Dry kiln scheduling in furniture production

In this paper, a dry kiln scheduling problem from the furniture manufacturing industry is considered. Factory-specified due dates for orders, kiln availability, kiln capacity, and travel time from the kilns to the factories are all incorporated in a model which is formulated as an integer linear program. The objective of the formulation is to minimize the maximum tardiness of orders arriving at the plants by solving a special case of scheduling n independent jobs on m non-identical parallel ciachines. Because of the computational complexity, and the fact that standard integer programming packages appear to perform very poorly on the problem, a heuristic approach is developed. Computational experience is provided which indicates that the heuristic gives very high quality solutions to problems in near real-time.     

Production scheduling with outsourcing scenarios: a mixed integer programming and efficient solution procedure

When market demand exceeds the company's capacity to manufacture, outsourcing is commonly considered as an effective alternative option. In traditional scheduling problems, processing of received orders is just possible via in-house resources, while in practice, outsourcing is frequently found in various manufacturing industries, especially in electronics, motor and printing companies. This paper deals with the scheduling problem, minimising the cost of outsourcing and a scheduling measure represented by weighted mean flow time, in which outsourcing of manufacturing operations is allowed through subcontracts. Each order can be either scheduled for in-house production or outsourced to an outside supplier in order to meet customer due dates. In this problem, not only should the sequence of orders be determined, but also decision on picking the jobs for outsourcing, selecting the appropriate subcontractor, and scheduling of the outsourced orders are considered as new variables. To formulate the given problem, four different outsourcing scenarios are derived and mixed integer programming models are developed for each one separately. Furthermore, to solve the suggested problem, a computationally effective team process algorithm is devised and then a constraint handling technique is embedded into the main algorithm in order to ensure satisfaction of customer due dates. Numerical results show that the suggested approach possesses high global solution rates as well as fast convergence.     

A Mixed-Integer Optimization Strategy for Oil Supply in Distribution Complexes

As a result of an increasingly competitive market, companies must find ways to organize their activities regarding their economic outcome. An important feature in this context involves transportation operations, usually considered one of the major bottlenecks in the production chain. While delays imply loss of time and lack of resources, deliveries ahead of the deadlines may cause excess of inventories. Therefore, every company must pursue efficient transportation schedules within their operational planning. This work addresses short-term crude oil scheduling problems in a distribution complex that contains ports, refineries and a pipeline infrastructure capable of transferring oil from the former to the latter. The ports comprise piers, which receive vessels for discharging, storage tanks and a network that connects each other. The refineries have their own storage infrastructure, modeled as a large storage unit, along with crude distillation units, considered as constant level consumers. The problem involves a number of other issues, including intermediate storage, settling tasks and allocation of crude oil by its qualitative characteristics. A decomposition strategy based on large-scale mixed-integer linear programming (MILP) continuous-time models is developed. First, an MILP model that considers an aggregate representation for the pipeline and intermediate storage infrastructure is proposed. Decision variables involve the assignment of oil tankers to piers as well as tanker unloading and pipeline loading operations. The solution of this model provides the initial conditions for MILP models that represent the pipeline and intermediate storage infrastructure at a detailed level. Algorithms based on the LP-based branch-and-bound method are employed. Results from a port scenario of 13 tankers, 4 piers, 14 crude types, 18 storage tanks and 2 pipelines were obtained in approximately 90 minutes from an MILP problem containing 1996 continuous variables, 1039 binary variables and 7203 constraints.     

