This paper introduces the Work Task Variation (WTV) problem, a novel scheduling post-processing challenge focused on improving worker shift quality by rearranging tasks within their assigned time slots. The objective is to avoid excessively short or long durations of specific task types, creating smoother and more ergonomic work patterns.

We present RosterLogic Variation, a constraint-based local search (CBLS) inspired solver originally developed at Optischedule and successfully deployed in real-world retail settings. This solver rapidly improves existing schedules using tailored invariants and heuristics. We also provide a complete MiniZinc model and a set of generated realistic publicly available benchmark instances.

We compare our solver’s performance with that of modern CP solvers using the MiniZinc model. Contemporary state-of-the-art CP solvers are approaching the interactive performance of our CBLS solver for coarse planning, representing a significant advancement since the original design and implementation of our solver.

Propagators are central to the success of constraint programming, that is contracting functions removing values proven not to be in any solution of a given constraint. The literature contains numerous propagation algorithms, for many different constraints, and common to all these propagation algorithms is the notion of correctness: only values that appear in no solution to the respective constraint may be removed.

In this paper half-checking propagators are introduced, for which the only requirements are that identified solutions (by the propagators) are actual solutions (to the corresponding constraints), and that the propagators are contracting. In particular, a half-checking propagator may remove solutions resulting in an incomplete solving process, but with the upside that (good) solutions may be found faster. Overall completeness can be obtained by running half-checking propagators as one component in a portfolio solving process. Half-checking propagators opens up a wider variety of techniques to be used when designing propagation algorithms, compared to what is currently available.

A formal model for half-checking propagators is introduced, together with a detailed description of how to support such propagators in a constraint programming system. Three general directions for creating half-checking propagation algorithms are introduced, and used for designing new half-checking propagators for the cost-circuit constraint as examples. The new propagators are implemented in the Gecode system.

Sheet metal cutting using lasers is ubiquitous in the industry, and is used to produce everything from home decorations to excavator scoops. Metal waste is costly for the industry, both in terms of money, but also in terms of an increased environmental footprint. Tomologic develops a unique optimisation system that can reduce this waste drastically. This paper presents a CP approach to the Laser Cutting Path Planning Problem (LCPPP), a very hard important sub problem within the Tomologic optimisation system. A solution to the LCPPP is, given a packing of some details on a metal sheet, an ordering of the cuts necessary to separate the details from the sheet. The problem is complicated by physical factors such as heat from the laser beam, or details moving or flexing. In the paper, we explain the problem in detail and present our CP approach that we developed for solving the problem. The possibility (in CP) of custom search heuristics turned out to be crucial to be able to solve the problem efficiently, as these could be made to guide the search to good first solutions.