Heuristic Solution Procedure Research Articles

Model and heuristics for the multi-manned assembly line worker integration and balancing problem

This paper examines the balancing of assembly lines with multi-manned stations and a heterogeneous workforce. Both topics received considerable attention in the literature, but not in an integrated fashion. Combining these two characteristics gives rise to a highly combinatorial Multi-manned Assembly Line Worker Integration and Balancing Problem. When considering multi-manned stations, the already coupled decisions on assigning tasks to heterogeneous workers and workers to stations must be further linked with task scheduling assessments. We propose a Mixed-Integer Linear Programming model and develop two heuristic solution procedures, which tackle the problem with a hierarchical decomposition approach. Computational tests on a large dataset indicate that the proposed method can obtain good primal bounds in short computational times. We demonstrate that these results can be applied to the monolithic model either as a warm start or in a proximity search procedure to obtain synergistic gains with statistically significant differences. From a managerial perspective, we show that multi-manned stations can reduce the assembly line's length even in the presence of a heterogeneous workforce, which is crucial for many industries manufacturing large-size products.

Scheduling of parallel continuous annealing lines with alternative processing modes to optimize efficiency under tardiness constraints

Continuous annealing is a core process in steel cold-rolling facilities. It is used to set desired material properties by passing coils of flat steel through a high-temperature furnace in a precisely controlled manner. High efficiency is achieved by feeding the steel through the furnace in the form of a continuous strand. For this purpose, the coils are welded together before being fed into the furnace. Whenever two consecutive coils are incompatible, a special dummy coil called stringer is used to connect them, which reduces efficiency and adds costs and emissions. We consider the scheduling of coils with specific due dates and alternative order-specific processing modes on parallel heterogeneous lines. The problem is to simultaneously assign coils to lines and sequence them on these lines with a defined processing mode with adherence to tardiness constraints while minimizing the number of stringers needed. To address this problem, we formulate a mixed-integer linear program based on a model from the literature and propose a two-phase heuristic solution procedure. The procedure combines an opening phase using shortest path algorithms and local search with an improvement phase based on problem-specific decompositions according to the principles of an Fix-and-Optimize procedure. The results show that our heuristic outperforms a state-of-the-art commercial solver in finding good solutions in short computation time. Based on a sensitivity analysis for several industry-inspired data sets, we observe a trade-off between efficiency and tardiness which strongly depends on the operating conditions.

A genetic algorithm for the personnel task rescheduling problem with time preemption

In this paper, we study the personnel task rescheduling problem with time preemption. We assume a baseline task schedule has been composed some time in advance that has been rendered infeasible due to operational uncertainty. When restoring the schedule feasibility, the personnel planner takes several considerations into account encompassing the provided service level, resource stability, and task adherence. The latter stems from the possibility that in the problem under study tasks can be interrupted and resumed later, better known as time preemption. We propose a genetic algorithm complemented with local search techniques to compose an operational schedule in an effective manner. The genetic algorithm operates on a dedicated decoding mechanism to compose high-quality duties for individual workers efficiently. Computational experiments are conducted to benchmark the performance of the proposed procedure with other exact and (meta-)heuristic solution procedures, and to demonstrate the value of the algorithm design choices. Furthermore, the impact of preempting tasks in time is assessed by changing the objective function structure and the proportion of non-preemptive tasks.

Dynamic Optimization of Conflict-Free Routing of Automated Guided Vehicles for Just-in-Time Delivery