Green permutation flowshop scheduling problem with sequence-dependent setup times: a case study

Increasing global energy consumption, large variations in its cost and the environmental degradation effects are good reasons for the manufacturing industries to become greener. Green shop floor scheduling is increasingly becoming a vital factor in the sustainable manufacturing. In this paper, a green permutation flowshop scheduling problem with sequence-dependent setup times is studied. Two objectives are considered including minimisation of makespan as a measure of service level and minimisation of total energy consumption as a measure of environmental sustainability. We extend a bi-objective mixed-integer linear programming model to formulate the stated problem. We develop a constructive heuristic algorithm to solve the model. The constructive heuristic algorithm includes iterated greedy (CHIG) and local search (CHLS) algorithms. We develop an efficient energy-saving method which decreases energy consumption, on average, by about 15%. To evaluate the effectiveness of the constructive heuristic algorithm, we compare it with the famous augmented ?-constraint method using various small-sized and large-sized problems. The results confirm that the heuristic algorithm obtains high-quality non-dominated solutions in comparison with the augmented ?-constraint method. Also, they show that the CHIG outperforms the CHLS. Finally, this paper follows a case-study, with in-depth analysis of the model and the constructive heuristic algorithm.     

Block spatial scheduling modelling and application in shipbuilding

With the wide application of module-shipbuilding technology, problems related to block spatial scheduling occur in various working areas, and this restricts the productivity of shipbuilding. To address the problems and to obtain the optimum block sequence and spatial layout, typical block features and work plates were investigated. A heuristic spatial scheduling model was established based on the investigation and proposed strategies with the objective to minimise makespan. With the heuristic algorithm, a block spatial scheduling system was developed and implemented with real data from a large ship. Through the spatial scheduling system, visual results of daily block layouts and progress charts for all blocks can be easily obtained and work orders can also be created for site workers. Several other spatial scheduling methods are described and compared with the above-mentioned heuristic algorithm. The result shows that the heuristic algorithm is better than Cplex and a genetic algorithm in solving large-scale block scheduling, and the heuristic algorithm is better than a grid algorithm and manual scheduling in all aspects such as makespan, utilisation of work plates, runtime of scheduling and on-time delivery. The developed block spatial scheduling system is applied in a block production shop of a modern shipyard and shows good performance.     

Hybrid genetic algorithm for test bed scheduling problems

In this paper, we address the scheduling problem for a heavy industry company which provides ship engines for shipbuilding companies. Before being delivered to customers, ship engines are assembled, tested and disassembled on the test beds. Because of limited test bed facilities, it is impossible for the ship engine company to satisfy all customers’ orders. Therefore, they must select the orders that can be feasibly scheduled to maximise profit. An integer programming model is developed for order selection and test bed scheduling but it cannot handle large problems in a reasonable amount of time. Consequently, a hybrid genetic algorithm (GA) is suggested to solve the developed model. Several experiments have been carried out to demonstrate the performance of the proposed hybrid GA in scheduling test beds. The results show that the hybrid GA performs with an outstanding run-time and small errors in comparison with the integer programming model.     

A heuristic for scheduling in flowshop and flowline-based manufacturing cell with multi-criteria

The problem of scheduling in flowshop and flowline-based manufacturing cell is considered with the bicriteria of minimizing makespan and total flowtime of jobs, The formulation of the scheduling problems for both the flowshop and the flowline-based manufacturing cell is first discussed. We then present the development of the proposed heuristic for flowshop scheduling. A heuristic preference relation is developed as the basis for the heuristic so that only the potential job interchanges are checked for possible improvement with respect to bicriteria, The proposed heuristic algorithm as well as the existing heuristic are evaluated in a large number of randomly generated large-sized flowshop problems. We also investigate the effectiveness of these heuristics with respect to the objective of minimizing total machine idletime. We then modify the proposed heuristic for scheduling in a cell, and evaluate its performance.     

