CP Methods for Scheduling and Routing with Time-Dependent Task Costs

A particularly difficult class of scheduling and routing problems in-
volves an objective that is a sum of time-varying action costs, which increases the
size and complexity of the problem. Solve-and-improve approaches, which find
an initial solution for a simplified model and improve it using a cost function,
and Mixed Integer Programming (MIP) are often used for solving such problems.
However, Constraint Programming (CP), particularly with Lazy Clause Genera-
tion (LCG), has been found to be faster than MIP for some scheduling problems
with time-varying action costs. In this paper, we compare CP and LCG against
a solve-and-improve approach for two recently introduced problems in maritime
logistics with time-varying action costs: the Liner Shipping Fleet Repositioning
Problem (LSFRP) and the Bulk Port Cargo Throughput Optimisation Problem
(BPCTOP). We present a novel CP model for the LSFRP, which is faster than
all previous methods and outperforms a simplified automated planning model
without time-varying costs. We show that a LCG solver is faster for solving the
BPCTOP than a standard finite domain CP solver with a simplified model. We
find that CP and LCG are effective methods for solving scheduling problems,
and are worth investigating for other scheduling and routing problems that are
currently being solved using MIP or solve-and-improve approaches.