Question

The Cruise

Their cruise would port out of New Orleans and promised seven days with a panoply of excursions in Jamaica, Cozumel, and Grand Cayman. A list of excursions at each site and key features of each appear in the table. The excursions were all day affairs, so it was possible to engage in only one per port. The cruise ship sailed at night and docked at each of these three ports at the crack of dawn. By dinner time, the ship was on its way to the next port and next set of excursions. The couple was energetic and active for a pair of 52 year-olds., and while enjoying an upper middle class lifestyle, they didn't want to spend money on excursions that might be better spent on tacky souvenirs. The couple therefore budgeted $250 for the excursions — the prices shown are per couple, so for example, the $60 will pay for both of them to fill up on jerk chicken and mannish water.

For each of the duplicate excursions (e.g., snorkeling is offered in all three ports), the couple researched the quality of the activity and ranked the excursion among the available alternatives, with higher numbers indicating better quality. Thus, snorkeling in Jamaica is better than in Cozumel, and snorkeling in Cozumel is better than in Grand Cayman. For the unique experiences, i.e., the turtle farm, the default rating was the a 3.

Site	Rating	Activity	Cost
Jamaica	3	snorkeling	$100
Jamaica	1	party island	$95
Jamaica	2	horseback ride	$120
Jamaica	3	local cuisine	$60
Cozumel	2	snorkeling	$110
Cozumel	3	party island	$55
Cozumel	1	horseback ride	$70
Cozumel	2	local cuisine	$90
Cozumel	3	tequila tasting	$130
Grand Cayman	1	snorkeling	$90
Grand Cayman	2	party island	$60
Grand Cayman	3	horseback ride	$110
Grand Cayman	1	local cuisine	$130
Grand Cayman	3	turtle farm	$95

QUESTION:

The vacationing management scientist sat down at his computer keyboard, cracked his knuckles and decided on the scheme of location (J, C, or G) and excursion (S, P, H, L, Te or Tu), for his decision variables. He wrote constraints that read:

JS + JP + JH + JL + CS + CP + CH + CL + CTe + GS + GP + GH + GL + GTu ≤ 3

JS + JP + JH + JL ≤ 1

CS + CP + CH + CL + CTe ≤ 1

GS + GP + GH + GL + GTu ≤ 1

What do these constraints accomplish in the model and which ones are necessary?

Answer 1

The first constraint indicates that a maximum of 3 activities across 3 locations can be done.

The second constraint indicates that a maximum of one activity in Jamaica can be undertaken

The third constraint indicates that a maximum of one activity in Cozumel can be undertaken

The fourth constraint indicates that a maximum of one activity in Grand Cayman can be undertaken

The second, third and fourth constraints are necessary.

The first one is redundant, because the other three constraints ensure that only one activity can be undertaken at each of the three locations. So total number of activities across all the locations will not exceed three in any case.