Scheduling on uniform parallel machines with periodic unavailability constraints

Scheduling problems under unavailability constraints has become a popular research topic in the last few years. Despite it’s important application in the real world, the uniform parallel machine scheduling problem was the least studied due to its complexity. In this paper, we investigated the uniform parallel machine scheduling problem under deterministic availability constraints. Each machine is subject to one unavailability period. Different versions of the problem regarding the type of jobs (identical and non-identical) and the performance measures (the total completion times and the makespan) were studied. For the case of identical jobs and for both performance measures, we developed linear programming models and optimal algorithms to provide a solution to the problem. For the case of non-identical jobs, we proved that the problem is NP-hard and propose a quadratic program. Because, this later cannot solve problems with very large number of jobs and machines, a heuristic was developed to find near optimal solutions to the problem especially with very large number of jobs and machines. The computational results showed that the heuristic’s performance is very high regardless the dimensions of problem instances.     

Multi-product continuous plant scheduling: combination of decomposition,genetic algorithm,and constructive heuristic

We propose a polylithic method for medium-term scheduling of a large-scale industrial plant operating in a continuous mode. The method combines a decomposition approach, a genetic algorithm (GA) and a constructive MILP-based heuristic. In the decomposition, decisions are made at two levels, using the rolling horizon approach. At the upper level, a reduced set of products and the time period is chosen to be considered in the lower level. At the lower level, a short-term scheduling MILP-model with event-based representation is used. A heuristic solution to the lower level problem is found using a constructive Moving Window heuristic guided by a genetic algorithm. The GA is applied for finding efficient utilisation of critical units in the lower level problem. For solving the one unit scheduling problem, a parallel dynamic programming algorithm is proposed. Implementation of the dynamic programming algorithm for a graphics processing unit (GPU) is incorporated in the GA for improving its performance. The experimental study of the proposed method on a real case of a large-scale plant shows a significant improvement of the solution quality and the solving time comparing to the pure decomposition algorithm proposed in the earlier study, and confirmed suitability of the proposed approach for the real-life production scheduling. In particular, the reduction of the number of changeovers and their duration in the obtained solution as well as the CPU time of solving the problem was about 60% using the new approach.     

Order acceptance and scheduling policies for a make-to-order environment with family-dependent lead and batch setup times

In many make-to-order production situations with batch setup times, customer orders are grouped into family-dependent batches to limit the loss of capacity due to setups. These batches, however, cannot be too large, since the make-to-order character requires that orders have to be produced in time. This trade-off between setup time efficiency and due-date adherence creates a challenging scheduling problem referred to in the literature as the Customised Stochastic Lot Scheduling Problem. Typically, suppliers reduce the complexity of the production problem by quoting lead times that are equal for all customer families. This choice, however, is in many cases too restrictive. In this paper, we show quantitatively by means of Markov decision processes (MDPs) that using family-dependent lead times can result in a significant gain in profit as compared with using standard lead times. We develop a simple heuristic acceptance/scheduling policy, and demonstrate that this heuristic performs very well compared with the optimal policy of the MDP for a wide range of parameters.     

ECONOMIC DESIGN OF REFRIGERATED AUTOMATED STORAGE AND RETRIEVAL SYSTEMS

The objective of this paper is the development of a design model for refrigerated automated storage and retrieval systems (R-AS/RS). Compared with ordinary unit-load AS/RS, the R-AS/RS under this study has several different design and operating characteristics: (I) greater emphasis is placed on the storage function and so it has a double-depth lane in the storage rack; (2) cooling units are required to maintain a cold temperature environment in the system; (3) the maximum number of storage orders handled per unit time is limited by the system capacity. Considering the above characteristics, the design problem is formulated as a non-linear mixed integer programming problem in which the cost of the system is minimized. The decision variables are the storage volume, the number of storage and retrieval (S/R) machines, the type and number of cooling units, and the physical configuration of the building. A case problem is solved to illustrate the model.     

