Production Scheduling Problems Research Articles

Integrated production and transportation scheduling with order-dependent inventory holding costs

In this study, we consider an integrated production and transportation scheduling problem faced by make-to-order manufacturers that adopt a commit-to-delivery business mode and cooperate with third-party logistics providers to deliver processed products to customers. The third-party logistics providers typically offer multiple shipping modes chosen by the manufacturers to deliver products, each shipping mode with a shipping time guarantee and a shipping cost function that is non-increasing in shipping time and sub-additive, non-decreasing in shipping quantity. The problem involves inventory holding costs which not only depend on the time that the products spend in temporary storage but also depend on customer types. The problem is to determine an integrated production and shipping schedule that satisfies the committed delivery due date limitations for the customers, such that the total cost of shipping and inventory holding is minimized. We investigate two cases with and without split delivery. For both cases, we first show that both of them are ordinarily NP-hard, prove that there exist no polynomial-time approximation algorithms with constant worst-case ratios, propose exact algorithms to solve them, and finally design column generation-based heuristic algorithms to find feasible solutions. The computational results demonstrate that the heuristic algorithms are capable of generating near-optimal solutions efficiently. We also consider two interesting practical variants of the problem.

Determining production capacity planning in the stochastic demand environment for the food processing manufacturers: A case study

This research studies production scheduling problems with stochastic customer demand for food processing factories to determine a multi-period production schedule that minimizes the total cost and achieves a predetermined customer service level. Based on the practical food processing conditions, this study constructs a mixed integer programming (MIP) mathematical model and applies chance constrained programming (CCP) to transform probabilistic constraints of customer demand into deterministic constraints of customer demand with the associated normal distributions. Using the numerical data, this research verifies the proposed methodology. For sensitivity analysis, the results show that increasing overtime hours decreases the total cost and enhancing customer service level increases the total cost. Furthermore, this study investigates the impacts of different forecasting and production schedules on out-of-stock costs, inventory costs, and both.

A Hybrid Discrete Bacterial Memetic Algorithm with Simulated Annealing for Optimization of the Flow Shop Scheduling Problem

This paper deals with the flow shop scheduling problem. To find the optimal solution is an NP-hard problem. The paper reviews some algorithms from the literature and applies a benchmark dataset to evaluate their efficiency. In this research work, the discrete bacterial memetic evolutionary algorithm (DBMEA) as a global searcher was investigated. The proposed algorithm improves the local search by applying the simulated annealing algorithm (SA). This paper presents the experimental results of solving the no-idle flow shop scheduling problem. To compare the proposed algorithm with other researchers’ work, a benchmark problem set was used. The calculated makespan times were compared against the best-known solutions in the literature. The proposed hybrid algorithm has provided better results than methods using genetic algorithm variants, thus it is a major improvement for the memetic algorithm family solving production scheduling problems.

Integrated scheduling and flexible maintenance in deteriorating multi-state single machine system using a reinforcement learning approach

This paper studies an integrated optimization problem of production scheduling and flexible preventive maintenance (PM) in a multi-state single machine system with deteriorating effects. A flexible PM strategy is proposed to proactively cope with machine failures while ensuring relatively regular PM intervals, which is composed of time-based PM (TBPM) and condition-based PM (CBPM). TBPM is conducted within every flexible time window and CBPM is implemented immediately after the most deteriorated yet still functional state. An illustrative case is presented using the enumeration approach to demonstrate the integration of production scheduling and machine maintenance. Then, Q-learning-based solution framework (QLSF) is further designed with proper state and action sets and reward functions to facilitate the determination of appropriate production scheduling rule under the constraint of the flexible maintenance. Numerical experiments show that the proposed QLSF outperforms the other four state-of-the-art scheduling rules in different scenarios. Moreover, the performance of the proposed flexible PM strategy is also examined and validated in comparison with three candidate maintenance strategies, i.e., run-to-failure corrective maintenance (CM), combination of TBPM and CM, and CBPM. The proposed flexible maintenance and solution approach can enrich the relevant academic knowledge base, and provide managerial insights and guidance in practical production systems.

