The problems
Fifteen introductory numerical models, three families of problems, nine mixed problems and forty problems to model.
The thirty-eight solved problems all follow the same scheme: model, proof of the links between the variables, instance, constructive heuristic, dual of the LP relaxation, solution with Gurobi and additional modelling questions.
The difficulty stars
Every problem carries a difficulty from ★☆☆☆☆ to ★★★★★. It measures how hard it is to build the model: how many families of variables are needed, which links must be recognised, whether there is a time structure, a big-M, a disjunction, a min-max, brackets, an "if and only if". It does not measure the size of the instance, the solver time or the length of the page: a problem with an elementary model stays at one star even when its dual is laborious.
Forty problems to model
Presented as they would arise in practice — a text, some data, a question — with no model already written: twenty with explicit numerical data and twenty in symbolic form. The solutions are reserved for instructors.
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Fifteen numerical models
The easiest examples, with explicit data and few variables: one per technique, to be read before the families to get your bearings. From EX 1 to EX 15.
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Assignment and scheduling
Jobs on machines with availability: assignment costs, fixed costs, selection, parallel jobs, classes with setup, ``if and only if'' bonuses, sequencing with big-M. Seven problems.
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Location and coverage
Where to open facilities and hubs: aggregated and disaggregated activation, an ``if and only if'' with two linking constraints, maximum variable. Four problems.
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Production planning
How much to produce, not merely whether: inventory balance, fixed setup cost, workforce and hirings, minimum lot with a variety bonus. Three problems.
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Mixed problems
The problems that have no family: alternative modes, minimum lots, containers, splitting and balancing. This is where the LP relaxation stops being useful and the dual bound must be found with combinatorial arguments. Nine solved problems.
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Problems to model
Forty problems presented as they would arise in practice, with no model already written: twenty with explicit numerical data and twenty in symbolic form. The solutions are reserved for instructors.