Formulate an assignment model for deciding the players

Reference no: EM133660760

Question 1: Chess matches are most interesting when the two players are approximately equal in ability. There are eight players from two teams, whose scores based on past performance are: Team 1 - 1600, 1825, 1670, and 1710; Team 2 -1920, 1750, 1660, and 1790. For the first round, the tournament organizers want to see close match-ups.

(a) Formulate an assignment model for deciding the players for the four matches.
(b) Solve the problem using (i) LINGO or (ii) the Excel Solver.

Question 2: The budget can be taken as a system constraint.

Journal	Annual Cost	Citations	Evaluations
1	$2900	150	8.2
2	$2300	135	7.7
3	$1800	140	9.8
4	$2600	190	9.3
5	$3200	128	8.3
6	$2400	155	7.6

There are three goals:

(i) The number of unsubscribed journals should be as low as possible.
(ii) The average number of citations of the subscribed journals should meet or exceed the average number of citations of all six journals.
(iii) The average faculty evaluations of the subscribed journals should be at least 8.1.

The first goal is four times as important as the third goal, and the second goal is three times as important as the third goal.

(a) Define the set of decision variables and the three deviational variables, write the three sets of deviational constraints, and finally put all this into a model with an objective function and the budget constraint. (Hint: For two of the deviational constraints, you will need to cross-multiply before inserting the deviational variable.)

(b) Put this algebraic model into LINGO or the Excel Solver.

Question 3: A firm wishes to produce a single product at one or more locations so that the total monthly cost is minimized subject to demand being satisfied. At each location there is a fixed charge to be paid if any are produced (but is nil otherwise), and a variable cost which depends on whether the units are produced on regular time or on overtime. Each location has capacity restrictions on regular and overtime production. The relevant data are:

Plant Location	Fixed Cost	Regular Time		Overtime
Plant Location	Fixed Cost	Unit Cost	Capacity	Unit Cost	Capacity
1	2100	3.80	1200	4.60	500
2	1900	2.90	1500	4.10	600
3	2300	4.20	1800	5.60	800
4	1700	3.40	2000	4.20	550
5	2700	3.60	2900	5.10	650
6	2000	3.10	3000	4.90	900

Demand is for 8000 units per month.

(a) Formulate the algebraic model.

(b) Put the model into LINGO or the Excel Solver.

Reference no: EM133660760

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