. 50 per order. Find what value of the holding cost adjusts this system. Also find the Reorder Level, if lead time is 10 days.
- A firm requires 18,000 units of raw materials in a period of 6 months. The carrying cost is 20% of cost. The set up cost per set up is Rs. 10. The cost per unit is Rs. 19. The average lead time is 5 days (Assuming 360 days in a year.)

Required

(a) Economic order quantity

(b) Total annual cost

(c) No of days between orders (i.e. cycle time)

(d) Reorder level

- A computer shop stocks and sells a mercantile brand of personal computer. It costs the store Rs. 450 each time it Places an order with the manufacturer for the personal computers. The annual cost of carrying the PCs in inventory is Rs. 170. The store manager estimates that annual demand for the PCs will be 1200 units. Lead time is given as 10 days and assuming working days per annum is 300.

Determine:

(a) Economic order quantity

(b) Re-order point

(c) Number of orders

- A firm consumes 50,000 units of an item per annum, each costing Rs. 10. The order costs are expected to be Rs.40 and inventory carrying costs 10% of the annual average inventory value. Find EOQ. If the company operates 250 days per year, the procurement time is 10 days and the buffer stock is 500 units, find the reorder level and average inventory level.
- A company demands 50,000 units per quarter. The ordering cost is Rs.40 per order and carrying cost is 10%. The cost price of inventory is Rs. 10 per unit. The lead time for placing order is 5 days. Required:

(a) Economic order quantity (EOQ)

(b) No of orders

(c) Cycle time

(d) Total cost of inventory.

(e) Reorder level (assuming 300 working days per annum)

- S and P company requires 1000 units of materials monthly. If ordering costs are Rs. 250 per order, expected lead time is 5 days, unit cost is Rs. 25 per unit and annual inventory holding costs are charged at 20%, and the company operates 250 days a year: compute EOQ and ROL.
- The production department of a food and beverage company requires 1800 units of raw materials for manufacturing a special food semi-annually. It has been estimated that the cost of placing an order is Rs. 36 and the cost of carrying inventory is 12.5% of the investment in the inventories. The price is Rs. 20 per unit. Purchase manager wishes to determine an ordering policy for the raw material. Recommend the manager in the following aspects:

(a) The optimal lot size

(b) The optimal reorder time.

- Star electronics is a dealer of the Sony mobile sets. It has observed that the annual demand is about 768 sets and the annual cost of the holding a mobile set in stock is Rs. 30 where as an order placed for the sets costs Rs.20. Using the information below find:

(a) Optimum order quantity.

(b) Optimum number of the orders to be placed in a year’s time.

(c) Total minimum variable cost.

- What are the main objectives of holding inventory in an organization? What are the major costs involved in holding inventory? The ABC requires 100 units per months though out the year at constant rate. If ordering cost are Rs. 250 per order, unit cost of he item is Rs. 25 and annual inventory holding cost are charged at 30%, then determine the EOQ for the item. [TU 2059]
- Nepal soft drink Co. has a soft drink product which has constant annual demand rate of 3000 cases and cost Rs. 200/case. If ordering cost are Rs. 20 and inventory holding cost are charged at 25%, what is the EOQ for this product? Also determine the cycle time

(in days). [TU 2060] - A manufacturer has to supply his customers with 600 units of his product per year. Shortages are not allowed and the storage cost amounts to Rs. 0.6 per unit per year. The set up cost per run is Rs. 80. Find the optimum run size and the minimum average yearly cost. [TU 2061]
- A manufacturing organization experienced constant annual demand of 10,000 unit of an item which cost Rs. 40 per unit. If the order cost is Rs. 20 per order and the holding cost is 25% of the item costs determine the economic order quantity and the reorder level with no lead-time known. [TU 2062]

# Answers

- No change 3. 18.35% decrement
- 63.3% increment 6. Q = 730.30; N = 4(approx); CT = 0.304
- Rs. 3.75 and 106.67 8. (a) 706.13; (b) Rs. 685851.47; (c) 0.0196; (d) 500
- (a) 80; (b) 40; (c) 15
- (a) 4000; (b) 50; (c) 2.02; (d) Rs. 2004000; (e) 3333.33
- 1095.45 and 240 13. 322 units (b) 32days
- 1095.45units 16. 49 cases and 6 days
- 400 units and Rs. 240 18. 283 units, 167 units.

**Quality Management**

- A machine is set to deliver packages of a given weight. 10 samples of size 5 were recorded and data are given below.

S.N. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

Mean | 15 | 17 | 15 | 18 | 17 | 14 | 18 | 15 | 17 | 16 |

Range | 7 | 7 | 4 | 9 | 8 | 7 | 12 | 4 | 11 | 5 |

Draw mean and range chart and then comment on the state of control.

- Construct mean and range chart for the following data in which samples of 4 being taken every hour.