This paper studies the solution procedure to the problem of conflict-free route planning for automated guided vehicles for just-in-time delivery to minimize the earliness and tardiness of a specified delivery time while minimizing the total completion time. The characteristic of the problem is that a vehicle can have an idle time at any nodes considering dispatching of dynamic task arrivals. This problem is modeled by a time-space network where the pickup and delivery tasks are dynamically scheduled. A heuristic solution procedure is developed to derive a conflict-free routing problem such that earliness and tardiness penalties are minimized while the total completion time of each task is also minimized under dynamic task arrivals. The effectiveness of the proposed method is demonstrated by comparing the performance with Gurobi from computational results. The results show that the proposed method can obtain a better solution that is close to an optimal solution with significantly shorter computational time than that derived from Gurobi. The trade-off relationship between earliness/tardiness penalties and the total completion time is investigated in various situations. The effects of the interval of task assignment on the performance of earliness/tardiness and the total completion time are studied. The computational results show the conditions when the trade-off relationship can be obtained. <i>Note to Practitioners</i>&#x2014;The multiple AGVs are used in public transportation and social systems with rapid development of artificial intelligence and optimization methods. The benefits of AGV affect the reduction of congestion, traffic police, legal services, and economic savings in the manufacturing and logistics industries. In order to satisfy the customer&#x2019;s demands, it is requested to deliver the products just-in-time for the desired time without decreasing the total system performance. This paper presents the dispatching and conflict-free routing of AGVs for just-in-time transportation while minimizing the total completion time of the tasks. In many real factories with multiple production processes, the shortest time transportation may sometimes cause the congestions of AGVs waiting for handling or overstocked. Just-in-time transportation is required not only to reduce inventories but also to supply only when it is needed. Computational results show the situations when the just-in-time delivery and the minimization of the total completion time can be achieved.

Heterogeneous instant delivery orders scheduling and routing problem

Scheduling a large number of time-sensitive orders of multiple types in a short time period is a major challenge for instant delivery platforms. This study introduces an integrated problem of heterogeneous order assignment and routing optimization in the real-world setting of third-party instant delivery platforms. A mixed integer programming model is presented to optimize the assignment of instant delivery orders of multiple types and the scheduling of couriers with different grades. We develop a column generation model and a heuristic solution procedure to yield a solution for the integrated problem and we design an exact sub-procedure to accelerate the pricing problem. Taking Songjiang District, Shanghai as an example, numerical experiments are performed to evaluate the effectiveness of the proposed model and the efficiency of the proposed algorithm. The results show that the algorithm can obtain near-optimal solutions within a reasonable computing time. Several managerial implications are obtained from sensitivity analysis. The proposed methodology can be recommended for platform operators to improve dispatch efficiency and optimize workforce resources.

Approximations for many-visits multiple traveling salesman problems

A fundamental variant of the classical traveling salesman problem (TSP) is the so-called multiple TSP (mTSP), where a set of m salesmen jointly visit all cities from a set of n cities. The mTSP models many important real-life applications, in particular for vehicle routing problems. An extensive survey by Bektas (Omega34(3), 2006) lists a variety of heuristic and exact solution procedures for the mTSP that solve particular problem instances. In this work we consider a further generalization of mTSP, the many-visits mTSP, where each city v has a request r(v) of how many times it should be visited by the salesmen. This problem opens up new real-life applications such as aircraft sequencing, while at the same time it poses several computational challenges. We provide polynomial-time algorithms for several variants of the many-visits mTSP that compute constant-factor approximate solutions.

Process mean selection and price differentiation in an imperfectly segmented market for a risk-averse firm

Abstract In this paper, we propose an integrated model for optimizing the process mean, the price of products and the production quantity. This optimization is conducted considering the impact of price differentiation in an imperfectly segmented market where demand leakages are common. The products that are produced by the production process are assigned to two market segments using sampling inspection. For optimization of the process mean, pricing and production quantities, a multi-objective model is formulated that maximizes (i) The expected total risk-adjusted profit across segments for a risk-tolerant firm, (ii) The satisficing level, that is, the probability of exceeding a target set for total risk-adjusted expected profit and (iii) The two conflicting objectives, expected total risk-adjusted profit and satisficing level. Depending on the complexity of models, either derivative-based closed form solutions or heuristic solution procedures are developed. The problem finds applications in process industries. A detailed numerical simulation is performed to corroborate the models, and it shows that a higher risk aversion results in a lower total expected risk-adjusted profit but a higher probability of achieving the target profit.

