The Newspaper Seller’s Problem

A classical inventory problem concerns the purchase and sale of newspapers. The paper seller buys the papers for 33 cents each and sells them for 50 cents each. Newspapers not sold at the end of the day are sold as scrap for 5 cents each. Newspapers can be purchased in bundles of 10. Thus, the paper seller can buy 50, 60, and so on.

There are three types of Newsday’s, “good,” “fair,” and “poor,” with probabilities of 0.35, 0.45, and 0.20, respectively. The distribution of papers demanded on each of these days is given in the table below.

The problem is to determine the optimal number of papers the newspaper seller should purchase. This will be accomplished by simulating demands for 20 days and recording profits from sales each day.

The profits are given by the following relationship:

Profit = Revenue from sales - Cost of newspapers - Lost profit from excess demand + Salvage from the sale of scrap papers

Distribution of Newspapers Demanded

Demand	Good	Fair	Poor
40	0.03	0.10	0.44
50	0.05	0.18	0.22
60	0.15	0.40	0.16
70	0.20	0.20	0.12
80	0.35	0.08	0.06
90	0.15	0.04	0.00
100	0.07	0.00	0.00

Random Digit Assignment for Type of Newsday

Type of Newsday	Probability	Cumulative Probability	Random Digit Assignment
Good	0.35	0.35	01−35
Fair	0.45	0.80	36−80
Poor	0.20	1.00	81−00

Random Digit Assignments for Newspapers Demanded

	Demand Distribution			Cumulative Probability			Random Digit Assignment
Demand	Good	Fair	Poor	Good	Fair	Poor	Good	Fair	Poor
40	0.03	0.10	0.44	0.03	0.10	0.44	01−03	01−10	01−44
50	0.05	0.18	0.22	0.08	0.28	0.66	04−08	11−28	45−66
60	0.15	0.40	0.16	0.23	0.68	0.82	09−23	29−68	67−82
70	0.20	0.20	0.12	0.43	0.88	0.94	24−43	69−88	83−94
80	0.35	0.08	0.06	0.78	0.96	1.00	44−78	89−96	95−00
90	0.15	0.04	0.00	0.93	1.00	1.00	79−93	97−00	-
100	0.07	0.00	0.00	1.00	1.00	1.00	94−00	-	-

Profit = Revenue from sales - Cost of newspapers - Lost profit from excess demand + Salvage from sale of scrap papers

Newspaper Bought each day is 60.

Random Digits for Type of Newsday: 86, 72, 6, 94, 45, 82, 48, 80, 24, 83, 11, 78, 79, 29, 64, 47, 20, 31, 51, 57

Random Digits for Demand: 90, 75, 9, 33, 69, 48, 12, 23, 87, 97, 65, 22, 88, 33, 24, 75, 93, 58, 31, 70

Sl	Random Digits for Type of Newsday	Type of Newsday	Random Digits for Demand	Demand for each day	Bought	Sell	Revenue from sales	Cost of news papers	Lost profit from excess demand	Salvage from sale of scrap papers	Profit for That day
1	86	Poor	90	70	60	60	$30	$19.8	$1.7	-	$8.5
2	72	Fair	75	70	60	60	$30	$19.8	$1.7	-	$8.5
3	6	Good	9	60	60	60	$30	$19.8	-	-	$10.2
4	94	Poor	33	40	60	40	$20	$19.8	-	$1	$1.2
5	45	Fair	69	70	60	60	$30	$19.8	$1.7	-	$8.5
6	82	Poor	48	50	60	50	$25	$19.8	-	$0.5	$5.7
7	48	Fair	12	50	60	50	$25	$19.8	-	$0.5	$5.7
											$48.3