Sequencing mixed-model assembly lines to minimize part inventory cost

A mixed-model assembly line enables the joint production of different models of a common base product in intermixed model sequence (lot size one). Previous approaches for the short-term planning task of model sequencing either aim at minimizing work overload (mixed-model sequencing and car sequencing) or leveling part usages (level scheduling). However, at many manufacturers parts are consolidated by a third party logistics provider, who stocks Just-in-Time delivered parts in a consignment warehouse adjacent to the line. The manufacturer issues a complete cargo carrier (e.g. a euro-pallet) whenever his own intermediate storage of parts is depleted. Thus, the manufacturer aims at a model sequence which minimizes his own inventory costs. This paper formalizes this novel model sequencing problem and describes different heuristic and exact procedures. Furthermore, the solutions yielded by these approaches are compared to the traditional level scheduling.     

Exact and approximate methods for parallel multiple-area spatial scheduling with release times

Spatial scheduling problems involve scheduling jobs that each require certain amounts of two-dimensional space within a processing area of limited width and length. Thus, this requires not only assigning time slots to each job but also locations and orientations within the limited physical processing space as well. Such problems, often encountered in shipbuilding and aircraft manufacturing, are generally difficult to solve, and there is a relatively small amount of literature addressing these problems compared to other types of scheduling. In this paper, we consider a particularly complex class of spatial scheduling problems that involve scheduling each job into one of several possible processing areas in parallel to minimize the total amount of tardy time. In addition, each job has a release time before which it may not be processed. We introduce two methods for solving this type of problem: an integer programming (IP) model and a heuristic algorithm. We perform computational tests and comparisons of each method over a large number of generated benchmark problems with varying characteristics, and also compare these to a more naïve heuristic. Solving the IP model was effective for small problems but required excessive amounts of time for larger ones. The heuristic was effective and produced solutions of comparable quality to the IP model for many problems while requiring very little computational time.     

Flow shop scheduling in serial multi-product processes with transfer and set-up times

Short-term production scheduling is a widely seen problem in multi-product batch operations. In this paper, an effective heuristic algorithm for scheduling a set of different tasks to be processed on serial processors is presented that provides an approach towards minimizing the entire makespan and improving productivity. Flow shops with an interstage storage policy, non-zero transfer times, and non-zero setup times are considered. The performance of the proposed algorithm was evaluated through numerous simulated problems. Statistical analysis of the output data indicates that in the situation containing up to seven tasks, the algorithm provides optimal or near optimal solutions and needs very short computation time. For a larger number of tasks, it gives up to 20% better solutions than a well-known existing algorithm.     

An MILP Continuous-Time Framework for Short-Term Scheduling of Multipurpose Batch Processes Under Different Operation Strategies

This work introduces a novel MILP continuous-time framework to the optimal short-term scheduling of non-sequential multipurpose batch processes with intermediate storage vessels. It is based on a problem representation that describes the batch sequence at any processing/storage unit by providing the full set of predecessors for every batch. Different operation modes can be considered by making minor changes in the problem model. The proposed framework can also handle sequence-dependent changeovers as well as multiple storage tanks available to receive material from one or several processing units. Three example problems involving up to fifteen batches and six processing tasks were successfully solved. Compared with previous work, a drastic reduction in both problem size and CPU time has been achieved.     

LP-based heuristics for scheduling chemical batch processes

A mixed-integer linear programming (MILP) model for scheduling chemical batch processes is presented. Since computational times are prohibitive for most problems of realistic size, a two-stage solution procedure is suggested. In the first stage, an initial solution is derived by use of a LP-based heuristic. The proposed heuristic defines a time grid that includes only a limited number of feasible periods in which a processing task is allowed to start. Thus, the size of the original multi-period MILP model is reduced in a controlled manner and optimal solutions to the relaxed model are obtained within reasonable computational time. The second stage consists of an improvement step that aims to compress the initial schedule by left-shifting operations over the time-axis. In order to evaluate the applicability of the heuristics a number of numerical experiments were performed. It is shown that near-optimal solutions are obtained for largesize problems with only modest computational effort.     

