Heuristic Solution Procedure Research Articles

Part feeding at high-variant mixed-model assembly lines

The part feeding problem at automotive assembly plants deals with the timely supply of parts to the designated stations at the assembly line. According to the just-in-time principle, buffer storages at the line are frequently refilled with parts retrieved from a central storage area. In the industrial application at hand, this is accomplished by means of an internal shuttle system which supplies the various stations with the needed parts based on a given assembly sequence. The main objective is to minimize the required number of shuttle drivers. To solve this in-house transportation problem, a heuristic solution procedure is developed which is based on the decomposition of the entire planning problem into two stages. First, transportation orders are derived from the given assembly sequence. In the second stage, these orders are assigned to tours of the shuttle system taking transportation capacity restrictions, due dates and tour scheduling constraints into account. Numerical results show that the proposed heuristic solves even large-sized problem instances in short computational time. Benchmark comparisons with Kanban systems reveal the superiority of the proposed predictive part feeding approach.

Adaptive policies for multi-mode project scheduling under uncertainty

In this paper we propose an adaptive model for multi-mode project scheduling under uncertainty. We assume that there is a due date for concluding the project and a tardiness penalty for failing to meet this due date, and that several distinct modes may be used to undertake each activity. We define scheduling policies based on a set of thresholds. The starting time of the activity is compared with those thresholds in order to define the execution mode. We propose a procedure, based on the electromagnetism heuristic, for choosing a scheduling policy. In computational tests, we conclude that the adaptive scheduling policy found by using the model and the heuristic solution procedure is consistently better than the optimal non-adaptive policy. When the different modes have very different characteristics and there is a reasonable difference between the average duration of the project and the due date, the cost advantage of the adaptive policy becomes very significant.

Sequencing mixed-model assembly lines to minimise the number of work overload situations

The mixed-model sequencing problem is to sequence different product models launched down an assembly line, so that work overload at the stations induced by direct succession of multiple labour-intensive models is avoided. As a concept of clearing overload situations, especially applied by Western automobile producers, a team of cross-trained utility workers stands by to support the regular workforce. Existing research assumes that regular and utility workers assemble side-by-side in an overload situation, so that the processing speed is doubled and the workpiece can be finished inside a station's boundaries. However, in many real-world assembly lines the application of utility workers is organised completely differently. Whenever it is foreseeable that a work overload will occur in a production cycle, a utility worker takes over to exclusively execute work, whereas the regular worker omits the respective cycle and starts processing the successive workpiece as soon as possible. This study investigates this more realistic sequencing problem and presents a binary linear program along with a complexity proof. Different exact and heuristic solution procedures are then introduced and tested. Additional experiments show that the new model is preferable from an economic point of view whenever utility work causes considerable setup activities, for example walking to the respective station.

The assembly line balancing and scheduling problem with sequence-dependent setup times: problem extension, model formulation and efficient heuristics

Assembly line balancing problems (ALBP) consist of distributing the total workload for manufacturing any unit of the products to be assembled among the work stations along a manufacturing line as used in the automotive or the electronics industries. Usually, theory assumes that, within each station, tasks can be executed in an arbitrary precedence-feasible sequence without changing station times. In practice, however, the task sequence may influence the station time considerably as sequence-dependent setups (e.g., walking distances, tool changes) have to be considered. Including this aspect leads to a joint balancing and scheduling problem, which we call SUALBSP (setup assembly line balancing and scheduling problem). In this paper, we modify the problem by modeling setups more realistically, give a new, more compact mathematical model formulation and develop effective heuristic solution procedures. Computational experiments based on existing and new data sets indicate that the new procedures outperform formerly proposed heuristics. They are able to solve problem instances of real-world size with small deviations from optimality in computation times short enough to be accepted in real-world decision support systems.

An enriched model for the integrated berth allocation and quay crane assignment problem

Given the increasing pressure to improve the efficiency of container terminals, a lot of research efforts have been devoted to optimizing container terminal operations. Most papers deal with either the berth allocation problem (BAP) or the (quay) crane assignment problem (CAP). In the literature on the BAP, handling times are often simplified to be berth dependent or proportional to vessel size, so the CAP can be ignored when scheduling vessels. This is unsatisfactory for real-life applications because the handling time primarily depends on the number of containers to be handled and the number of cranes deployed. Only a limited number of papers deals with the combination of berth allocation and crane assignment. In these papers however, authors often have resorted to algorithmic simplifications that limit the practical use of the models. This paper presents a MILP model for the integrated BAP–CAP taking into account vessel priorities, preferred berthing locations and handling time considerations. The model is used in a hybrid heuristic solution procedure that is validated on real-life data illustrating the potential to support operational and tactical decision-making.

