Scheduling projects with multi-skilled personnel by a hybrid MILP/CP benders decomposition algorithm

We study an assignment type resource-con- strained project scheduling problem with resources being multi-skilled personnel to minimize the total staffing costs. We develop a hybrid Benders decomposition (HBD) algorithm that combines the complimentary strengths of both mixed-integer linear programming (MILP) and constraint programming (CP) to solve this NP-hard optimization problem. An effective cut-generating scheme based on temporal analysis in project scheduling is devised for resolving resource conflicts. The computational study shows that our hybrid MILP/CP algorithm is both effective and efficient compared to the pure MILP or CP method alone.     

A Hybrid Method for the Planning and Scheduling

We combine mixed integer linear programming (MILP) and constraint programming (CP) to solve planning and scheduling problems. Tasks are allocated to facilities using MILP and scheduled using CP, and the two are linked via logic-based Benders decomposition. Tasks assigned to a facility may run in parallel subject to resource constraints (cumulative scheduling). We solve minimum cost problems, as well as minimum makespan problems in which all tasks have the same release date and deadline. We obtain computational speedups of several orders of magnitude relative to the state of the art in both MILP and CP.     

Maintenance costs and makespan minimization for assembly permutation flow shop scheduling by considering preventive and corrective maintenance

The joint optimization of production scheduling and maintenance planning has a significant influence on production continuity and machine reliability. However, limited research considers preventive maintenance (PM) and corrective maintenance (CM) in assembly permutation flow shop scheduling. This paper addresses the bi-objective joint optimization of both PM and CM costs in assembly permutation flow shop scheduling. We also propose a new mixed integer linear programming model for the minimization of the makespan and maintenance costs. Two lemmas are inferred to relax the expected number of failures and CM cost to make the model linear. A restarted iterated Pareto greedy (RIPG) algorithm is applied to solve the problem by including a new evaluation of the solutions, based on a PM strategy. The RIPG algorithm makes use of novel bi-objective-oriented greedy and referenced local search phases to find non-dominated solutions. Three types of experiments are conducted to evaluate the proposed MILP model and the performance of the RIPG algorithm. In the first experiment, the MILP model is solved with an epsilon-constraint method, showing the effectiveness of the MILP model in small-scale instances. In the remaining two experiments, the RIPG algorithm shows its superiority for all the instances with respect to four well-known multi-objective metaheuristics.     

New model and heuristics for safety stock placement in general acyclic supply chain networks

We model the safety stock placement problem in general acyclic supply chain networks as a project scheduling problem, for which the constraint programming (CP) techniques are both effective and efficient in finding high quality solutions. We further integrate CP with a genetic algorithm (GA), which improves the CP solution quality significantly. The performance of our hybrid CP-GA algorithm is evaluated on randomly generated test instances. CP-GA is able to find optimal solutions to small problems in fractions of a second, and near optimal solutions of about 5% optimality gap to medium size problems in several minutes on average.     

A hybrid integer and constraint programming approach to solve nurse rostering problems

The Nurse Rostering Problem can be defined as assigning a series of shift sequences (schedules) to several nurses over a planning horizon according to some limitations and preferences. The inherent benefits of generating higher-quality schedules are a reduction in outsourcing costs and an increase in job satisfaction of employees. In this paper, we present a hybrid algorithm, which combines Integer Programming and Constraint Programming to efficiently solve the highly-constrained Nurse Rostering Problem. We exploit the strength of IP in obtaining lower-bounds and finding an optimal solution with the capability of CP in finding feasible solutions in a co-operative manner. To improve the performance of the algorithm, and therefore, to obtain high-quality solutions as well as strong lower-bounds for a relatively short time, we apply some innovative ways to extract useful information such as the computational difficulty of instances and constraints to adaptively set the search parameters. We test our algorithm using two different datasets consisting of various problem instances, and report competitive results benchmarked with the state-of-the-art algorithms from the recent literature as well as standard IP and CP solvers, showing that the proposed algorithm is able to solve a wide variety of instances effectively.     

