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Optimal Methods for Resource Allocation and Scheduling: a CrossDisciplinary Survey
, 2010
"... Classical scheduling formulations typically assume static resource requirements and focus on deciding when to start the problem activities, so as to optimize some performance metric. In many practical cases, however, the decision maker has the ability to choose the resource assignment as well as th ..."
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Classical scheduling formulations typically assume static resource requirements and focus on deciding when to start the problem activities, so as to optimize some performance metric. In many practical cases, however, the decision maker has the ability to choose the resource assignment as well as the starting times: this is a farfromtrivial task, with deep implications on the quality of the final schedule. Joint resource assignment and scheduling problems are incredibly challenging from a computational perspective. They have been subject of active research in Constraint Programming (CP) and in Operations Research (OR) for a few decades, with quite difference techniques. Both the approaches report individual successes, but they overall perform equally well or (from a different perspective) equally poorly. In particular, despite the well known effectiveness of global constraints for scheduling, comparable results for joint filtering of assignment and scheduling variables have not yet been achieved. Recently, hybrid approaches have been applied to this class of problems: most of them work by splitting the overall problem into an assignment and a scheduling subparts; those are solved in an iterative and interactive fashion with a mix of CP and
Solving an integrated employee timetabling and jobshop scheduling problem via hybrid branchandbound
 COMPUTERS & OPERATIONS RESEARCH
, 2009
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Field Operations Planning for Agricultural Vehicles: A Hierarchical Modeling Framework
 Agricultural Engineering International: the CIGR Journal of Scientific Research and Development. IX: Manuscript PM
, 2007
"... The execution of field operations by a fleet of cooperating machines needs to be carefully planned, in order to achieve maximum efficiency. Hence, it is necessary to describe these operations with mathematical models that can be used for optimal planning. The complexity of agricultural operations ma ..."
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The execution of field operations by a fleet of cooperating machines needs to be carefully planned, in order to achieve maximum efficiency. Hence, it is necessary to describe these operations with mathematical models that can be used for optimal planning. The complexity of agricultural operations makes such modeling difficult. Important variables for planning, such as logistics for crop yield, cannot be accurately known in advance. Furthermore, unexpected events may happen during operations, such as harvester blockages and restarting operations. In this paper the overall planning problem is decomposed into a hierarchy of simpler problems that can be solved independently and efficiently. Each lowerlevel problem is modeled in a way that optimization algorithms from the operations research area can be adopted for their solution. The dynamic nature of the problem and the inherent uncertainties of many parameters suggest the adoption of a closed loop control system, which results in a sequence of planning, execution and replanning. The resulting optimal operation plans can be complex and their execution requires an advanced degree of machine, or field robot autonomy. Overall, the adoption and modification of existing methods from other research areas such as logistics, routing, factory scheduling, and robotics offer a very promising approach for the efficient planning of operations executed by agricultural vehicles.
On the Reformulation of Vehicle Routing Problems and Scheduling Problems
, 2002
"... In the capacitated vehicle routing problem with time windows (CVRPTW) we have a set of customer visits, each with a demand and time window in which the visit must be serviced, and a eet of vehicles, each vehicle of limited capacity. The problem is to visit all customers whilst minimising total t ..."
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In the capacitated vehicle routing problem with time windows (CVRPTW) we have a set of customer visits, each with a demand and time window in which the visit must be serviced, and a eet of vehicles, each vehicle of limited capacity. The problem is to visit all customers whilst minimising total travel distance and the use of vehicles. In the jobshop scheduling problem (JSSP) we have a set of jobs, composed of a sequence of activities, and a set of resources. Each activity requires exclusive use of a resource for a given amount of time. The problem is then to sequence activities on resources such that all precedence constraints are respected and the makespan is minimised. We can reformulate a VRP to an open shop scheduling problem by representing visits as activities, vehicles as resources on the factory oor, and travel as set up costs between activities. We also have the inverse reformulation. In this paper we present two reformulations: from VRP to open shop, and the inverse, from JSSP to VRP. Not surprisingly, we show that VRP technology performs poorly on reformulated JSSP, as does scheduling technology on reformulated VRPs. We then present a preprocessing transformation that \compresses" the VRP, transforming an element of travel into the duration of the visits. The compressed VRPs are then reformulated as scheduling problem, to determine if it is primarily distance in the VRP that causes scheduling technology to degrade on the reformulated problem.