Scheduling Multi-Mode Resource-Constrained Projects Using Heuristic Rules Under Uncertainty Environment

Project scheduling is a key objective of many models and is the proposed method for project planning and management. Project scheduling problems depend on precedence relationships and resource constraints, in addition to some other limitations for achieving a subset of goals. Project scheduling problems are dependent on many limitations, including limitations of precedence relationships, resource constraints, and some other limitations for achieving a subset of goals. Deterministic project scheduling models consider all information about the scheduling problem such as activity durations and precedence relationships information resources available and required, which are known and stable during the implementation process. The concept of deterministic project scheduling conflicts with real situations, in which in many cases, some data on the activity' s durations of the project and the degree of availability of resources change or may have different modes and strategies during the process of project implementation for dealing with multi-mode conditions surrounded by projects and their activity durations. Scheduling the multi-mode resource-constrained project problem is an optimization problem whose minimum project duration subject to the availability of resources is of particular interest to us. We use the multi-mode resource allocation and scheduling model that takes into account the dynamicity features of all parameters, that is, the scheduling process must be flexible to dynamic environment features. In this paper, we propose five priority heuristic rules for scheduling multi-mode resource-constrained projects under dynamicity features for more realistic situations, in which we apply the proposed heuristic rules (PHR) for scheduling multi-mode resource-constrained projects. Five projects are considered test problems for the PHR. The obtained results rendered by these priority rules for the test problems are compared by the results obtained from 10 well-known heuristics rules rendered for the same test problems. The results in many cases of the proposed priority rules are very promising, where they achieve better scheduling dates in many test case problems and the same results for the others. The proposed model is based on the dynamic features for project topography.     

Optimization Models for Scheduling of Jobs

This work is motivated by a particular scheduling problem that is faced by logistics centers that perform aircraft maintenance and modification. Here we concentrate on a single facility (hangar) which is equipped with several work stations (bays). Specifically, a number of jobs have already been scheduled for processing at the facility; the starting times, durations, and work station assignments for these jobs are assumed to be known. We are interested in how best to schedule a number of new jobs that the facility will be processing in the near future. We first develop a mixed integer quadratic programming model (MIQP) for this problem. Since the exact solution of this MIQP formulation is time consuming, we develop a heuristic procedure, based on existing bin packing techniques. This heuristic is further enhanced by application of certain local optimality conditions.     

New scheduling algorithms and digital tool for dynamic permutation flowshop with newly arrived order

The permutation flowshop scheduling problem has been widely studied under static environment by assuming machines and jobs are available at the time of zero. However, in reality, new orders arrive at production systems randomly, which leads to sheer complexity in scheduling due to the dynamic changes given various constraints of resources. Previous studies simply attach new orders directly after the existing schedule. Recent study shows mixing jobs of old and new orders could result in better scheduling solutions. But the heuristic algorithms are still lacking to implement the job mixing policy. To address this problem, a novel scheduling strategy is herein proposed by integrating match-up strategy and real-time strategy (MR) in order to make use of the remaining time before the old order due date. Based on the new MR strategy, eleven new heuristics are introduced with ten existing and one new priority rules. Computational results illustrate the effectiveness of the new heuristics. A digital tool is developed for ease of application of these heuristics, and it is validated by case studies.     

Level scheduling of mixed-model assembly lines under storage constraints

In a mixed-model assembly line, different models of a common base product can be manufactured in intermixed production sequences. A famous solution approach for the resulting short-term sequencing problem is the so-called level scheduling problem, which aims at evenly smoothing the material requirements over time in order to facilitate a just-in-time supply. However, if materials are delivered in discrete quantities, the resulting spread of material usages implies that issued cargo carriers of a respective material remain at a station for a longer period of time. In practical applications with many materials required per station, this procedure might lead to bottlenecks with respect to the scarce storage space at stations. This paper investigates level scheduling under the constraint that the induced part usage patterns may not violate given storage constraints. The resulting sequencing problem is formalised and solved by suitable exact and heuristic solution approaches.