A hybrid method for the Probabilistic Maximal Covering Location–Allocation Problem

This paper presents a hybrid algorithm that combines a metaheuristic and an exact method to solve the Probabilistic Maximal Covering Location–Allocation Problem. A linear programming formulation for the problem presents variables that can be partitioned into location and allocation decisions. This model is solved to optimality for small- and medium-size instances. To tackle larger instances, a flexible adaptive large neighborhood search heuristic was developed to obtain location solutions, whereas the allocation subproblems are solved to optimality. An improvement procedure based on an integer programming method is also applied. Extensive computational experiments on benchmark instances from the literature confirm the efficiency of the proposed method. The exact approach found new best solutions for 19 instances, proving the optimality for 18 of them. The hybrid method performed consistently, finding the best known solutions for 94.5% of the instances and 17 new best solutions (15 of them optimal) for a larger dataset in one-third of the time of a state-of-the-art solver.     

Modeling and scheduling a case of flexible flowshops: Total weighted tardiness minimization

Two of the most realistic assumptions in the field of scheduling are the consideration of setup and transportation times. In this paper, we study the flexible flowshop scheduling where setup times are anticipatory sequence-dependent and transportation times are job-independent. We also assume that there are several transporters to carry jobs. The objective is to minimize total weighted tardiness. We first formulate the problem as a mixed integer linear programming (MILP) model. With this, we solve small-sized instances to optimality. Since this problem is known to be NP-hard, we then propose an effective metaheuristic to tackle large-sized instances. This metaheuristic, called electromagnetism algorithm (EMA), originates from the attraction–repulsion mechanism of the electromagnetism theory. We conduct a series of experiments and complete statistical analyses to evaluate the performance of the proposed MILP model and EMA. On a set of instances, we first tune the parameters of EMA. Then, the efficiency of the model and general performance of the proposed EMA are assessed over a set of small-sized instances. To further evaluate EMA, we compare it against two high performing metaheuristics existing in the literature over a set of large-sized instances. The results demonstrate that the proposed MILP model and EMA are effective for this problem.     

An Integrated Method for Planning and Scheduling to Minimize Tardiness

We combine mixed integer linear programming (MILP) and constraint programming (CP) to minimize tardiness in planning and scheduling. Tasks are allocated to facilities using MILP and scheduled using CP, and the two are linked via logic-based Benders decomposition. We consider two objectives: minimizing the number of late tasks, and minimizing total tardiness. Our main theoretical contribution is a relaxation of the cumulative scheduling subproblem, which is critical to performance. We obtain substantial computational speedups relative to the state of the art in both MILP and CP. We also obtain much better solutions for problems that cannot be solved to optimality.     

Distributed assembly permutation flow shop problem; Single seekers society algorithm

The distributed manufacturing and assembly systems have an important role at the point of overcoming the difficulties faced by today's mass-production industry. By using both of these systems together in the same production system, the advantages of this integration can make industries more flexible and stronger. Besides, optimizing these systems is more complicated since the multiple production systems can undoubtfully affect the production system’s performance. In this paper, two new mixed-integer linear programming (MILP) models are proposed for the distributed assembly permutation flow shop problem (DAPFSP), inspiring by the multiple-travelling salesman structure. Moreover, a single seekers society (SSS) algorithm is proposed for solving the DAPFSP to minimize the maximum completion time of all products. The performance of the proposed MILP models is evaluated using 900 small-sized benchmark instances. The proposed MILP models were effective and were able to find more optimal solutions or improve the best-found solutions for the small-sized DAPFSP benchmark instances. Similarly, the SSS algorithm is statistically compared with the best-known algorithms developed for solving the DAPFSP on 900 small and 810 large-sized benchmark instances. The proposed SSS algorithm shows superior performance compared to other algorithms in solving the small-sized DAPFSP instances in terms of finding better solutions. In addition, it is as effective as the best performing algorithms developed to solve the large-sized DAPFSP instances. Furthermore, the best-found solutions for 40 numbers of test problems reported to be improved in this paper.     

