Medium-sized Problems Research Articles

Solving the buffer allocation problem using simulation-based optimisation

In production lines, buffers function as a means to decouple stations, which reduce the effect that station failures and varying process times have on the complete line’s throughput. However, adding larger buffers can be costly, for example, in the automotive industry where it results in increased working capital. This manuscript addresses the buffer allocation problem (BAP), seeking the smallest total buffer size while meeting a prescribed throughput by employing a simulation-based optimisation approach. A Tabu Search algorithm searches the solution space for the optimal buffer configuration while a discrete event simulation model evaluates each configuration, accounting for the machine (un)reliability. Since the multiple simulations add a sizeable computational burden, our approach introduces a novel neighbourhood search mechanism, which borrows from the Theory of Constrains. Solving test sets available in the literature suggest that this approach is 18 times faster than prior Adaptive Tabu Search approaches for small problems, and more than five times faster for medium-sized problems.

Cyclic Flow Shop Robotic Cell Scheduling Problem With Multiple Part Types

This article considers the problem of cyclic flow shop (CFS) scheduling problems in robotic cells deploying several single and dual gripper robots. In this problem, different part types are successively processed on multiple machines with different pickup criteria including free pickup, pickup within time windows, and no-waiting times. The parts are transported between the machines by the robots. We propose a novel integer programming approach that determines the optimal sequence of parts simultaneously for the sequencing of the robots’ movements and the cyclic schedule, which also results in maximizing the throughput rate. The proposed mathematical model is validated on a number of randomly generated test instances. These problem instances are constructed by varying the number of machines, part types, robots, and gripper options. This allows a detailed analysis of the model including how it scales with increasing numbers of machines, part types, robots, and grippers. An experimental evaluation shows that our proposed model is very effective for a range of small medium-sized problems. In particular, we find that differing number of robots and gripper options directly affects the cycle time and in turn, the throughput rate. Overall, our integer programming model finds good feasible solutions for up to 20 machines and 10 part types, which is comparable to real-world industrial problems.

A novel two-stage framework for reducing ergonomic risks of a mixed-model parallel U-shaped assembly-line

Considering ergonomic factors in assembly line balancing problems can significantly improve human ergonomic conditions. In this study, a two-stage framework is developed to balance a mixed-model parallel U-shaped assembly line by considering ergonomic risks. In the first stage, according to various ergonomic standards and using the best-worst method and ELECTRE TRI, ergonomic risks of each task are identified and each task is classified into hard, normal, or easy class. In the second stage, a mathematical model of the problem is developed by considering a new objective function to level the number of tasks of each class between stations. This objective ensures that the tasks of each class are distributed equally among stations, resulting in having a roughly equal number of hard, normal, and easy tasks in each station. To solve the problem, a constraint programming model and a heuristic algorithm are developed. Numerical results show that the proposed objective function can level ergonomic risks well. The performance of the proposed solution approaches is examined against six different metaheuristic algorithms. Numerical results indicate the superiority of the constraint programming model for small and medium-size problems and that of the heuristic algorithm for large-size problems.

Customer order scheduling with job-based processing on a single-machine to minimize the total completion time

This study considers a customer order scheduling (COS) problem in which each customer requests a variety of products (jobs) processed on a single flexible machine, such as the computer numerical control (CNC) machine. A sequence-independent setup for the machine is needed before processing each product. All products in a customer order are delivered to the customer when they are processed. The product ordered by a customer and completed as the last product in the order defines the customer order’s completion time. We aim to find the optimal schedule of the customer orders and the products to minimize the customer orders’ total completion time. We have studied this customer order scheduling problem with a job-based processing approach in which the same products from different customer orders form a product lot and are processed successively without being intermingled with other products. We have developed two mixed-integer linear programming models capable of solving the small and medium-sized problem instances optimally and a heuristic algorithm for large-sized problem instances. Our empirical study results show that our proposed tabu search algorithm provides optimal or near-optimal solutions in a very short time. We have also compared the job-based and order-based processing approaches for both setup and no-setup cases and observed that the job-based processing approach yields better results when jobs have setup times.

