Pertemuan II

News Vendor Problem ( Continuous

Demand )Asumsi : D merupakan variabel random

kontinu yang merepresentasikan jumlah Permintaan

Nilai q (jmlh pesanan) optimal, dinotasikan q*, adalah nilai q yang memenuhi :

Contoh

Nita berjualan tas untuk membayar biaya kuliahnya. Tas dibelinya seharga Rp 100.000 dan dijual seharga Rp 250.000 per tas. Jumlah tas yang dpt Nita jual berdistribusi normal dengan mean 100 tas dan standar deviasi 30 tas. Berapa jmlh tas yg seharusnya Nita pesan?

Penyelesaian :

Diketahui : harga beli = Rp 100.000 harga jual = Rp 250.000 mean = 100 std dev = 30

Kasus 1 : d<=q TCbeli q tas = 100.000qjual d tas = -250.000d

TC = 100.000q-250.000dC0 = 100.000

Kasus 2 : d>=q+1 TCbeli q tas = 100.000qjual q tas = -250.000q

TC = -150.000qCu = 150.000 Cu/(C0+Cu)=3/5=0,6

Latihan 1The American Bar Association (ABA) is holding its annual convention in Las Vegas. Six months before the convention begins, the ABA must decide how many rooms should be reserved in the convention hotel. At this time the ABA can reserve room at a cost of $50 per room, but six months before the convention the ABA does not know with certainty how many people will attend the convention. The ABA believes, however, that the number of rooms required is normally distributed with a mean of 5000 rooms and standard deviation of 2000 rooms. If the number of rooms required exceeds the number of rooms reserved at the convention hotel, extra rooms will have to found at neighboring hotels at a cost of $80 per room. It is inconvenient for convention participants to stay at neighboring hotels. We measure this inconvenience by assessing an additional cost of $10 for each room obtained at a neighboring hotel. If a goal is to minimize the expected cost to ABA and its members, how many rooms should the ABA reserve at the convention hotel?

Latihan 2The ticket price for a New York – Indianapolis flight is $200. Each plane can hold up to 100 passengers. Usually some of the passengers who have purchased tickets for a flight fail to show up (no-show). To protect against no shows, the airline will try to sell more than 100 tickets for each flight. Federal law states that any ticketed customer who unable to board the plane is entitled to compensation (say,$ 100). Past data indicate that the number of no-shows for each NY – Indianapolis flight is normally distributed with a mean of 20 and a standard deviation of 5. In order to maximize expected revenues less compensation costs, how many tickets should the airline sell for each flight ? Assume that anybody who doesn’t use a ticket receives a $ 200 refund.