Variable neighborhood search based approaches to a vehicle scheduling problem in agriculture

A vehicle scheduling problem (VSP) that arises from sugar beet transportation within minimum working time under the set of constraints reflecting a real‐life situation is considered. A mixed integer quadratically constrained programming (MIQCP) model of the considered VSP and reformulation to a mixed integer linear program (MILP) are proposed and used within the framework of Lingo 17 solver, producing optimal solutions only for small‐sized problem instances. Two variants of the variable neighborhood search (VNS) metaheuristic—basic VNS (BVNS) and skewed VNS (SVNS) are designed to efficiently deal with large‐sized problem instances. The proposed VNS approaches are evaluated and compared against Lingo 17 and each other on the set of real‐life and generated problem instances. Computational results show that both BVNS and SVNS reach all known optimal solutions on small‐sized instances and are comparable on medium‐ and large‐sized instances. In general, SVNS significantly outperforms BVNS in terms of running times.     

A novel MILP model for job shop scheduling problem with mobile robots

The mobile robot is the essential equipment for automated logistics in the intelligent workshop, but the literature on shop scheduling rarely considers transport resources. This paper studies the integrated scheduling of machines and mobile robots, which can facilitate the efficiency of production systems. For the job shop scheduling problem with mobile robots (JSPMR), the existing mathematical models are too complex to obtain the optimal solution in an efficient time. Therefore, a novel mixed integer linear programming (MILP) model is proposed to minimize the makespan. Firstly, in view of the property of the problem, a disjunctive graph model is modified to describe the relationship between transport and processing tasks. Secondly, a more accurate and simplified MILP is proposed based on the modified disjunctive graph model. Two related proofs are given to prove the proposed model satisfies all special situations. Thirdly, the proposed MILP is tested on the well-known benchmark, including 82 instances. The proposed model is the first MILP model to obtain optimal solutions for all instances. Finally, 40 larger-scale instances are presented based on a real-world engineering case and used to validate the performance of models further. The comparison results verify the effectiveness and superior computational performance of the proposed model.     

The contractor time–cost–credit trade‐off problem: integer programming model,heuristic solution,and business insights

Contractors in the construction sector face several trade‐offs between time and cost. The time–cost trade‐off (TCT) is one of these trade‐offs where contractors can reduce a project completion time by assigning more resources to activities, which means spending more money, to shorten the execution times of project activities. On the other hand, contractors who finance their projects through credit lines from banks such that if they reach their credit limits, then the start times of some project activities can be delayed until cash is available again, which might lead to an increase in the project execution time; thus, contractors need to consider the time–credit trade‐off. In this work, we simultaneously consider these two trade‐offs that affect the project completion time and use mixed integer linear programming (MILP) to model the contractor time–cost–credit trade‐off (TCCT) problem. The MILP model minimizes the project execution time given the contractor's budgetary and financial constraints. In addition to the MILP model, we also develop a heuristic solution algorithm to solve the problem. Through a set of benchmark instances, we study the effectiveness of the heuristic algorithm and the computation time of the exact model. It is found that a good upper bound for the MILP results in less computation time. We also study some practical aspects of the problem where we highlight the importance of expediting contractor payments in addition to selecting a financially stable contractor. Finally, we use our MILP model to help a contractor bid for a project.     

MILP-based heuristics for the design of rural community electrification projects

Wind–photovoltaic systems are a suitable option to provide electricity to isolated communities autonomously. To design these systems, there are recent mathematical models that solve the location and type of each of the electrification components and the design of the possible distribution microgrids. When the amount of demand points to electrify increases, solving the mathematical model requires a computational time that becomes infeasible in practice. To speed up the solving process, three heuristic methods based on mixed integer linear programming (MILP) are presented in this paper: Relax and Fix heuristics, heuristics based on a Corridor Method and Increasing Radius heuristics. In all algorithms first a relaxed MILP is solved to obtain a base solution and then it is used as a starting point to find a feasible solution by searching in a reduced search space. For each type of heuristic several options to relax and to reduce the solution space are developed and tested. Extensive computational experiments based on real projects are carried out and results show that the best heuristic vary according to the size of instances.     

