Question

The Baruch Star Hotel in Miami, FL is considering doing overbooking in order to deal with the constant problem they have with no-shows. The table given below presents the number of no-shows and the probability of each occurring. # of No-Probability of No- Shows Shows occurring (d) Pd) 0 0.07 0.07 2 0.10 3 0.02 4 0.12 5 0.01 6 0.04 7 0.19 8 0.16 9 0.22 a) What would be your recommendation for overbooking if the average rate per room per night is $145 and the cost of not honoring a reservation is $205? b) What is the expected loss for your overbooking choice?

Answer 1

DEMAND	PROBABILITY	PRODUCED	----------------------->
		0	1	2	3	4	5	6	7	8	9
0	0.07	0	145	290	435	580	725	870	1015	1160	1305
1	0.07	205	0	145	290	435	580	725	870	1015	1160
2	0.1	410	205	0	145	290	435	580	725	870	1015
3	0.02	615	410	205	0	145	290	435	580	725	870
4	0.12	820	615	410	205	0	145	290	435	580	725
5	0.01	1025	820	615	410	205	0	145	290	435	580
6	0.04	1230	1025	820	615	410	205	0	145	290	435
7	0.19	1435	1230	1025	820	615	410	205	0	145	290
8	0.16	1640	1435	1230	1025	820	615	410	205	0	145
9	0.22	1845	1640	1435	1230	1025	820	615	410	205	0
EXPECTED COST		1166.45	985.95	829.95	708.95	594.95	522.95	454.45	399.95	411.95	479.95

OPTIMAL COST = 399.95

OPTIMAL COURSE OF ACTION IS TO PRODUCE = 7

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