Nature-Inspired Metaheuristics for Two-Agent Scheduling with Due Date and Release Time

This paper delves into a two-agent scheduling problem in which two agents are competing for a single resource. Each agent has a set of jobs to be processed by a single machine. The processing time, release time, weight, and the due dates of each job are known in advance. Both agents have their objectives, which are conflicting in nature. The first agent tries to minimize the total completion time, while the second agent tries to minimize the number of tardy jobs. The two agents’ scheduling problem, an NP-hard problem, has a wide variety of applications ranging from the manufacturing industry to the cloud computing service provider. Due to the wide applicability, each variation of the problem requires a different algorithm, adapted according to the user’s requirements. This paper provides mathematical models, heuristic algorithms, and two nature-based metaheuristic algorithms to solve the problem. The algorithm’s performance was gauged against the optimal solution obtained from the AMPL-CPLEX solver for both solution quality and computational time. The outlined metaheuristics produce a solution that is comparable with a short computational time. The proposed metaheuristics even have a better solution than the CPLEX solver for medium-size problems, whereas the computation times are much less than the CPLEX solvers.

Minimal covering unrestricted location of obnoxious facilities: bi-objective formulation and a case study

This paper addresses the problem of locating obnoxious facilities aiming to mitigate the adverse effects of such facilities by minimizing the total covered demand and reducing the harmful effects of multiple-coverage by placing the facilities far from each other. Unlike the classical approaches, it is assumed that the facilities can be located not only on the nodes but also on the network’s edges. Additionally, demands are not restricted to reside on the nodes but are distributed along the edges. In such a condition, the problem of locating obnoxious facilities is much closer to the real-world. A bi-objective mixed-integer linear programming formulation is developed for this novel problem. This bi-objective problem is solved using the e-constraint method and NSGA-II. The e-constraint method can be used to solve the small and medium-sized problems optimally in a reasonable time. As a realistic example, this approach is implemented in a case study in Isfahan for a particular urban planning problem. The case is locating obnoxious solid waste disposal facilities that should be located as far away as possible and simultaneously cover the least demands. Large scale problems cannot be solved efficiently using the e-constraint method. However, the numerical analysis showed the efficiency and effectiveness of the NSGA-II approach for these problems. Finally, sensitivity analysis is applied to evaluate the effect of changes in coverage distance and the number of facilities on the conflicting objective functions.

The Commute Trip-Sharing Problem

Parking pressure has been steadily increasing in cities as well as on university and corporate campuses. To relieve this pressure, this paper studies a carpooling platform that would match riders and drivers while guaranteeing a ride back and exploiting spatial and temporal locality. In particular, the paper formalizes the commute trip-sharing problem (CTSP) to find a routing plan that maximizes ride sharing for a set of commute trips. The CTSP is a generalization of the vehicle routing problem with routes that satisfy time-window, capacity, pairing, precedence, ride-duration, and driver constraints. The paper introduces two exact algorithms for the CTSP: a route-enumeration algorithm and a branch-and-price algorithm. Experimental results show that on a high-fidelity real-world data set of commute trips from a midsize city, both algorithms optimally solve small and medium-sized problems and produce high-quality solutions for larger problem instances. The results show that carpooling, if widely adopted, has the potential to reduce vehicle usage by up to 57% and decrease vehicle miles traveled by up to 46% while incurring only a 22% increase in average ride time per commuter for the trips considered.

Solution Merging in Matheuristics for Resource Constrained Job Scheduling

Matheuristics have been gaining in popularity for solving combinatorial optimisation problems in recent years. This new class of hybrid method combines elements of both mathematical programming for intensification and metaheuristic searches for diversification. A recent approach in this direction has been to build a neighbourhood for integer programs by merging information from several heuristic solutions, namely construct, solve, merge and adapt (CMSA). In this study, we investigate this method alongside a closely related novel approach—merge search (MS). Both methods rely on a population of solutions, and for the purposes of this study, we examine two options: (a) a constructive heuristic and (b) ant colony optimisation (ACO); that is, a method based on learning. These methods are also implemented in a parallel framework using multi-core shared memory, which leads to improving the overall efficiency. Using a resource constrained job scheduling problem as a test case, different aspects of the algorithms are investigated. We find that both methods, using ACO, are competitive with current state-of-the-art methods, outperforming them for a range of problems. Regarding MS and CMSA, the former seems more effective on medium-sized problems, whereas the latter performs better on large problems.

