5 research outputs found
Introducing Financial Derivatives into Football Transfer Markets
Εθνικό Μετσόβιο Πολυτεχνείο--Μεταπτυχιακή Εργασία. Διεπιστημονικό-Διατμηματικό Πρόγραμμα Μεταπτυχιακών Σπουδών (Δ.Π.Μ.Σ.) “Μαθηματική Προτυποποίηση σε Σύγχρονες Τεχνολογίες και στα Χρηματοοικονομικά
Weighted tardiness minimization for unrelated machines with sequence-dependent and resource-constrained setups
Motivated by the need of quick job (re-)scheduling, we examine an elaborate
scheduling environment under the objective of total weighted tardiness
minimization. The examined problem variant moves well beyond existing
literature, as it considers unrelated machines, sequence-dependent and
machine-dependent setup times and a renewable resource constraint on the number
of simultaneous setups. For this variant, we provide a relaxed MILP to
calculate lower bounds, thus estimating a worst-case optimality gap. As a fast
exact approach appears not plausible for instances of practical importance, we
extend known (meta-)heuristics to deal with the problem at hand, coupling them
with a Constraint Programming (CP) component - vital to guarantee the
non-violation of the problem's constraints - which optimally allocates
resources with respect to tardiness minimization. The validity and versatility
of employing different (meta-)heuristics exploiting a relaxed MILP as a quality
measure is revealed by our extensive experimental study, which shows that the
methods deployed have complementary strengths depending on the instance
parameters. Since the problem description has been obtained from a textile
manufacturer where jobs of diverse size arrive continuously under tight
deadlines, we also discuss the practical impact of our approach in terms of
both tardiness decrease and broader managerial insights
One Benders cut to rule all schedules in the neighbourhood
Logic-Based Benders Decomposition (LBBD) and its Branch-and-Cut variant,
namely Branch-and-Check, enjoy an extensive applicability on a broad variety of
problems, including scheduling. Although LBBD offers problem-specific cuts to
impose tighter dual bounds, its application to resource-constrained scheduling
remains less explored. Given a position-based Mixed-Integer Linear Programming
(MILP) formulation for scheduling on unrelated parallel machines, we notice
that certain OPT neighbourhoods could implicitly be explored by regular
local search operators, thus allowing us to integrate Local Branching into
Branch-and-Check schemes. After enumerating such neighbourhoods and obtaining
their local optima - hence, proving that they are suboptimal - a local
branching cut (applied as a Benders cut) eliminates all their solutions at
once, thus avoiding an overload of the master problem with thousands of Benders
cuts. However, to guarantee convergence to optimality, the constructed
neighbourhood should be exhaustively explored, hence this time-consuming
procedure must be accelerated by domination rules or selectively implemented on
nodes which are more likely to reduce the optimality gap. In this study, the
realisation of this idea is limited on the common 'internal (job) swaps' to
construct formulation-specific -OPT neighbourhoods. Nonetheless, the
experimentation on two challenging scheduling problems (i.e., the minimisation
of total completion times and the minimisation of total tardiness on unrelated
machines with sequence-dependent and resource-constrained setups) shows that
the proposed methodology offers considerable reductions of optimality gaps or
faster convergence to optimality. The simplicity of our approach allows its
transferability to other neighbourhoods and different sequencing optimisation
problems, hence providing a promising prospect to improve Branch-and-Check
methods