Analysis of a Parallel Machine Scheduling Problem with Sequence Dependent Setup Times and Job Availability Intervals

In this study, we propose constraint programming (CP) model and logic-based Benders algorithms in order to make the best decisions for scheduling non-identical jobs with availability intervals and sequence dependent setup times on unrelated parallel machines in a fixed planning horizon. In this problem, each job has a profit, cost and must be assigned to at most one machine in such a way that total profit is maximized. In addition, the total cost has to be less than or equal to a budget level. Computational tests are performed on a real-life case study prepared in collaboration with the U.S. Army Corps of Engineers (USACE). Our initial investigations show that the pure CP model is very efficient in obtaining good quality feasible solutions but, fails to report the optimal solution for the majority of the problem instances. On the other hand, the two logic-based Benders decomposition algorithms are able to obtain near optimal solutions for 86 instances out of 90 examinees. For the remaining instances, they provide a feasible solution. Further investigations show the high quality of the solutions obtained by the pure CP model

A linear programming based heuristic framework for min-max regret combinatorial optimization problems with interval costs

This work deals with a class of problems under interval data uncertainty, namely interval robust-hard problems, composed of interval data min-max regret generalizations of classical NP-hard combinatorial problems modeled as 0-1 integer linear programming problems. These problems are more challenging than other interval data min-max regret problems, as solely computing the cost of any feasible solution requires solving an instance of an NP-hard problem. The state-of-the-art exact algorithms in the literature are based on the generation of a possibly exponential number of cuts. As each cut separation involves the resolution of an NP-hard classical optimization problem, the size of the instances that can be solved efficiently is relatively small. To smooth this issue, we present a modeling technique for interval robust-hard problems in the context of a heuristic framework. The heuristic obtains feasible solutions by exploring dual information of a linearly relaxed model associated with the classical optimization problem counterpart. Computational experiments for interval data min-max regret versions of the restricted shortest path problem and the set covering problem show that our heuristic is able to find optimal or near-optimal solutions and also improves the primal bounds obtained by a state-of-the-art exact algorithm and a 2-approximation procedure for interval data min-max regret problems

Finite domain constraint programming systems

Tutorial at CP'2002, Principles and Practice of Constraint Programming. Powerpoint slides.</p

Network Migration Problem: A Logic-based Benders Decomposition Approach Driven by Column Generation and Constraint Programming

Telecommunication networks frequently face technological advancements and need to upgrade their infrastructure. Adapting legacy networks to the latest technology requires synchronized technicians responsible for migrating the equipment. The goal of the network migration problem is to find an optimal plan for this process. This is a defining step in the customer acquisition of telecommunications service suppliers, and its outcome directly impacts the network owners' purchasing behaviour. We propose the first exact method for the network migration problem, a logic-based Benders decomposition approach that benefits from a hybrid constraint programming-based column generation in its master problem and a constraint programming model in its subproblem. This integrated solution technique is applicable to any integer programming problem with similar structure, most notably the vehicle routing problem with node synchronization constraints. Comprehensive evaluation of our method over instances based on six real networks demonstrates the computational efficiency of the algorithm in obtaining quality solutions. We also show the merit of each incorporated optimization paradigm in achieving this performance