Joint optimization of preventive maintenance and production scheduling for multi-state production systems based on reinforcement learning

Preventive maintenance and production scheduling are two important and interactive activities in production systems. In this work, the integrated optimization problem of production scheduling for multi-state single-machine production systems experiencing degradation processes is investigated. Preventive maintenance tasks and jobs scheduling are jointly considered to find the optimal production policy by considering the processing costs, the maintenance costs, and the completion rewards, simultaneously. We formulate the integrated optimization problem as Markov decision process framework. R-learning algorithm is introduced to maximize the long-run expected average rewards per time unit over infinite horizon. On the basis of the analysis of the optimal stationary policy, the appropriate condition to perform preventive maintenance following optimal stationary policy is presented. This provides the basis for the improvement in R-learning algorithm. Furthermore, a novel heuristic reinforcement learning method is proposed to deal with the integrated model more efficiently. Finally, we present the simulation results and analysis of the proposed algorithm's performance in terms of the number of job types and machine states. The simulation results and analysis show the effectiveness of the proposed approach for solving the integrated problems.

PARALLEL MACHINE SCHEDULING WITH MONTE CARLO TREE SEARCH

In this article, a specific production scheduling problem (PSP), the Parallel Machine Scheduling Problem (PMSP) with Job and Machine Sequence Setup Times, Due Dates and Maintenance Times is presented. In this article after the introduction and literature review the mathematical model of the Parallel Machines Scheduling Problem with Job and Machine Sequence Setup Times, Due Dates and Maintenance Times is presented. After that the Monte Carlo Tree Search and Simulated Annealing are detailed. Our representation technique and its evaluation are also introduced. After that, the efficiency of the algorithms is tested with benchmark data, which result, that algorithms are suitable for solving production scheduling problems. In this article, after the literature review, a suitable mathematical model is presented. The problem is solved with a specific Monte Carlo Tree Search (MCTS) algorithm, which uses a neighbourhood search method (2-opt). In the article, we present the efficiency of our Iterative Monte Carlo Tree Search (IMCTS) algorithm on randomly generated datasets.

Level-based multi-objective particle swarm optimizer for integrated production scheduling and vehicle routing decision with inventory holding, delivery, and tardiness costs

Integrated optimisation of production scheduling and distribution decision is necessary for reducing the whole cost of the supply chain in the make-to-order business environment. This paper studies a new integrated production scheduling and vehicle routing problem (IPSVRP) with inventory holding, delivery, and tardiness costs. The considered IPSVRP is modelled as a triple-objective optimisation problem, where the first objective aims to obtain the minimal total holding cost in the inventory, the second one attempts to achieve the minimal total travelling cost, and the third one tries to acquire the minimal total tardiness cost. To obtain a set of diverse non-dominated solutions in the Pareto-optimal front of the problem, we first derive several key structural properties used to provide necessary conditions for any solution to be Pareto-optimal through theoretical investigation. Based on the derived structural properties, a level-based multi-objective particle swarm optimizer (LMPSO) is subsequently designed. The performance of LMPSO is analysed by conducting a set of experiments, and its superiority is verified through comparing with other optimisation algorithms. Moreover, the convergence behaviour of LMPSO is also investigated, and the experimental results prove that it has the ability to achieve a set of non-dominated solutions proximity to the true Pareto front.

