### Problem 1 (Economic Order Quantity)

Electronic Village stocks and sells a particular brand of personal computer. It costs the store $450 each time it places an order with manufacturer for the personal computers. The annual cost of carrying/holding a PC in inventory is $170 (per unit). The store manager estimates that annual demand for the PCs will be 1200 units.

a) Determine the optimal order quantity (EOQ)?

b) What is the total annual cost (ordering & carrying/holding)?

c) What is the maximum inventory level if we order the EOQ quantity?

d) How many times we will order if we use the EOQ quantity?

e) What is the total cost is we order Q=100?

How many times we will order in this case?

### Problem 2 (POQ)

Discount Carpets manufactures Caskade Carpet, which it sells in its adjoining showroom store near the interstate. Estimated annual demand is 20,000 yards of carpet with an annual carrying/holding cost of $2.75 per yard. The manufacturing facility operates the same 360 days the store is open and produces 400 yards of carpet per day. The cost of setting up the manufacturing process for a production run is $720.

1. Determine the optimal order size.

2. What is the total inventory cost?

3. What is the length of time to receive an order?

4. What is the maximum inventory level?

### Problem 3: Probabilistic EOQ

A computer products store stocks color graphics monitors, and the daily demand is normally distributed with a mean of 1.6 monitors and a standard deviation of 0.4 monitor. The lead time to receive an order from the manufacturer is 15 days. Determine the reorder point that will achieve a :

a. 98% service level

b. 95% service level

c. 90% service level

### Problem 4: Scheduling Rules

The following jobs are waiting to be processed at the same machine center. Jobs are logged as they arrive:

Job | Due Date | Duration (days) |

A | 412 | 12 |

B | 418 | 22 |

C | 420 | 34 |

D | 429 | 45 |

E | 435 | 48 |

F | 451 | 52 |

In what sequence would the jobs be ranked according to the following decision rules:

1. FCFS

2. EDD

3. SPT

4. LPT

All dates are specified as manufacturing planning calendar days. Assume that all jobs arrive on day 265. Which decision is best and why?.

### Problem 5 (MRP)

Period | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |

Gross Requirements | 30 | 20 | 40 | 10 | 40 | 60 | 20 | 80 | 10 | 90 | 70 | 10 |

Holding cost is $2.50/unit/week (period)

setup cost: $175

Lead time 1 week

beginning inventory 50

stockout cost=$10

1. Develop a lot for lot solution and calculate total relevant costs for the data in the above tables.

2. Develop a EOQ solution and calculate total relevant costs for the data in the above tables.

3. Develop a POQ solution and calculate total relevant costs for the data in the above tables.

4. Using the data above which is the best technique and why?

### Problem 6 Materials Requirements Planning

A manufacturing plant produces an end-item A, according to the following bill of materials:

The MPS for the end-item A is given in table 1. The manufacturing / assembly lead times, the lot sizing rules, and the current on-hand inventory for all constituting items are given in table 2. There are scheduled receipts for item C at week 1 (100 pieces) and for item D at week 3 (80 pieces).

Table 1: MPS Quantities

MPS Quantities | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

Gross Requirements(A) | – | 30 | – | 50 | – | 200 | – | 120 | 180 | 60 |

Table 2: Lead times, lot sizing rules, on-hand inventory

Item | Lead Time | Lot sizing rule | On-hand inventory |

A | 2 weeks | Lot-for- Lot | 40 |

B | 1 week | Lot-for- Lot | 20 |

C | 2 weeks | Lot-for- Lot | 20 |

D | 3 weeks | Lot-for- Lot | 300 |

Determine the material requirement plan (fill the following tables).

### Problem 7

Five jobs are waiting for processing through two work centres. Their processing time (in minutes) at each work center is contained in the table below. Each job requires work centre Sigma before work centre Delta. According to Johnson's rule, what sequence of jobs will minimise the completion time for all jobs? Please show all your work and provide the GANT chart.

Job | Sigma | Delta |

R | 40 | 10 |

S | 25 | 30 |

T | 50 | 20 |

U | 35 | 35 |

V | 55 | 15 |

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