How to park freight trains on rail–rail transshipment yards: the train location problem

In modern rail---rail transshipment yards huge gantry cranes spanning all railway tracks allow for an efficient transshipment of containers between different freight trains. This way, multiple trains loaded with cargo for varying destinations can be consolidated to a reduced number of homogeneous trains, which is an essential requirement of hub-and-spoke railway systems. An important problem during the daily operations of such a transshipment yard is the train location problem, which assigns each train of a given pulse to a railway track (vertical position) and decides on each train's parking position on the track (horizontal position), so that the distances of container movements are minimized and the overall workload is equally shared among cranes. For this problem a mathematical model is presented; different heuristic solution procedures are described and tested in a comprehensive computational study. The results show that our procedures allow for a remarkable reduction of train processing time compared with typical real-world train location policies.

Simultaneous determination of lot size and production rate at capacity-constrained multiple-product systems

In the capacity constrained manufacturing systems where multiple product types are manufactured, the products are often produced in lots. Although the lot production may increase the system throughput by reducing changeover times, it may also increase production lead time because each item in a large lot has a long waiting time. Hence, a production manager should consider both throughput and lead time at the same time when deciding production lot sizes. This paper, which is an extension to the previous work done in Koo et al. (2007) that assumes homogeneous setup times, addresses a lot sizing problem in the system with multiple product types and unequal setup times. We develop a non-linear optimization model for simultaneous determination of throughput rate and lot size for each product. Since this optimization model cannot be solved analytically, we propose a heuristic solution procedure by analyzing the characteristics of the problem. Some numerical examples are presented to validate the proposed model, and finally the performance of the heuristic procedure is evaluated by comparison with the results of simulation experiments.

Integrated market selection and production planning: complexity and solution approaches

Emphasis on effective demand management is becoming increasingly recognized as an important factor in operations performance. Operations models that account for supply costs and constraints as well as a supplier’s ability to influence demand characteristics can lead to an improved match between supply and demand. This paper presents a class of optimization models that allow a supplier to select, from a set of potential markets, those markets that provide maximum profit when production/procurement economies of scale exist in the supply process. The resulting optimization problem we study possesses an interesting structure and we show that although the general problem is $${\mathcal{NP}}$$ -complete, a number of relevant and practical special cases can be solved in polynomial time. We also provide a computationally very efficient and intuitively attractive heuristic solution procedure that performs extremely well on a large number of test instances.

A column generation heuristic for dynamic capacitated lot sizing with random demand under a fill rate constraint

This paper deals with the dynamic multi-item capacitated lot-sizing problem under random period demands (SCLSP). Unfilled demands are backordered and a fill rate constraint is in effect. It is assumed that, according to the static-uncertainty strategy of Bookbinder and Tan [1], all decisions concerning the time and the production quantities are made in advance for the entire planning horizon regardless of the realization of the demands. The problem is approximated with the set partitioning model and a heuristic solution procedure that combines column generation and the recently developed ABC β heuristic is proposed.

Scheduling just-in-time part supply for mixed-model assembly lines

With increasing cost competition and product variety, providing an efficient just-in-time (JIT) supply has become one of the greatest challenges in the use of mixed-model assembly line production systems. In the present paper, therefore, we propose a new approach for scheduling JIT part supply from a central storage center. Usually, materials are stored in boxes that are allotted to the consumptive stations of the line by a forklift. For such a real-world problem, a new model, a complexity proof as well as different exact and heuristic solution procedures are provided. Furthermore, a direct comparison with a simple two-bin kanban system is provided. Such a system is currently applied in the real-world industrial process that motivates our research. It becomes obvious that this policy is considerably outperformed according to the resulting inventory- and α-service levels. Moreover, at the interface between logistics and assembly operations, strategic management implications are obtained. Specifically, based on the new approach, it is the first time a statistical analysis is being made as to whether widespread Level Scheduling policies, which are well-known from the Toyota Production System, indeed facilitate material supply. Note that in the literature it is frequently claimed that this causality exists.