Integrated production and distribution scheduling in distributed hybrid flow shops

To improve the operational efficiency and competitive advantage of supply chains, integrated production and distribution has attracted an increasing attention in recent years. This paper focuses on a novel integrated production and distribution scheduling problem (IPDSP) with consideration of factory eligibility and third-party logistics (3PL). In this problem, products are firstly produced in a number of distributed hybrid flow shops (HFS) and then delivered to a customer in batches. To satisfy the production and distribution practice, some products can only be manufactured in a subset of distributed HFSs, and the transportation of some finished products is outsourced to a 3PL provider. Considering the NP-hardness of IPDSP, three fast heuristics (CR-based heuristic, SLACK-based heuristic, and EDD-based heuristic) and an adaptive human-learning-based genetic algorithm (AHLBGA) are proposed to minimize the sum of earliness, tardiness and delivery costs. Motivated by human learning behaviours, AHLBGA integrates an adaptive learning operator with traditional genetic operators to generate candidate solutions. Such learning operator performs social learning, family learning, and individual random learning to improve offspring individuals. The computational experiments on small-sized and large-sized test problems show the superiority of AHLBGA.

Integrated inventory and production policy for manufacturing with perishable raw materials

This research investigates an integrated inventory and production scheduling problem (IIPSP) in a manufacturer that deals with the perishable goods. The objective is to find an optimal schedule to minimize the sum of inventory cost and production cost. Both single-plant problem and multi-plant problem are investigated in this paper. For the single-plant problem, we prove that it is optimal to arrange the processing of raw materials in descending order of the value of the product of consumption rate and unit inventory cost. For the more complex multi-plant problem, we first prove that it is NP-hard, and then, we propose a hybrid intelligent algorithm to solve it. The experiments show that the proposed algorithm is superior to several other algorithms in both effectiveness and efficiency.

Iterated Greedy Algorithms for Flow-Shop Scheduling Problems: A Tutorial

An iterated greedy algorithm (IGA) is a simple and powerful heuristic algorithm. It is widely used to solve flow-shop scheduling problems (FSPs), an important branch of production scheduling problems. IGA was first developed to solve an FSP in 2007. Since then, various FSPs have been tackled by using IGA-based methods, including basic IGA, its variants, and hybrid algorithms with IGA integrated. Up until now, over 100 articles related to this field have been published. However, to the best of our knowledge, there is no existing tutorial or review paper of IGA. Thus, we focus on FSPs and provide a tutorial and comprehensive literature review of IGA-based methods. First, we introduce a framework of basic IGA and give an example to clearly show its procedure. To help researchers and engineers learn and apply IGA to their FSPs, we provide an open platform to collect and share related materials. Then, we make classifications of the solved FSPs according to their scheduling scenarios, objective functions, and constraints. Next, we classify and introduce the specific methods and strategies used in each phase of IGA for FSPs. Besides, we summarize IGA variants and hybrid algorithms with IGA integrated, respectively. Finally, we discuss the current IGA-based methods and already-solved FSP instances, as well as some important future research directions according to their deficiency and open issues. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Many practical scheduling problems can be transformed into flow-shop scheduling problems (FSPs), most of which are NP-hard. In order to solve them in an industrial system setting, designing effective heuristics is important and practically useful and has, thus, attracted much attention from both researchers and engineers. As an easy and high-performance heuristic, an iterated greedy algorithm (IGA) is widely used and adapted to solve numerous FSPs. Its simple framework makes it easy to be implemented by practitioners, and its high performance implies its great potential to solve industrial scheduling problems. In this work, we aim to give practitioners a comprehensive overview of IGA and help them apply IGA to solve their particular industrial scheduling problems. We review the papers that solve FSPs with IGA-based methods, including basic IGA, its variants, and hybrid algorithms with IGA integrated. First, we provide practitioners with a tutorial on IGA, where an example for solving an FSP is introduced and an open platform is constructed. The platform collects and shares the related materials, e.g., open-source code, benchmarks, and website links of important papers. Then, we introduce various FSPs and specific designs of IGA-based methods. Finally, we discuss the current research and point out future research issues.

