JOSH Editorial

Planning and scheduling have an interesting relationship. In informal usage, planning and scheduling are frequently treated almost interchangeably. In contrast, formally, their refined and tightly specified descriptions appear quite different: planning is a PSPACE-hard problem, while scheduling is an archetypal NP-hard problem. The research communities that examine these problems seem, to a large extent, to share this dichotomy, with surprisingly distinct research communities having developed around the two problems. Despite this division, there have been many individuals in both communities who have recognised the importance and relevance of the relationships between the two problems. The apparent simplicity of the separation offered by the complexity classes of the different problems belies the difficulty of giving a clean intuition to the differences between planning and scheduling — a difficulty which seems to return to the much less sharply drawn boundaries of the informal usage of the terms. The common characterisation is that planning is the problem of deciding what actions should be performed to solve a problem, while scheduling is about deciding when to execute them and with what resources. For example, this is the characterisation used by Garrido et al in their paper in this issue. Although this characterisation is convenient, it is a simplification: which action to use to solve a problem frequently depends on how resources are to be allocated, so that plans depend on scheduling choices, while equally, what resources are available to support the scheduling decisions depend on which actions are selected to solve a problem. Thus, the choices made in planning and scheduling are interlocked and interdependent. The papers in this special issue were carefully selected, following a relatively extended reviewing process, from a large number of original submissions. These papers were selected both for their quality (which, of course, had to meet the regular requirements of the journal) and for their relevance to the special relationship between planning and scheduling. The paper ”A constraint programming reformulation for planning: from plan scheduling to plan generation” by Garrido et al particularly highlights the tight interdependence between the problems, while also highlighting some of the important differences in the methods commonly employed in solving problems within the two communities. While scheduling researchers develop highly sophisticated solutions to particular problems, such as nurse rostering or vehicle routing, planning researchers look for generic solutions that are, necessarily, less sophisticated but have wider applicability. In the paper by Garrido et al, an interesting class of planning problems has been addressed that require resource management to be scheduled in time. Since the experiments were performed on a collection of planning bench marks it remains to be seen how well the approach taken will perform on more traditional scheduling problems prduction, inventory, distribution and routing problems. While planners frequently depend on cleverly generated heuristics to guide a relatively simple search, schedulers more often rely on local search techniques to steadily refine and improve one or more candidate solutions. Tabu search is one such example, appearing as a basic tool in Bard’s paper ”The Integrated Production, Iventory and Distribution and Routing Problem for a Single Commodity” in this issue. This paper also exploits the use of a Mixed Integer Linear Programming (MILP) formulation in tackling the problem. Although the link with planning is not made highly explicit, there is a clear relationship between some of the strategies explored in this paper and those coming to the fore in recent developments in planning. In planning there is increasing interest in decomposition-based approaches, planning with numeric quantities and under complex resource constraints and integration of propositional planning with solvers for real, integer and mixed integer linear optimisation problems. Heuristics and bounds computations based on relaxations are also commonly explored in planning. In this paper an approach is proposed that combines