A primogenitary linked quad tree approach for solution storage and retrieval in heuristic binary optimization

A data structure, called the primogenitary linked quad tree (PLQT), is used to store and retrieve solutions in heuristic solution procedures for binary optimization problems. Two ways are proposed to use integer vectors to represent solutions represented by binary vectors. One way is to encode binary vectors into integer vectors in a much lower dimension and the other is to use the sorted indices of binary variables with values equal to 0 or equal to 1. The integer vectors are used as composite keys to store and retrieve solutions in the PLQT. An algorithm processing trial solutions for insertion into or retrieval from the PLQT is developed. Examples are provided to demonstrate the way the algorithm works. Another algorithm traversing the PLQT is also developed. Computational results show that the PLQT approach takes only a very tiny portion of the CPU time taken by a linear list approach for the same purpose for any reasonable application. The CPU time taken by the PLQT managing trial solutions is negligible as compared to that taken by a heuristic procedure for any reasonably hard to solve binary optimization problem, as shown in a tabu search heuristic procedure for the capacitated facility location problem. Compared to the hashing approach, the PLQT approach takes the same or less amount of CPU time but much less memory space while completely eliminating collision.

Joint consideration of assembly-line production smoothing and finished-goods delivery efficiency in an automobile plant

This paper presents a Heuristic solution procedure to achieve an integrated consideration of production scheduling on the assembly line and the efficiency in the finished-goods delivery. For production scheduling, production smoothing in models and product attributes is considered; for finished-goods delivery, it considers effective grouping of finished goods and even distribution in delivery dates for a destination, in order to ship products as they are produced. The Heuristic procedure first forms packages of units and then assigns packages to various days. The computational results based on randomly-generated problems showed the advantage in cost savings by an integrated consideration. A simulated annealing procedure is developed for package assignment.

Scheduling aircraft landings to balance workload of ground staff

Scheduling landings of aircrafts is an essential problem which is continuously solved as part of the daily operations of an airport control tower. All planes in the airspace of an airport are to be assigned to landing slots by the responsible air-traffic controller. The support of this decision problem with suited optimization approaches has a long lasting tradition in operations research. However, none of the former approaches investigates the impact of the landing sequence on the workload of ground staff. The paper on hand presents three novel objectives for the aircraft landing problem, which aim at leveling the workload of ground staff by evenly spreading: (1) number of landed passengers, (2) landings per airline, and (3) number of landed passengers per airline over the planning horizon. Mathematical models along with complexity results are developed and exact and heuristic solution procedures are presented.

Integrated Location and Inventory Decision Problem in a Three-Tier Supply Chain Network

This paper considers a three-tier distribution network with one manufacturer, multiple warehouses and multiple retailers. The demand at the retailers is constant and shortages are not allowed. The problem is to determine location of the plant, number and location of warehouses, allocation of retailers to these warehouses and inventory policy for the warehouses and the retailers. The objective is to minimize long run average total costs. We consider a tradeoff between location costs, transportation costs and inventory holding costs.This work falls under the class of integrated location inventory problem in a three-tier supply chain. Previous work has considered a single warehouse with multiple retailers where the location of the warehouse and inventory policy for the network is determined simultaneously. However the multiple warehouse multiple retailer integrated location inventory problem in a three-tier supply chain network has not been studied. We develop a math formulation and a heuristic solution procedure for this problem. The solution gives lower cost over the one warehouse multiple retailer problem.

To Wait or Not to Wait—And Who Goes First? Delay Management with Priority Decisions

Delay management is an important issue in the daily operations of any railway company. The task is to update the planned timetable to a disposition timetable in such a way that the inconvenience for the passengers is as small as possible. The two main decisions that have to be made in this respect are the wait-depart decisions, to decide which connections should be maintained in case of delays, and the priority decisions, which determine the order in which trains are allowed to pass a specific piece of track. The latter are necessary to take the limited capacity of the track system into account. While the wait-depart decisions have been intensively studied in the literature, the priority decisions in the capacitated case have been neglected so far in delay management optimization models. In the current paper, we add the priority decisions to the integer programming formulation of the delay management problem and are hence able to deal with the capacitated case. The corresponding constraints are disjunctive constraints leading to cycles in the resulting event-activity network. Nevertheless, we are able to derive reduction techniques for the network that enable us to extend the formulation of the never-meet property from the uncapacitated delay management problem to the capacitated case. We then use our results to derive exact and heuristic solution procedures for solving the delay management problem. The results of the algorithms are evaluated both from a theoretical and a numerical point of view. The latter has been done within a case study using the railway network in the region of Harz, Germany.

