1 Andrew McGregor forecast weekly demand for MP 411 pumps as follows:
|
Week
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
|
Demand
|
1
|
6
|
10
|
21
|
18
|
7
|
4
|
3
|
2
|
4
|
15
|
|
Week
|
12
|
13
|
14
|
15
|
16
|
17
|
18
|
19
|
20
|
21
|
22
|
|
Demand
|
27
|
38
|
51
|
40
|
22
|
12
|
8
|
6
|
7
|
2
|
3
|
Each pump costs £80, it costs £800 to place an order and get delivery, and holding cost is 20 per cent of value a year. Design a reasonable ordering policy for the pump. How much does this cost a year?
2 At the beginning of December Southern Conifers Limited employ a contractor to cut enough trees to meet the expected demand for Christmas trees. They sell these to a local wholesaler in batches of 100. Over the past few years the demand has been as follows.
|
Batches
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
|
Probability
|
0.1
|
0.1
|
0.2
|
0.2
|
0.1
|
0.1
|
0.1
|
0.1
|
0
|
If it costs £16 to cut and trim a tree that sells for £25, how many trees should the company cut down?
3 The demand for an item is Normally distributed with mean of 40 units and standard deviation of 4 units a month. The lead time is one month, shortage cost is £200, reorder cost is £40, and holding cost is £4. What are optimal values for the order quantity and reorder level? 5.6 Lee Brothers advertise a 90 per cent cycle-service level for all stock items. Stock is replenished from a single supplier who guarantees a lead time of 4 weeks. What reorder level should they use for an item that has a Normally distributed demand with mean 2,000 units a week and standard deviation of 200 units? What is the reorder level for a 95 per cent cycle-service level? What is the effect of moving to a periodic review method with interval of 2 weeks?
4 Demand for an item is 100 units a week with a standard deviation of 10 units. Lead time is one week and the reorder level used is 115 units. What is the probability of running out of stock?