Review of Solution Methodologies for Open Pit Mine Production Scheduling Problem

ABSTRACT The open pit mine production scheduling problem determines a sequence of three-dimensional, notional block extraction that maximises net present value (NPV) of future cash flows and satisfies technical and operational constraints such as precedence between blocks and resource availability. Since the 1960s, researchers have developed a variety of mathematical models that address block extraction at the strategic, tactical and operational levels, and the complexities associated therewith, e.g. risk and uncertainty, inventory strategies, environmental concerns and downstream processing. Given that these mathematical models are computationally complex, i.e. they are generally categorised as NP hard, a significant portion of the literature is dedicated to the development and performance of solution approaches spanning from exact and heuristics to recent meta-heuristic methods. This paper provides a comprehensive overview of recent contributions (from 2012 to early 2019) and discusses proposed future studies.

An enhanced branch-and-price algorithm for the integrated production and transportation scheduling problem

ABSTRACT Industry 4.0 technologies, such as artificial intelligence, the internet of things and 3D printing are aiding the manufacturers by complementing their skilled workforce and transforming the way factories are run. This paper studies an integrated production and transportation scheduling problem in the context of the spare parts supply chain by integrating 3D printing with JIT delivery systems. This work aims to find a synchronised production and distribution schedule that minimises the weighted sum of delivery times and transportation costs. Based on the characteristics of the problem, we propose a new set-covering formulation. An enhanced branch-and-price algorithm is designed to solve the problem instances to optimality. To expedite the column generation process, two acceleration strategies are also used. The computational results are in favour of the proposed algorithm and the acceleration strategies. Further, the results indicate that integrating the production and transportation scheduling decisions leads to an average savings of about 16.27% of the total costs.

Modeling Production Scheduling Problems as Reinforcement Learning Environments based on Discrete-Event Simulation and OpenAI Gym

Abstract Reinforcement learning (RL) is an emerging research topic in production and logistics, as it offers potentials to solve complex planning and control problems in real time. In recent years, many researchers investigated RL algorithms for solving production scheduling problems. However, most of the related articles reveal only little information about the process of developing and implementing RL applications. Against this background, we present a method for modeling production scheduling problems as RL environments. More specifically, we propose the application of Discrete-Event Simulation for modeling production scheduling problems as an interoperable environments and the Gym interface of the OpenAI foundation to allow a simple integration of pre-built RL algorithms from OpenAI Baselines and Stable Baselines. We support our explanations with a simple example of a job shop scheduling problem.

Research on Piano Batch Scheduling Method Based on Constraint Model

Research on the batch scheduling problem of piano production, with the goal of optimizing the production cycle, using a two-segment matrix coding method to solve the problems of batch division and sub-batch sorting, combining multicolor sets with genetic algorithms, and proposing a genetic algorithm based on model constraints (MCGA) in order to solve the problem of slow solution speed and low efficiency in batch scheduling problems. And by comparing the production cycle of overall scheduling, equal batch scheduling, and unequal batch scheduling, the experimental results show that non-equal batching has more advantages, and the feasibility and effectiveness of the algorithm are shown through example simulation.

INTEGRATED LOTSIZING, SCHEDULING AND BLENDING DECISIONS IN THE SPINNING INDUSTRY

In this paper, the relevance of integrated planning concerning decisions of production and blending in a spinning industry is studied. The scenario regards a plant that produces several yarn packages over a planning horizon. Each yarn type is produced using a blend of several cotton bales that must contain attributes to ensure the quality of the produced yarns. Three approaches to managing production and blending are compared; the first deals with the solution to the production scheduling and blending problems in a single integrated model. The second approach hierarchically addresses these problems. The third procedure combines features from the integrated and hierarchical approaches. These approaches are applied to a real-world problem, and their respective performances are analyzed. The third approach proved to deal with lot sizing, scheduling and blending in the spinning industry more efficiently. Moreover, the results indicate the importance of coordinating production and blending decisions.