A LAGRANGIAN-BASED SOLUTION ALGORITHM FOR STRATEGIC SUPPLY CHAIN DISTRIBUTION DESIGN IN UNCERTAIN ENVIRONMENT

In this paper a multi-product, multi-echelon location–allocation model for the optimization of a supply chain design is proposed. This model integrated inventory decisions into distribution network design with stochastic market demands. The goal is to select the optimum numbers, locations, and capacities of the opening warehouses so that all customer demands to be satisfied at minimum total costs of the distribution network. We develop a nonlinear mixed-integer model and propose an efficient heuristic solution procedure for the problem. The solution approach is based on Lagrangian relaxation, improved with efficient heuristic to solve complex sub-problems. Computational results indicate that the proposed method yields good solutions with high quality within a reasonable computational time for various real-size problems.

Design of multi-product manufacturing lines with the consideration of product change dependent inter-task times, reduced changeover and machine flexibility

Traditional research work in manufacturing line design assumes that the times between manufacturing tasks performed on a workstation are independent of the task sequence on that station. Furthermore, such studies paid little attention to the sequence dependent inter-task times in multi-model production. Since the inter-task times related to product model changeover have significant impact on manufacturing line performance, it is necessary to take into account the inter-task times explicitly in multi-model manufacturing line design. The need for this consideration is growing as product variety increases. This paper presents mathematical models of manufacturing line design with the consideration of product change related inter-task times in evaluating station times for multi-model production. An optimization model is developed using mixed integer programming to minimize manufacturing line cost. The model takes into account the recurrence of manufacturing tasks in a station to determine the machine type in a station. This paper also presents a heuristic solution procedure developed for efficient calculation. This paper also investigates how product model build sequences and inter-task times affect manufacturing line performance. The developed models will help enhance task-station assignment in multi- and mixed-model production by increasing line cost effectiveness and reducing line changeover impact as well as shortening long re-balancing processes.

The capacitated plant location problem with customers and suppliers matching

This paper introduces a new problem called the capacitated plant location problem with customer and supplier matching (CLCSM). The product distribution from plants to customers and the material supply from suppliers to plants are considered together. We merge a distribution trip and a supply trip into one triangular trip for saving allocation cost. Vehicles from plants visit a customer and a supplier for each trip. We provide a heuristic solution procedure based on Lagrangian relaxation. Computational results indicate that the proposed heuristic solution procedure is shown to be efficient yielding optimal or near-optimal solutions for randomly generated instances.

A double genetic algorithm for the MRCPSP/max

This paper presents a heuristic solution procedure for a very general resource-constrained project scheduling problem. Here, multiple execution modes are available for the individual activities of the project. In addition, minimum as well as maximum time lags between different activities may be given. The objective is to determine a mode and a start time for each activity such that the temporal and resource constraints are met and the project duration is minimised. Project scheduling problems of this type occur e.g. in process industries. The heuristic is a two-phased genetic algorithm with different representation, fitness, crossover operator, etc., in each of them. One of the contributions of the paper is the optimisation in the first phase of a problem dual to the original, the searching for the best modes of the activities. Computational results show that the algorithm outperforms the state-of-the-art algorithms in medium and large instances.

ABC β–a heuristic for dynamic capacitated lot sizing with random demand under a fill rate constraint

This paper deals with the dynamic multi-item capacitated lot-sizing problem (CLSP) with random demand over a finite discrete time horizon. Unfilled demands are backordered. It is assumed that a fill rate constraint is in effect. We propose a heuristic solution procedure called ABC β that extends the A/B/C heuristic introduced by Maes and Van Wassenhove for the deterministic CLSP to the case of random demands.