S.N | 1 | 2 | 3 | 4 | 5 | 6 |

1 | 42 | 39 | 41 | 69 | 61 | 67 |

2 | 65 | 44 | 54 | 89 | 78 | 73 |

3 | 75 | 80 | 68 | 91 | 94 | 81 |

4 | 78 | 81 | 77 | 98 | 99 | 95 |

- Draw mean chart and R chart from the following measurement and comment on the process control.

S.N | Measurement in mm | ||||

1
2 3 4 5 6 7 |
40
44 45 35 46 45 41 |
40
40 42 46 40 42 45 |
42
34 41 47 44 46 43 |
38
46 40 48 42 44 44 |
42
44 43 45 40 43 42 |

- A company manufacturers a product which is packed in one kg tins. It utilizes automatic filling equipment. It takes a sample of 5 cans every two hours and measures the filling in each of the 5 cans. Set up control chart and state whether the process in under control.

S.N. | 1 | 2 | 3 | 4 |

1
2 3 4 5 |
1001
999 995 1000 994 |
1002
998 1002 1001 996 |
1000
1001 1003 999 996 |
999
999 1002 1002 999 |

- Construct mean and range chart for the following data of sample size 5.

S.N | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |

1 | 42 | 42 | 19 | 36 | 42 | 51 | 60 | 18 | 15 | 69 | 64 | 61 |

2 | 65 | 45 | 24 | 54 | 51 | 74 | 60 | 20 | 30 | 109 | 90 | 78 |

3 | 75 | 68 | 80 | 69 | 57 | 75 | 72 | 27 | 39 | 113 | 93 | 94 |

4 | 78 | 72 | 81 | 77 | 59 | 78 | 95 | 42 | 62 | 118 | 109 | 109 |

5 | 87 | 90 | 81 | 84 | 78 | 132 | 138 | 60 | 84 | 153 | 112 | 136 |

- Draw a control chart for the following data and state your conclusion. Sample no. (each of 100) no. of defectives fraction defectives.

Sample no. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

No. of defectives
Fraction defectives |
12
0.12 |
10
0.10 |
6
0.06 |
8
0.08 |
9
0.09 |
9
0.09 |
7
0.07 |
10
0.10 |
11
0.11 |
8
0.08 |

- A sample of 300 pieces is drawn from the hourly production of semi automatic machine and each item is checked. The numbers of defective items found in ten successive sample of this type are: 17, 12, 14, 22, 9, 14, 12, 9, 15, 19.

Draw the suitable control chart and comment on the state of control.

- Twenty samples of n = 200 were taken by a worker at a workstation in a production process. The number of defectives found in each sample are given.

Sample | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

Defectives | 20 | 18 | 20 | 21 | 22 | 18 | 16 | 12 | 14 | 16 |

Sample | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |

Defectives | 12 | 14 | 18 | 11 | 12 | 1 | 17 | 14 | 16 | 19 |

Set up control chart for defective. Was the process in control throughout?

- The following data refer to visual defects found in the inspection of the first 10 samples of size 100. Use the data to obtain upper and lower control limits for fraction defective in sample of 100. Represent the first 10 samples result in the chart you prepare to show the central line and control limits.

Sample | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

Defectives | 2 | 1 | 1 | 3 | 2 | 3 | 4 | 2 | 2 | 0 |

- Construct a suitable central chart for the following information and comment on the result.

Sample | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

Defectives | 12 | 10 | 6 | 8 | 9 | 9 | 7 | 11 | 11 | 9 |

- Draw a suitable central chart for the following data pertaining to the number of foreign threats (considered as defects) in 15 pieces of cloth 2m × 2n of certain make of synthetic fiber and state your conclusion.

7, 12, 3, 20, 21, 5, 4, 3, 10, 8, 0, 9, 6, 7, 20

# Answer

- For Mean Chart :

CL = 16.2, LCL = 11.908 and UCL = 20.492

For Range Chart :

CL = 7.4, LCL = 0 and UCL = 15.651

- For Mean Chart :

CL = 72.45, LCL = 47.05 and UCL = 97.84

For Range Chart :

CL = 34.83, LCL = 0 and UCL = 79.482

- For Mean Chart :

CL = 42.54, LCL = 38.75 and UCL = 46.33

For Range Chart :

CL = 6.57, LCL = 0 and UCL = 13.895

- For Mean Chart :

CL = 999.4, LCL = 996.065 and UCL = 1002.735

For Range Chart :

CL = 5.75, LCL = 0 and UCL = 12.16

- For Mean Chart :

CL = 71.6, LCL = 37.17 and UCL = 106.03

For Range Chart :

CL = 59.67, LCL = 0 and UCL = 126.20

- CL = 0.09, LCL = 0.0042 and UCL = 0.1785,
- CL = 14.31, LCL = 3.24 and UCL = 25.38
- CL = 15.56, LCL = 4.20 and UCL = 26.92
- CL = 2, LCL = 0 and UCL = 6.2

- CL = 9.2, LCL = 0.53 and UCL = 17.87
- CL = 9, LCL = 0 and UCL = 18