Multi-objective optimization of the maritime cargo routing and scheduling problem

This paper addresses the multi-objective maritime cargo routing and scheduling problem, in which the delivery of bulk products from pickup to delivery ports is served by a heterogeneous fleet of vessels. A mixed integer linear programming (MILP) model is formulated to simultaneously minimize total operation costs, the scheduling makespan, and delays in selected deliveries. The model accounts for several real features, such as time windows, capacity of the vessel's compartments, and ports requirements. A fuzzy weighted max–min method was applied to solve the problem. Two heuristics were developed to effectively handle the complex generated MILP models during the solution process. Experiments were conducted to evaluate the optimization approach using real-life instances provided by a fertilizer company. Finally, a case study shows that the developed model and algorithmic framework are flexible and effective in coping with real problems, incorporating specific business rules from different companies.     

Hybridization of very large neighborhood search for ready-mixed concrete delivery problems

Companies in the concrete industry are facing the following scheduling problem on a daily basis: concrete produced at several plants has to be delivered at customers’ construction sites using a heterogeneous fleet of vehicles in a timely, but cost-effective manner. The distribution of ready-mixed concrete (RMC) is a highly complex problem in logistics and combinatorial optimization.This paper proposes two hybrid solution procedures for dealing with this problem. They are based on a combination of an exact algorithm and a variable neighborhood search (VNS) approach. The VNS is used at first to generate feasible solutions and is trying to further improve them. The exact method is based on a mixed integer linear programming (MILP) formulation, which is solved (after an appropriated variable fixing phase) by using a general-purpose MILP solver. An approach based on very large neighborhood search (VLNS) determines which variables are supposed to be fixed. In a sense, the approaches follows a local branching scheme. The hybrid metaheuristics are compared with the pure VNS approach and the conclusion is that the new metaheuristics outperform the VNS if applied solely.     

A heuristic algorithm for optimal fleet composition with vehicle routing considerations

This paper proposes a fast heuristic algorithm for solving a combined optimal fleet composition and multi-period vehicle routing problem. The aim of the problem is to determine an optimal fleet mix, together with the corresponding vehicle routes, to minimize total cost subject to various customer delivery requirements and vehicle capacity constraints. The total cost includes not only the fixed, variable, and transportation costs associated with operating the fleet, but also the hiring costs incurred whenever vehicle requirements exceed fleet capacity. Although the problem under consideration can be formulated as a mixed-integer linear program (MILP), the MILP formulation for realistic problem instances is too large to solve using standard commercial solvers such as the IBM ILOG CPLEX optimization tool. Our proposed heuristic decomposes the problem into two tractable stages: in the first (outer) stage, the vehicle routes are optimized using cross entropy; in the second (inner) stage, the optimal fleet mix corresponding to a fixed set of routes is determined using dynamic programming and golden section search. Numerical results show that this heuristic approach generates high-quality solutions and significantly outperforms CPLEX in terms of computational speed.     

Hybrid discrete differential evolution algorithm for biobjective cyclic hoist scheduling with reentrance

Cyclic hoist scheduling problems in automated electroplating lines and surface processing shops attract many attentions and interests both from practitioners and researchers. In such systems, parts are transported from a workstation to another by a material handling hoist. The existing literature mainly addressed how to find an optimal cyclic schedule to minimize the cycle time that measures the productivity of the lines. The material handling cost is an important factor that needs to be considered in practice but seldom addressed in the literature. This study focuses on a biobjective cyclic hoist scheduling problem to minimize the cycle time and the material handling cost simultaneously. We consider the reentrant workstations that are usually encountered in real-life lines but inevitably make the part-flow more complicated. The problem is formulated as a biobjective linear programming model with a given hoist move sequence and transformed into finding a set of Pareto optimal hoist move sequences with respect to the bicriteria. To obtain the Pareto optimal or near-optimal front, a hybrid discrete differential evolution (DDE) algorithm is proposed. In this hybrid evolutional algorithm, the population is divided into several subpopulations according to the maximal work-in-process (WIP) level of the system and the sizes of subpopulations are dynamically adjusted to balance the exploration and exploitation of the search. We propose a constructive heuristic to generate initial subpopulations with different WIP levels, hybrid mutation and crossover operators, an evaluation method that can tackle infeasible individuals and a one-to-one greedy tabu selection method. Computational results on both benchmark instances and randomly generated instances show that our proposed hybrid DDE algorithm outperforms the basic DDE algorithm and can solve larger-size instances than the existing ε-constraint method.     

