PROBLEM 6: Multi-Criteria Decision Making

The fast-food chain, Snabbmat, has been planning to expand for some time. Three avenues for expansion are under consideration:

1) Service counter: These are counters primarily located in office blocks where office workers pass by and buy their meals. The menu consists only of take-away meals. Currently, five sites are available for this type of activity.

2) Extended counter: These are counters located in shopping centres where an area is especially landscaped and maintained for on-site dining. The menu could be a little more varied to integrate meals on the spot. Currently, seven sites are available for this type of activity.

3) Stand-alone restaurant with dining room: The menu would be similar to that of the extended counters, but service would be done at the tables. Currently, three sites are available for this type of activity.

Snabbmat now wishes to determine the best way to expand its activities while taking into account the number of jobs created and the return on investment. The following table presents these data for each type of activity along with the start-up costs:

Snabbmat has a budget of €2 million to launch these activities.

Question 1:

Formulate an integer linear program (ILP) for Snabbmat to determine the number of counters/restaurants of each type that would maximise the annual return of the expansion plan. In this case, the ILP will include only hard constraints: total start-up costs cannot exceed the budget, the number of counters/restaurants of each type must be non-negative integers, and the maximum number of counters/restaurants of each type is limited as described in points 1-3 above. Clearly define the variables, the objective function, and the constraints.

Question 2:

Suppose that Snabbmat has two goals:

1) Create 141 jobs.

2) Obtain an annual return of €965,000.

Formulate a multi-objective model with deviational variables that would enable the minimisation of the maximum deviation (expressed as the percentage deviation from the target value) for the two objectives considered here. Note that excess or surplus deviational variables are not necessary as Snabbmat is concerned only about falling below the targets.