Constraint programming approaches to disassembly line balancing problem with sequencing decisions

Recovery of products has received much attention in the last decade due to the increase in both environmental awareness and regulations enacted by governments. In product recovery, disassembly of a product into its constituent parts on a line is one of the most significant operations. This paper deals with a disassembly line balancing and sequencing (DLBS) problem subject to balancing issues, hazardousness of parts, demand quantities and direction changes considered in a lexicographic order. Due to the combinatorial nature of this problem, exact methods, e.g., mixed integer linear programming (MILP), are able to solve only small and medium size problems. Therefore, various metaheuristic algorithms are proposed in literature to find near-optimal solutions. In this paper, constraint programming (CP), which is a suitable technique especially for highly-constrained discrete problems, is used to develop models and solution approaches. To the best of author’s knowledge, this study is the first that uses CP for the disassembly line balancing problems. For the DLBS problem, first, a generic CP model is developed. This CP model provides efficient results for small/medium size disassembly problems and benchmark instances. Observing that the generic CP model could not produce even feasible sequence of tasks for some large-sized benchmark instances, a CP-based solution approach is proposed. This approach generates a feasible sequence subject to a fixed assignment of tasks to the workstations by using a CP model and uses this sequence as an initial feasible solution within a warm-start context in CP sequencing models. The computational results show that the proposed CP model improves the several best solutions of medium-sized benchmark instances, while the proposed CP-based solution approach produces excellent results in all large test instances by either improving the best solutions (found so far) or establishing new benchmark solutions.

Material Requirements Planning Using Variable-Sized Bin-Packing Problem Formulation with Due Date and Grouping Constraints

Correct planning is crucial for efficient production and best quality of products. The planning processes are commonly supported with computer solutions; however manual interactions are commonly needed, as sometimes the problems do not fit the general-purpose planning systems. The manual planning approach is time consuming and prone to errors. Solutions to automatize structured problems are needed. In this paper, we deal with material requirements planning for a specific problem, where a group of work orders for one product must be produced from the same batch of material. The presented problem is motivated by the steel-processing industry, where raw materials defined in a purchase order must be cut in order to satisfy the needs of the planned work order while also minimizing waste (leftover) and tardiness, if applicable. The specific requirements of the problem (i.e., restrictions of which work orders can be produced from a particular group of raw materials) does not fit the regular planning system used by the production company, therefore a case-specific solution was developed that can be generalized also to other similar cases. To solve this problem, we propose using the generalized bin-packing problem formulation which is described as an integer programming problem. An extension of the bin-packing problem formulation was developed based on: (i) variable bin sizes, (ii) consideration of time constraints and (iii) grouping of items/bins. The method presented in the article can be applied for small- to medium-sized problems as first verified by several examples of increasing complexity and later by an industrial case study.

Exact and heuristic solutions of a discrete competitive location model with Pareto-Huff customer choice rule

An entering firm wants to compete for market share of an area by opening some new facilities selected among a finite set of potential locations (discrete space). Customers are spatially separated and there already are other firms operating in that area. In this paper, we use a variant of the well known Huff (proportional) customer choice rule, the so called Pareto-Huff, which have had little attention on the literature because of its nonlinear formulation. This untested rule considers that customers split their demand among the facilities that are Pareto optimal with respect to quality (to be maximized) and distance (to be minimized), proportionally to their attractions, i.e., a distant facility will capture demand of a customer only if it has higher quality than any other closer facility. A first formulation as a nonlinear programming problem is proposed, and then an equivalent formulation as a linear programming problem is presented, which allows us to obtain exact solutions for medium size problems. For large size problems, a heuristic procedure is also proposed to obtain the best approximate solutions. Its performance is checked for small size problems and its solutions are compared with the optimal solutions given by a standard optimizer, Xpress, using real geographical coordinates and population data of municipalities in Spain.

Automatic Controller Code Generation for Swarm Robotics Using Probabilistic Timed Supervisory Control Theory (ptSCT)

The development of flexible swarm robotics systems capable of adapting to the task and environmental changes is a serious challenge. The main motivations of Swarm robotics are decentralized control, stability, adaptivity, and flexibility. Usually, ad-hoc approaches are employed to design a controller capable of meeting the problem specifications. However, these methods cannot be easily verified, and in some cases, it is not even shown that they meet the specifications. Moreover, the controller source code has to be developed separately, primarily when formal methods are employed; As a result, it cannot be guaranteed that the implementation matches the design. This paper proposes a new method - probabilistic timed supervisory control (ptSCT) - to formally design a controller from systems specifications. The proposed ptSCT has several advantages: 1) the automatic generation of the controller source code utilizable in ARGoS platform, 2) formal designing capability using the implemented software tool, 3) set of powerful design components like probabilistic decisions and time constraints, and 4) the reusability of formally designed modules among different scenarios and multiple robotic platforms. Two case studies are considered to investigate various aspects of the proposed system. Firstly, the synchronization case study is implemented for a comparison between SCT and ptSCT in terms of design capabilities and memory consumption. Secondly, the foraging case study as a complex and medium-sized problem is modeled using ptSCT step by step. More than 2400 experiments with a varying number of obstacles, targets, and robots are executed in ARGoS platform in order to show the performance of the automatically generated source code.