Fast scheduling of human-robot teams collaboration on synchronised production-logistics tasks in aircraft assembly

The deployment of human-robot teams (HRTs) promises to realise the potential of each team member regarding their distinct abilities and combines efficiency and flexibility in manufacturing operations. However, enabling effective coordination amongst collaborative tasks performed by humans and robots while ensuring safety and satisfying specific constraints is challenging. Motivated by real-world applications that Boeing and Airbus adopt HRTs in manufacturing operations, this paper investigates the allocating and coordinating of HRTs to support safe and efficient human-robot collaboration on synchronised production-logistics tasks in aircraft assembly. We connect the operations research and robotics communities by formulating the problem with precedence constraints, spatial constraints, temporal constraints, and synchronisation constraints that fits within the classic multi-robot task allocation (MRTA) category into a flexible job shop scheduling problem. Two exact approaches, including mixed-integer linear programming (MILP) and constraint programming (CP), are proposed to formulate and solve this problem. A benchmark set with 80 instances (e.g., small/medium-scale and large-scale instances) that corresponds to real dimensions of industrial problems with production tasks, subtasks, locations, deadlines, human worker eligibility and capacity, robot eligibility and capacity, material handling system capacity, and travel times is developed. Experimental evaluation with a total of 1200 independent tests on the benchmark set shows the superiority of the CP approach comparing the MILP approach for efficiently solving real-life scheduling problems of HRTs collaboration on synchronised production-logistics tasks in aircraft assembly.     

A hybrid tabu search for batching and sequencing decisions in a single machine environment

This paper proposes a hybrid tabu search (HTS) to minimise the total weighted tardiness (TWT) for the batching and sequencing of jobs originating from incompatible families in which sequence dependent family setup times exist on single machine. The developed HTS includes distinguished features such as the strict arc based tabu classification along with dynamic tabu tenures, hybrid neighbourhood structures and iterative phases which consist of job and batch sequencing phases. The authors developed a testing methodology to determine the quality of the HTS solution. A mixed integer linear programing (MILP) model was developed to evaluate the optimality of the solution of the HTS for a small-size instance that consists of 640 problems. In addition, three dispatching rule heuristic combinations (EDD–EDD, EDD–BATCS and ATC–BATCS) were developed to test the HTS for large-size instances that deals with 1440 problems. The HTS provided comparable results with the MILP for small-size instances and outperformed the developed dispatching heuristics.     

Joint gateway selection,transmission slot assignment,routing and power control for wireless mesh networks

Wireless mesh networks (WMNs) provide cost effective solutions for setting up a communications network over a certain geographic area. In this paper, we study strategic problems of WMNs such as selecting the gateway nodes along with several operational problems such as routing, power control, and transmission slot assignment. Under the assumptions of the physical interference model and the tree-based routing restriction for traffic flow, a mixed integer linear programming (MILP) formulation is presented, in which the objective is to maximize the minimum service level provided at the nodes. A set of valid inequalities is derived and added to the model in an attempt to improve the solution quality. Since the MILP formulation becomes computationally infeasible for larger instances, we propose a heuristic method that is aimed at solving the problem in two stages. In the first stage, we devise a simple MILP problem that is concerned only with the selection of gateway nodes. In the second stage, the MILP problem in the original formulation is solved by fixing the gateway nodes from the first stage. Computational experiments are provided to evaluate the proposed models and the heuristic method.