Make or break: Coordinated assignment of parking space for breaks and rest periods in long-haul trucking

To avoid traffic accidents due to driver fatigue in long-haul trucking, there are laws and provisions all over the world that regulate breaks and rest periods of truck drivers. When aiming to follow the existing hours of service regulations, however, parking space for trucks in service areas is often scarce, especially along crowded mainlines. In this context, the paper on hand investigates whether a central platform coordinating the usage of limited parking capacity on the supply side and truck drivers’ individual drive and rest schedules on the demand side can be advantageous. Specifically, we formulate a holistic optimization problem, which jointly determines the drive and rest schedules for a given set of trucks with fixed routes and coordinates their assignment to a limited number of available parking spaces over time. To solve this problem, we introduce a heuristic solution procedure, which is benchmarked with the status quo, where each driver seeks parking space individually, and a booking platform that allows to reserve parking space ahead of arrival. Our computational results reveal that a booking platform that produces much less organizational overhead is almost as effective as a central matching platform based on perfect knowledge of all truck schedules.

Stronger mixed-integer programming-formulations for order- and rack-sequencing in robotic mobile fulfillment systems

This paper addresses the order- and rack-sequencing problem at a single picking station in the context of robotic mobile fulfillment systems, a warehouse technology typically applied in large distribution centers. Following the parts-to-picker concept, items are stored on movable racks that are lifted and transported by automated guided vehicles from the storage area to picking stations for order-processing. The order-picking process involves two linked decisions: How to sequence the processing of orders and how to sequence the rack visits to supply the picking station with the requested items. We present a novel mixed-integer linear programming formulation achieving stronger linear programming bounds than a previous formulation. Including preprocessing techniques it quickly solves instances of medium-size to proven optimality for the first time in literature. For large real-world instances, we provide a three-stage heuristic solution procedure suitable in a dynamic environment, while providing competitive solutions within a short run time. Computational experiments on a broad set of benchmark instances and a comparative study with approaches from literature verify our results.

The repair kit problem with imperfect advance demand information

To promote customer loyalty and generate revenue in after-sales service, many companies provide field repair services to their customers. Service technicians who perform these repair jobs typically carry a set of spare parts called a repair kit in their company van. The repair kit problem aims to determine which parts to include in this kit and in what quantity. Currently, many appliances are equipped with sensors that monitor their different functionalities. If an appliance breaks down because one of these functionalities is disturbed, then the respective sensor triggers a failure code that describes the appliance’s condition. From the service technician’s perspective, this failure code serves as potentially imperfect advance demand information for spare parts. In this paper, we present an extension of the repair kit problem that uses this information for the replenishment decision. We formulate this repair kit problem with advance demand information as a Markov decision process and propose two heuristic solution procedures. Our first heuristic is far-sighted and optimizes the inventory of all parts individually, while our second heuristic is a myopic greedy algorithm that considers all parts at once. We conduct an extensive numerical study to evaluate the performance of both heuristics and to identify which heuristic performs best under which circumstances. Comparing both heuristics to a state-of-the-art algorithm that disregards any available advance demand information, we find that utilizing this information yields substantial cost savings.

A multi-method approach to scheduling and efficiency analysis in dual-resource constrained job shops with processing time uncertainty

In dual-resource constrained job shop scheduling, jobs have to be assigned to workers and machines. While the problem is notoriously hard in terms of computational complexity, additional practical difficulties arise from data uncertainty and worker efficiency variation. In this paper, we propose a methodological pipeline combining mathematical optimization, simulation, and data analysis to cope with these aspects over time. Accounting for uncertain worker processing times, we employ an iterative two-stage optimization-simulation approach: A first-stage optimization model determines an assignment of workers to jobs; in the second stage, the scheduling of this assignment is evaluated operationally using sampled realizations of worker processing times. Both stages are executed in an alternating fashion until no further improvement is possible in the average realized makespan. At the end of a work day, realized worker efficiencies are then measured in a slacks-based data envelopment analysis on the operations level. Workers learn about their individual efficiency and are prompted to reduce inefficiencies. The resulting overall methodology not only provides robustified schedules for dual-resource constrained job shops under uncertainty, but also reduces the impact of uncertainty over time by motivating workers to operate on the efficient frontier. Computational results are conducted in several settings with both heuristic and exact solution procedures for the second-stage dual-resource constrained job shop scheduling problem. The results demonstrate the versatility of the outline with respect to addressing uncertainty and worker inefficiency.

