CP methods for scheduling and routing with time-dependent task costs

Abstract

A particularly difficult class of scheduling and routing problems involves an objective that is a sum of time-varying action costs, which increases the size and complexity of such problems. 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 generation (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 the area of 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 problems with time-dependent task costs and are worth investigating for other scheduling and routing problems that are currently being solved using MIP or solve-and-improve approaches, E. Kelareva · P. Kilby Australian National University, Canberra, Australia E. Kelareva (B) · P. Kilby NICTA, Canberra, Australia e-mail: elena.kelareva@nicta.com.au even when customized global constraints are not available. We also investigate a novel approach to solving the BPCTOP-converting the problem into a vehicle routing problem (VRP) and solving using an existing VRP solver.

The matroid team surviving orienteers problem and its variants: Constrained routing of heterogeneous teams with risky traversal

“…A second closely related area of research is the vehicle routing problem (VRP) (Psaraftis et al 2016), which is a family of problems focused on finding a set of paths that maximize quality of service subject to budget or time constraints. The rich vehicle routing problem (RVRP) (Lahyani et al 2015) considers settings such as routing heterogeneous teams (Koç et al 2016), "fleet dimensioning" (choosing team composition) (Hoff et al 2010), and incompatability constraints (Kelareva et al 2014). The vast majority of solution algorithms for the RVRP are heuristic (Lahyani et al 2015) and do not consider risky traversal.…”

Column Generation and Lazy Constraints for solving the Liner Ship Fleet Repositioning Problem with cargo flows

“…Another approach to solving the LSFRP is proposed by Kelareva, Tierney and Kilby [13]. In this study, they solve the full LSFRP with SOS opportunities, however they do not incorporate cargo flows into their model.…”

“…The objective value is unchanged from the reduced MIP, except that now the x variables are also summed over all ships s ∈ S. Constraints (13)(14)(15)(16) are identical to the original formulation, and constraints (17)(18)(19)(20) are disaggregated versions of constraints (7-10), so there is now one constraint for each ship. Finally, constraint ( 21) is a disaggregated version of constraint (9a), which ensures that for each ship, and on each arc, no more cargo can be transported than is either available or able to be transported on the ship.…”

Planning Navigation in Inland Waterways with Tidal Depth Restrictions

“…In terms of scheduling vessel navigation, only Kelareva et al (2012) addressed the problem of assigning arrival and departure times to a fleet of ships in a port subject to tides. They presented mathematical models to maximise total port throughput subject to berth, tugboat and sailing draught availability.…”