Global Convergence of a Modified Two-Parameter Scaled BFGS Method with Yuan-Wei-Lu Line Search for Unconstrained Optimization

The BFGS method is one of the most efficient quasi-Newton methods for solving small- and medium-size unconstrained optimization problems. For the sake of exploring its more interesting properties, a modified two-parameter scaled BFGS method is stated in this paper. The intention of the modified scaled BFGS method is to improve the eigenvalues structure of the BFGS update. In this method, the first two terms and the last term of the standard BFGS update formula are scaled with two different positive parameters, and the new value of yk is given. Meanwhile, Yuan-Wei-Lu line search is also proposed. Under the mentioned line search, the modified two-parameter scaled BFGS method is globally convergent for nonconvex functions. The extensive numerical experiments show that this form of the scaled BFGS method outperforms the standard BFGS method or some similar scaled methods.

The Modified Particle Swarm Optimization for a Special Case of the Assignment Problem: A Case Study in Chicken Transportation

This research aims at solving the special case of multistate assignment problem. The problem includes many special characteristics which are not normally included in the assignment problem. There are many types and conditions of vehicles included in the planning and different road conditions of traveling, which would have different effects on fuel consumption, which is the objective function of the study. The proposed problem is determined as a large and complicated problem making the optimization software unable to find an optimal solution within the proper time. Therefore, the researchers had developed a method for determining the optimal solution by using particle swarm optimization (PSO) in which the methods were developed for solving the proposed problem. This method is called the modified particle swarm optimization (modified PSO). The proposed method was tested with three groups of tested instances, i.e., small, medium, and large groups. The computational result shows that, in small-sized and medium-sized problems, the proposed method performed not significantly different from the optimization software, and in the large-sized problems, the modified PSO method gave 3.61% lower cost than the cost generated from best solution generated from optimization software within 72 hours and it gave 11.03% better solution than that of the best existing heuristics published so far (differential evolution algorithm).

A hybrid algorithm combining genetic algorithm and variable neighborhood search for process sequencing optimization of large-size problem

ABSTRACT On the premise of satisfying the process priority relationship, there are many kinds of feasible sequencing schemes. How to obtain the optimal process sequencing meeting the process priority relationship has always been a popular research area in the field of CAPP (Computer-Aided Process Planning). Currently, some achievements have been made in the field of small and medium-size problems. For large-size problems, due to the explosion of solution space, the existing bionic algorithms are easy to fall into local optimum or even non-convergence. In this paper, a hybrid algorithm combining genetic algorithm and variable neighborhood search is proposed to solve the above problems. The basic idea is to decompose the complex and huge solution space into relatively simple multi-neighborhood spaces, and then search in each neighborhood space by genetic algorithm in turn. The global optimal solution is obtained when a solution is the best solution through all neighborhood spaces. Based on this idea, the hybrid algorithm framework and neighborhood construction rules are developed, and the implementation steps of the hybrid algorithm are detailed. Taking a real-world case as the case study, the feasibility and superiority of the proposed hybrid algorithm are demonstrated by algorithm comparison tests.

Coordinated appointment scheduling with multiple providers and patient-and-physician matching cost in specialty care