Energy and Route Optimization of Moving Devices

This thesis highlights our efforts in energy and route optimization of moving devices. We have focused on three categories of such devices; industrial robots in a multi-robot environment, generic vehicles in a vehicle routing problem (VRP) context, automatedguided vehicles (AGVs) in a large-scale flexible manufacturing system (FMS). In the first category, the aim is to develop a non-intrusive energy optimization technique, based on a given set of paths and sequences of operations, such that the original cycle time is not exceeded. We develop an optimization procedure based on a mathematical programming model that aims to minimize the energy consumption and peak power. Our technique has several advantages. It is non-intrusive, i.e. it requires limited changes in the robot program and can be implemented easily. Moreover,it is model-free, in the sense that no particular, and perhaps secret, parameter or dynamic model is required. Furthermore, the optimization can be done offline, within seconds using a generic solver. Through careful experiments, we have shown that it is possible to reduce energy and peak-power up to about 30% and 50% respectively. The second category of moving devices comprises of generic vehicles in a VRP context. We have developed a hybrid optimization approach that integrates a distributed algorithm based on a gossip protocol with a column generation (CG) algorithm, which manages to solve the tested problems faster than the CG algorithm alone. The algorithm is developed for a VRP variation including time windows (VRPTW), which is meant to model the task of scheduling and routing of caregivers in the context of home healthcare routing and scheduling problems (HHRSPs). Moreover,the developed algorithm can easily be parallelized to further increase its efficiency. The last category deals with AGVs. The choice of AGVs was not arbitrary; by design, we decided to transfer our knowledge of energy optimization and routing algorithms to a class of moving devices in which both techniques are of interest. Initially, we improve an existing method of conflict-free AGV scheduling and routing, such that the new algorithm can manage larger problems. A heuristic version of the algorithm manages to solve the problem instances in a reasonable amount of time. Later, we develop strategies to reduce the energy consumption. The study is carried out using an AGV system installed at Volvo Cars. The results are promising; (1)the algorithm reduces performance measures such as makespan up to 50%, while reducing the total travelled distance of the vehicles about 14%, leading to an energy saving of roughly 14%, compared to the results obtained from the original traffic controller. (2) It is possible to reduce the cruise velocities such that more energy is saved, up to 20%, while the new makespan remains better than the original one

One Benders cut to rule all schedules in the neighbourhood

Logic-Based Benders Decomposition (LBBD) and its Branch-and-Cut variant, namely Branch-and-Check, enjoy an extensive applicability on a broad variety of problems, including scheduling. Although LBBD offers problem-specific cuts to impose tighter dual bounds, its application to resource-constrained scheduling remains less explored. Given a position-based Mixed-Integer Linear Programming (MILP) formulation for scheduling on unrelated parallel machines, we notice that certain $k-$OPT neighbourhoods could implicitly be explored by regular local search operators, thus allowing us to integrate Local Branching into Branch-and-Check schemes. After enumerating such neighbourhoods and obtaining their local optima - hence, proving that they are suboptimal - a local branching cut (applied as a Benders cut) eliminates all their solutions at once, thus avoiding an overload of the master problem with thousands of Benders cuts. However, to guarantee convergence to optimality, the constructed neighbourhood should be exhaustively explored, hence this time-consuming procedure must be accelerated by domination rules or selectively implemented on nodes which are more likely to reduce the optimality gap. In this study, the realisation of this idea is limited on the common 'internal (job) swaps' to construct formulation-specific $4$-OPT neighbourhoods. Nonetheless, the experimentation on two challenging scheduling problems (i.e., the minimisation of total completion times and the minimisation of total tardiness on unrelated machines with sequence-dependent and resource-constrained setups) shows that the proposed methodology offers considerable reductions of optimality gaps or faster convergence to optimality. The simplicity of our approach allows its transferability to other neighbourhoods and different sequencing optimisation problems, hence providing a promising prospect to improve Branch-and-Check methods

Optimal logistics scheduling with dynamic information in emergency response: case studies for humanitarian objectives

The mathematical model of infectious disease is a typical problem in mathematical modeling, and the common infectious disease models include the susceptible-infected (SI) model, the susceptible-infected-recovered model (SIR), the susceptible-infected-recovered-susceptible model (SIRS) and the susceptible-exposed-infected-recovered (SEIR) model. These models can be used to predict the impact of regional return to work after the epidemic. In this paper, we use the SEIR model to solve the dynamic medicine demand information in humanitarian relief phase. A multistage mixed integer programming model for the humanitarian logistics and transport resource is proposed. The objective functions of the model include delay cost and minimum running time in the time-space network. The model describes that how to distribute and deliver medicine resources from supply locations to demand locations with an efficient and lower-cost way through a transportation network. The linear programming problem is solved by the proposed Benders decomposition algorithm. Finally, we use two cases to calculate model and algorithm. The results of the case prove the validity of the model and algorithm