Multi-objective optimization for a combined location-routing-inventory system considering carbon-capped differences

&lt;p style='text-indent:20px;'&gt;A combined location-routing-inventory system (CLRIS) in a three-echelon supply chain network is studied with environmental considerations. Specifically, a bi-objective mixed integer programming model is formulated for the CLRIS to deal with the trade-offs between the total cost and the carbon-capped difference (CCD). A multi-objective particle swarm optimization (MOPSO) heuristic solution procedure is developed and implemented to solve the bi-objective mixed integer programming problem. The bi-objective mixed integer programming model and the MOPSO heuristic procedure are applied to a real-life problem as an illustrative example. The approximate nondominated frontier formed by solutions not dominated by others can be used for the decision makers to make trade-offs between the total cost and the CCD. Sensitivity analyses are conducted, and the relationship among the carbon cap, CCD, the total cost and the carbon prices are examined, and relevant managerial insights are provided. Comparisons with other existing algorithms show that the MSPSO heuristic procedure has very good performance.&lt;/p&gt;

Levelling crane workload in multi-yard rail-road container terminals

In modern rail-road container terminals, container transshipment between trains and trucks is carried out by large gantry cranes that span over rail tracks and road lanes. Prior optimization approaches have mainly focused on the short-term scheduling of these crucial transshipment resources. In this work, we focus on a midterm planning level that assigns inbound trains to yard tracks such that trains can be serviced by yard resources on schedule. This planning task is especially crucial in larger terminal settings which comprise more than a single yard, which is increasingly typical in growing intermodal networks. We describe the planning situation we encountered at a large rail-road terminal in Germany and propose a mixed-integer model formulation that captures the core of the decision problem. Further, we carry out a complexity analysis of problem variants and develop a heuristic solution procedure in a simulated annealing framework based on these structural insights. The approach is tested in a comprehensive computational study which demonstrates the viability of the approach to solve instances of real-world size.

Increasing Trust in Development Processes Using Robust, Data-Driven Markov Games: An Application to PRESTIGE

In this article, we consider how to increase trust in development processes in which there is a risk for adversarial manipulation, and the adversary's objectives and resources are either ill-specified, imprecisely specified, or unknown. In such problems, we must hedge against the risk of misapprehension of attacker objectives and resources, which is further complicated in the absence of adversarial training data. We show how to model dynamic agent interaction, on the basis of partially observed or noise-corrupted data, using a partially observable Markov game (POMG) framework. We then propose a threefold heuristic solution procedure that: 1) uses the POMG to generate potential adversarial policies; 2) explicitly incorporates these adversarial policies in the construction of a robust defender policy by solving a robust dynamic program (DP); and 3) employs a probability matching heuristic in partially observable environments.

Assembly line balancing with parallel workstations

ABSTRACT The simple assembly line balancing problem (SALBP) considers work division among different workstations of a serially arranged assembly process to maximise its efficiency under workload (cumulative) and technological (precedence) constraints. In this work, we consider a variant of the SALBP which allows parallel workstations. To study the effect of parallel stations, we propose a new problem (the parallel station assembly line balancing problem or PSALBP) in which the objective is to minimise the number of parallel stations required to obtain the maximum theoretical efficiency of the assembly process. We study the complexity of the problem and identify a polynomially solvable case. This result is then used as a building block for the development of a heuristic solution procedure. Finally, we carry out a computational experiment to identify the characteristics of assembly lines that may benefit from station paralleling and to evaluate the performance of the proposed heuristic.

Grouping products for the optimization of production processes: A case in the steel manufacturing industry

The optimization of a production process is often based on the efficient utilization of the production facility and equipment. In particular, reducing the time to change from producing one product to another is critical to the fulfillment of demand at a minimum cost. We study the production of steel coils in the context of searching for groups of products with similar characteristics in order to create production batches that minimize the cost of fulfilling production orders originated by a known demand. We formulate the problem as mixed-integer program and develop a heuristic solution procedure. We show that a simplified version of the problem is equivalent to the clique partition problem, which in turn is equivalent to the graph-coloring problem. Computational experiments show that the heuristic procedure is effective in finding high-quality solutions to both the clique partition problem and the original grouping problem that includes additional costs.