A TimeDependent NoOverlap Constraint: Application to Urban Delivery Problems
"... Abstract. The TimeDependent Traveling Salesman Problem (TDTSP) is the extended version of the TSP where arc costs depend on the time when the arc is traveled. When we consider urban deliveries, travel times vary considerably during the day and optimizing a delivery tour comes down to solving an ins ..."
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Abstract. The TimeDependent Traveling Salesman Problem (TDTSP) is the extended version of the TSP where arc costs depend on the time when the arc is traveled. When we consider urban deliveries, travel times vary considerably during the day and optimizing a delivery tour comes down to solving an instance of the TDTSP. In this paper we propose a set of benchmarks for the TDTSP based on real traffic data and show the interest of handling time dependency in the problem. We then present a new global constraint (an extension of nooverlap) that integrates timedependent transition times and show that this new constraint outperforms the classical CP approach. 1
ConstraintBased Scheduling: A Tutorial
"... Given a set of resources with given capacities, a set of activities with given processing times and resource requirements, and a set of temporal constraints between activities, a “pure ” scheduling problem consists of deciding when to execute each activity, so that both temporal constraints and reso ..."
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Given a set of resources with given capacities, a set of activities with given processing times and resource requirements, and a set of temporal constraints between activities, a “pure ” scheduling problem consists of deciding when to execute each activity, so that both temporal constraints and resource constraints are satisfied. Most scheduling problems can easily be represented as instances of the constraint satisfaction problem (Kumar, 1992): given a set of variables, a set of possible values (domain) for each variable, and a set of constraints between the variables, assign a value to each variable, so that all the constraints are satisfied. The diversity of scheduling problems, the existence of many specific constraints or preferences in each problem, and the emergence of efficient constraintbased scheduling
Unary Resource Constraint with Optional Activities
"... Abstract. Scheduling is one of the most successful application areas of constraint programming mainly thanks to special global constraints designed to model resource restrictions. Among these global constraints, edgefinding filtering algorithm for unary resources is one of the most popular techniqu ..."
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Abstract. Scheduling is one of the most successful application areas of constraint programming mainly thanks to special global constraints designed to model resource restrictions. Among these global constraints, edgefinding filtering algorithm for unary resources is one of the most popular techniques. In this paper we propose a new O(n log n) version of the edgefinding algorithm that uses a special data structure called ΘΛtree. This data structure is especially designed for ”whatif ” reasoning about a set of activities so we also propose to use it for handling so called optional activities, i.e. activities which may or may not appear on the resource. In particular, we propose new O(n log n) variants of filtering algorithms which are able to handle optional activities: overload checking, detectable precedences and notfirst/notlast. 1
Nested Temporal Networks with Alternatives
"... Temporal networks play a crucial role in modeling temporal relations in planning and scheduling applications. Recently, several extensions of temporal networks were proposed to integrate nontemporal information such as resource consumption or logical dependencies. Temporal Networks with Alternative ..."
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Temporal networks play a crucial role in modeling temporal relations in planning and scheduling applications. Recently, several extensions of temporal networks were proposed to integrate nontemporal information such as resource consumption or logical dependencies. Temporal Networks with Alternatives were proposed to model alternative and parallel processes, however the problem of deciding which nodes can be consistently included in such networks is NPcomplete. In this paper we propose a tractable subclass of Temporal Networks with Alternatives that can still cover a wide range of reallife processes, while the problem of deciding node validity is solvable in polynomial time. We also present an algorithm that can effectively recognize whether a given network belongs to the proposed subclass.
A Constraint Model for State Transitions in Disjunctive Resources
, 2006
"... Abstract. Traditional resources in scheduling are simple machines where a capacity is the main restriction. However, in practice there frequently appear resources with more complex behaviour that is described using state transition diagrams. This paper presents new filtering rules for constraints mo ..."
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Abstract. Traditional resources in scheduling are simple machines where a capacity is the main restriction. However, in practice there frequently appear resources with more complex behaviour that is described using state transition diagrams. This paper presents new filtering rules for constraints modelling the state transition diagrams. These rules are based on the idea of extending traditional precedence graphs by direct precedence relations. The proposed model also assumes optional activities and it can be used as an open model accepting new activities during the solving process.