A joint production and delivery schedule for a single-vendor single-buyer system over finite horizon

In this paper, we address a joint production and delivery scheduling problem in which a single-vendor supplies goods to a single-buyer over a finite horizon. The vendor's production rate and the buyer's demand rate can vary from period to period and are known in advance. The objective is to determine a production/shipment schedule that minimises the total cost of production setup, shipment, and holding of inventory at both the vendor and the buyer. We approach this problem using a dynamic programming framework, each stage of which constitutes solutions to different types of single-period problems depending on the production phase encountered. We develop effective methods for the solutions of these single-period problems, which are then embedded within the dynamic programming framework. We show that the optimal solution in each period follows a pattern of geometric-then-equal shipment sizes except for the last shipment, which may be larger in size. Furthermore, we show that an optimal solution for the infinite horizon problem can be obtained by using a special case of our finite horizon approach. In addition, we propose two fast heuristic methods for the finite horizon problem, which, as we show, can obtain almost optimal solutions.

A joint production and delivery schedule for a single-vendor single-buyer system over finite horizon

In this paper, we address a joint production and delivery scheduling problem in which a single-vendor supplies goods to a single-buyer over a finite horizon. The vendor's production rate and the buyer's demand rate can vary from period to period and are known in advance. The objective is to determine a production/shipment schedule that minimises the total cost of production setup, shipment, and holding of inventory at both the vendor and the buyer. We approach this problem using a dynamic programming framework, each stage of which constitutes solutions to different types of single-period problems depending on the production phase encountered. We develop effective methods for the solutions of these single-period problems, which are then embedded within the dynamic programming framework. We show that the optimal solution in each period follows a pattern of geometric-then-equal shipment sizes except for the last shipment, which may be larger in size. Furthermore, we show that an optimal solution for the infinite horizon problem can be obtained by using a special case of our finite horizon approach. In addition, we propose two fast heuristic methods for the finite horizon problem, which, as we show, can obtain almost optimal solutions.

Two meta-heuristic algorithms for optimizing a multi-objective supply chain scheduling problem in an identical parallel machines environment

Optimizing the trade-off between crucial decisions has been a prominent issue to help decision-makers for synchronizing the production scheduling and distribution planning in supply chain management. In this article, a bi-objective integrated scheduling problem of production and distribution is addressed in a production environment with identical parallel machines. Besides, two objective functions are considered as measures for customer satisfaction and reduction of the manufacturer’s costs. The first objective is considered aiming at minimizing the total weighted tardiness and total operation time. The second objective is considered aiming at minimizing the total cost of the company’s reputational damage due to the number of tardy orders, total earliness penalty, and total batch delivery costs. First, a mathematical programming model is developed for the problem. Then, two well-known meta-heuristic algorithms are designed to spot near-optimal solutions since the problem is strongly NP-hard. A multi-objective particle swarm optimization (MOPSO) is designed using a mutation function, followed by a non-dominated sorting genetic algorithm (NSGA-II) with a one-point crossover operator and a heuristic mutation operator. The experiments on MOPSO and NSGA-II are carried out on small, medium, and large scale problems. Moreover, the performance of the two algorithms is compared according to some comparing criteria. The computational results reveal that the NSGA-II performs highly better than the MOPSO algorithm in small scale problems. In the case of medium and large scale problems, the efficiency of the MOPSO algorithm was significantly improved. Nevertheless, the NSGA-II performs robustly in the most important criteria.

Production scheduling problem of automobile mixed model assembly line

Nowadays, the mode of production has changed from mass production to multi variety and small batch production, and mixed model assembly line has emerged. Mixed model assembly is widely used in automobile enterprises. This paper summarizes the theory and method of automobile mixed model assembly line scheduling, analyzes its characteristics and difficulties, summarizes the related optimization objectives, and introduces the related algorithms, so as to make the scheduling problem of mixed model assembly line more clear.

Production optimization by using integer linear programming under a practical approach

This paper addresses the problem of production scheduling under a practical approach, which seeks to find out what would be the product mix to ensure the company to obtain the most useful, also requires that these combinations of products obtained from quickly and efficiently contributing thus to achieve lower costs associated with production. A specific mathematical model based on integer linear programming applied specifically to the product mix is presented, as well as the results obtained from the practical problem from the use of the model in integer linear programming, the use of the software and considering the own conditions of the problem addressed here.