High-density storage with mobile racks: Picker routing and product location

In response to the scarce space in many urban areas, high-density storage has become a widely discussed topic in warehousing research and practice. We investigate a storage setting where mobile racks are mounted on rails, so that a strong engine moves whole blocks of racks aside, opening an aisle and enabling access to a specific rack. Moving the heavy racks takes a considerable amount of time and, consequently, it strongly affects the total pick time. We formalise the resulting operational picker-routing problem, which aims at routing the picker such that as few aisles as possible need to be accessed and the total distance covered is minimal. Moreover, we address the interdependent tactical product-location problem, which deals with deciding on the storage locations of the items to be picked. We present suitable exact and heuristic solution procedures for both problems. In a comprehensive computational study, we apply these algorithms to explore the interdependencies between product location and picker routing, and derive recommendations as to suitable storage policies in a mobile rack warehouse.

Joint design of multimodal transit networks and shared autonomous mobility fleets

Providing quality transit service to travelers in low-density areas, particularly travelers without personal vehicles, is a constant challenge for transit agencies. The advent of fully-autonomous vehicles (AVs) and their inclusion in mobility service fleets may allow transit agencies to offer better service and/or reduce their own capital and operational costs. This study focuses on the problem of allocating resources between transit patterns and operating (or subsidizing) shared-use AV mobility services (SAMSs) in a large metropolitan area. To address this question, a joint transit network redesign and SAMS fleet size determination problem (JTNR-SFSDP) is introduced, and a bi-level mathematical programming formulation and solution approach are presented. The upper-level problem modifies a transit network frequency setting problem (TNFSP) formulation via incorporating SAMS fleet size as a decision variable and allowing the removal of bus routes. The lower-level problem consists of a dynamic combined mode choice-traveler assignment problem (DCMC-TAP) formulation. The heuristic solution procedure involves solving the upper-level problem using a nonlinear programming solver and solving the lower-level problem using an iterative agent-based assignment-simulation approach. To illustrate the effectiveness of the modeling framework, this study uses traveler demand from Chicago along with the region’s existing multimodal transit network. The computational results indicate significant traveler benefits, in terms of improved average traveler wait times, associated with optimizing the joint design of multimodal transit networks and SAMS fleets compared with the initial transit network design.

The cafeteria problem: order sequencing and picker routing in on-the-line picking systems

This paper is dedicated to the cafeteria problem: given a single waiter operating multiple counters for different dishes arranged along a line and a set of customers with given subsets of dishes they desire, find a sequence of customers, which may not overtake each other, and a service schedule for the waiter, such that the makespan is minimized. This generic problem is shown to have different real-world applications in order picking with blocking restrictions. We present different heuristic and exact solution procedures for both problem parts, i.e., customer sequencing and waiter scheduling, and systematically compare these approaches. Our computational results reveal that the largest performance gains are enabled by not strictly processing order after order. Instead, the waiter should be allowed to flexibly swap between customers waiting along the line. Such a flexible service policy considerably reduces the makespan and the total walking distance of the waiter.

A multilevel evaluation method for heuristics with an application to the VRPTW

AbstractThe field of combinatorial optimization has inspired the development of a large number of heuristic solution procedures. These methods are commonly assessed using a competitive evaluation methodology that may give an indication of which algorithm has a better performance. A next step in the experimental analysis is to uncover “why” one algorithm performs better. Which elements are responsible for good or bad performance? How does the performance of elements vary across the design space? What is the influence of the specific problem instance that is being solved? We focus on gaining a better understanding of heuristic algorithm performance and demonstrate that the application of a proper statistical methodology can provide researchers insight into how performance is affected by the different algorithm parameters and components. As an example, we apply a multilevel statistical analysis to a large neighborhood search algorithm for the vehicle routing problem with time windows.