ENGSCI / STATS 255 MODELLING AND ANALYTICS IN OPERATIONS RESEARCH OPTIMISATION AND DATA-DRIVEN DECISION MAKING

Question 1 (16 marks)

Kwantas is an Australian airline that is restarting Trans-Tasman operations after a 12-month suspension due to recent events.   Given the expected demand, Kwantas is scheduling their Airbus A330-300 aircraft on Trans-Tasman routes; this aircraft-type has 270 economy seats.

For a particular Sydney-to-Auckland flight, Kwantas needs to decide how many economy seats to allocate to each of four fare categories.   Each fare category is associated with a ticket price. Each economy seat with a passenger costs Kwantas ·100 in operational costs, except for Premium seats which cost Kwantas ·150 per seat.

Kwantas requires there to be at least 10, and no more than 30 reward seats.  No more than 30% of total seats can be Discounted seats.  At least 20% of seats allocated with a non-zero ticket price must be Full or Premium seats. All 270 seats must be allocated into one of the fare categories.

Kwantas would like to maximise the profit from allocating seats on this Sydney to Auckland flight. You can assume that all seats allocated into each category will be sold/occupied.

(a) Define the decision variables required to formulate this problem, and give their units.

(2 marks)

once in the objective and in each constraint, and that all expressions are linear.(b) Formulate this problem as a linear program.  Ensure that each variable appears at most

(8 marks)

The following relate to independent changes to the formulation in Question 1(b).

Show the changes needed in your formulation in order to model these additional requirements. Ensure that you define any new variables that are needed, and that all resulting expressions are linear, with each variable appearing no more than once. Giving expressions such as 0.5 × 73 is acceptable in your answers.

(c) Kwantas would like to ensure that if any seats are to be allocated as Premium, then at least five seats are allocated as such.   Because Premium customers expect luxury, a fixed ·500 cost must be paid for top-quality Champagne if any Premium seats are allo- cated.                                                                                                                      (3 marks)

(d) If there are too many reward seats offered on a flight, the total cost of operating the flight increases due to increased administration costs.  Specifically, if 21 or more reward seats are allocated and sold on this flight, then an additional fixed cost of ·2000 must be paid.                                                                                                                        (3 marks)