To achieve effective care, it is critical to match patients with capable physicians in specialty care. Motivated by the rising popularity of patient-and-physician matching applications in specialty care, this study optimizes the matching and appointment scheduling problems simultaneously in a stochastic environment, in which a decision-maker determines the patient-and-physician pair assignment and the starting times of services. We develop a stochastic optimization model to minimize the matching and operational costs (i.e., patients’ waiting time costs, service providers’ idle time and overtime costs). This paper is the first study that incorporates matching and appointment scheduling problems together. The benefits of combining these two problems are enormous. The experimental results show that the operational costs gap is as large as 51% between the ill-matched and the well-matched patient-and-physician scenarios. We first reformulate this problem as a two-stage optimization problem. With the analysis for the optimal solution of the second stage problem, a Benders decomposition algorithm is developed. To improve the efficiency of the proposed algorithm, we also prove a low bound of our problem and use it to construct a set of feasibility cuts. Then, we extend our method to incorporate no-shows. Our algorithm can solve problems efficiently, and it can obtain optimal solutions for medium-size problems within 2 or 3 min. In contrast, traditional optimal methods require nearly 2 h. For large-size problems, our algorithm can obtain optimal solutions within 5 or 6 min, whereas traditional optimal methods cannot generate a result within 5 h. Finally, numerical experiments are conducted to evaluate the performance of our proposed algorithm and to investigate the variation of the optimal solutions in different scenarios. To provide quality care as well as minimize the total cost of appointment scheduling in specialty care, we suggest that physicians should develop or train their specialties based on the local patients’ disease pattern. We also disclose that the no-show has less influence on the service system when the weight of the matching cost is substantial.

A generalised model for container drayage operations with heterogeneous fleet, multi-container sizes and two modes of operation

We propose a generalized model of drayage operations that incorporates the coupling and precedence principles, allows for live and separation operation modes, relaxes the assumptions about fleet composition and truck size, and operates in a realistic network. The results of the experiments reveal that the model efficiently and effectively allocates container transport requests and can find close to optimal solution in reasonable time for small and medium size problems. The results also suggest the existence of a threshold strongly related to the ratio of the fleet capacity over the number of requests where the fleet is utilised most effectively.

Flexible job shop scheduling problem with reconfigurable machine tools: An improved differential evolution algorithm

Developing reconfigurable machine tools (RMTs) has attracted increasing attention recently. An RMT can be utilized as a group of machines, which can obtain different configurations to satisfy manufacturing requirements. This paper deals with a production scheduling problem in a shop-floor with RMTs as an extension of a flexible job shop scheduling problem (FJSSP). To begin with, two mixed-integer linear programming models with the position- and sequence-based decision variables are formulated to minimize the maximum completion time (i.e., makespan). The CPLEX solver is used to solve the small- and medium-sized instances. The computational experiments show that the sequence-based model significantly outperforms the other one. Since even the sequence-based model cannot optimally solve most of the medium-sized problems, a self-adaptive differential evolution (DE) algorithm is proposed to efficiently solve the given problem. Moreover, the effectiveness of the proposed algorithm is enhanced by introducing a new mutation strategy based on a searching approach hired from a Nelder–Mead method. The performance of the proposed method and three other well-known variants of the DE algorithm are first validated by comparing their results with the results of the sequence-based model. Additional experiments on another data set including large-sized problems also confirm that the proposed algorithm is extremely efficient and effective.

Single machine scheduling to maximize the number of on-time jobs with generalized due-dates

In scheduling problems with generalized due dates (gdd), the due dates are specified according to their position in the sequence, and the j-th due date is assigned to the job in the j-th position. We study a single-machine problem with generalized due dates, where the objective is maximizing the number of jobs completed exactly on time. We prove that the problem is NP-hard in the strong sense. To our knowledge, this is the only example of a scheduling problem where the job-specific version has a polynomial-time solution, and the gdd version is strongly NP-hard. A branch-and-bound (B&B) algorithm, an integer programming (IP)-based procedure, and an efficient heuristic are introduced and tested. Both the B&B algorithm and the IP-based solution procedure can solve most medium-sized problems in a reasonable computational effort. The heuristic serves as the initial step of the B&B algorithm and in itself obtains the optimum in most cases. We also study two special cases: max-on-time for a given job sequence and max-on-time with unit-execution-time jobs. For both cases, polynomial-time dynamic programming algorithms are introduced, and large-sized problems are easily solved.

A Mathematical Model for Multiple-Load AGVs in Tandem Layout

Reducing cost of material handling has been a big challenge for companies. Flexible manufacturing system employed automated guided vehicles (AGV) to maintain efficiency and flexibility. This paper presents a new non-linear mathematical programming model to group n machines into N loops, to make an efficient configuration for AGV system in Tandem layout. The model minimizes both inter-loop, intra-loop flow and use balanced-loops strategy to balance workload in system simultaneously. This paper significantly considers multiple-load AGVs, which has capability of reducing fleet size and waiting time of works. A modified variable neighborhood search method is applied for large size problems, which has good accuracy for small and medium size problems. The results indicate that using multiple load AGV instead of single load AGV will reduce system penalty cost up to 44%.