Tardiness Of Orders Research Articles

Dynamic flexible job shop scheduling based on deep reinforcement learning

The unpredictable dynamic events in smart factory seriously influence the scheduling schemes and production efficiency. To minimize the total tardiness of orders, this paper proposes a Deep Reinforcement Learning (DRL) method to solve the Dynamic Flexible Job Shop Scheduling Problem (DFJSP) with random job arrival. In the scheduling process, the intelligent agent can select the operations to be processed on the available machines according to the job shop state at each scheduling point by transforming DFJSP into a Markov Decision Process (MDP). For reflecting the job shop environment, eight state features are extracted, and six composite dispatching rules are designed as the action space. Moreover, a reward function is developed to enhance the learning efficiency and solution quality of the intelligent agent, the Soft-max selection strategy is applied to balance exploration and exploitation. The Dueling Double Deep Q-Network (Dueling DDQN) algorithm is introduced to train the intelligent agent, which effectively alleviates the overestimation problem. Numerical simulation results show that the proposed Dueling DDQN method effectively solves the DFJSP. Compared with existing scheduling strategies, the proposed approach not only exhibits superior performance but also maintains its advantages among different scale instances.

A novel predictive–reactive scheduling method for parallel batch processor lot-sizing and scheduling with sequence-dependent setup time

In practical printed circuit boards (PCB) drilling production systems, multiple spindle processing capabilities and uncertainties are commonplace. This paper addresses predictive–reactive scheduling, considering parallel batch processor lot-sizing and scheduling with sequence-dependent setup times in a dynamic environment. We propose a predictive scheduling algorithm named S-AGAIG to balance machine spindle utilization and order tardiness in steps. Multiple splitting solutions are first formed by using a split heuristic algorithm to size the sub-lots of orders. Then the adaptive genetic algorithm with iterated greedy search is applied to select the solutions and scheduling. Furthermore, we present a schedule repair strategy based on sub-lot co-processing considering the impact of critical sub-lots, and construct a scheduling stability metric for rescheduling. In 36 sets of case experiments encompassing diverse load and machine type configurations, S-AGAIG showcases a 21.27% enhancement in average tardiness performance when compared to its closest rival. Across 28 cases involving varying disturbances, the framework demonstrates exceptional robustness.

A Simulation-Based Experimental Design for Analyzing Energy Consumption and Order Tardiness in Warehousing Systems

For warehouses to be more sustainable and cost-effective, it is essential to consider energy consumption (EC) and order tardiness (OT) together in evaluating warehouse activities since improving both EC and OT at the same time is very demanding. While existing studies try to improve EC and OT, the current studies consider only either a reserve area or a forward area between the two major warehouse areas. Thus, this study proposes a simulation-based approach to assessing EC and OT when reserve and forward areas are considered together in one framework for different configurations of five important warehousing parameters: (i) number of forklifts, (ii) number of storage/retrieval (S/R) machines, (iii) number of automated storage/retrieval systems (AS/RS) input/output (I/O) points, (iv) order size, and (v) proportions of order flows through a reserve or forward area. In particular, we use real forklift movement and energy data for our simulation models to provide a more realistic analysis. By building the simulation model with the 25 full factorial experimental design, we analyze the results with analysis of variance (ANOVA). The resulting Pareto-optimal solutions show that less traffic flows through a reserve area can help improve both EC and OT while other factors have smaller or limited effects on the two responses. Also, the order flow factor has the largest effect on EC while order size has the largest effect on OT. The results from this study can help warehouse operators make informed decisions in considering and finding a trade-off between sustainability and customer satisfaction.

Order Picking Problem: A Model for the Joint Optimisation of Order Batching, Batch Assignment Sequencing, and Picking Routing

Background: Order picking is a critical activity in end-product warehouses, particularly using the picker-to-part system, entail substantial manual labor, representing approximately 60% of warehouse work. Methods: This study develops a new linear model to perform batching, which allows for defining, assigning, and sequencing batches and determining the best routing strategy. Its goal is to minimise the completion time and the weighted sum of tardiness and earliness of orders. We developed a second linear model without the constraints related to the picking routing to reduce complexity. This model searches for the best routing using the closest neighbour approach. As both models were too complex to test, the earliest due date constructive heuristic algorithm was developed. To improve the solution, we implemented various algorithms, from multi-start with random ordering to more complex like iterated local search. Results: The proposed models were tested on a real case study where the picking time was reduced by 57% compared to single-order strategy. Conclusions: The results showed that the iterated local search multiple perturbation algorithms could successfully identify the minimum solution and significantly improve the solution initially obtained with the heuristic earliest due date algorithm.

Supply Chain Planning for IC Design House Back-End Production Network With Turnkey Service

Owing to global competition, integrated circuit (IC) design houses are facing challenges in the optimal use of capacity and resources to fulfill customer demands and maximize profit. A hybrid make-to-stock (MTS) and make-to-order (MTO) model is generally used. Wafer procurement is made according to customers’ long-term demand forecast based on MTS. Limited wafer fab resources and back-end capacity are first allocated to on-hand orders and then to forecast demand. In production planning, several factors need to be considered to determine the production quantity and inventory level, such as the material, capacity, substitute, technical constraint, and order tardiness. This study considers a typical multi-stage supply chain network of semiconductor back-end production with turnkey service for IC design houses. The objective is to maximize the total profit with the constraints of equipment capacity, the flexibility of substitutes, and the usage of the turnkey mode. The problem is formulated with a mixed-integer programming model and solved using two novel heuristic algorithms: a product-based decomposition (PD_SCP) with profit-based criteria and a Lagrangian decomposition combined with the product-based decomposition (LD-SCP) method. Using the LD-SCP algorithm takes a long time but results in a great solution. Sensitivity analysis is conducted to investigate the impact of different parameters on production cost and total profit.

Improving Energy Consumption and Order Tardiness in Picker-to-Part Warehouses with Electric Forklifts: A Comparison of Four Evolutionary Algorithms

Improving energy consumption (EC) and order tardiness (OT) for a warehouse picker-to-parts system is a challenging task since these two objectives are interrelated in a complex way with forklift activities. Thus, this research aims to minimize EC and OT with a multi-objective mixed-integer mathematical model by considering electric forklift operations. The proposed model addresses a lack of studies by controlling (i) order batching, (ii) batch assignment, (iii) batch sequencing, (iv) forklift routing, and (v) forklift battery charging schedule. The feasibility of the presented mathematical model is validated by solving small-sized examples. To solve medium- to large-sized case studies, we also propose and compare four multi-objective evolutionary algorithms (MOEAs). In illustrative examples, this study identifies the number of battery charging, orders, and forklifts as significant parameters affecting EC and OT. Our analysis also provides regression models connecting EC and OT from Pareto-optimal frontiers, and these results can help industrial practitioners and academic researchers find and investigate the relationship between EC and OT for making relevant decisions in warehouses served by electric forklifts. Among the four MOEAs developed, we show that the NSGA-II non-dominated sorting variable neighborhood search dynamic learning strategy (NSGA-VNS-DLS) outperforms other algorithms in accuracy, diversity, and CPU time.

An iterated local search for customer order scheduling in additive manufacturing

This paper studies the customer order scheduling problem in the context of additive manufacturing. The study discusses an integrated problem involving the nesting of parts as well as the scheduling of batches of nested parts onto unrelated parallel machines. A mixed-integer programming model is presented, based on existing formulations from the literature, that integrates different materials and sequence-dependent setup times. Additionally, a metaheuristic based on an iterated local search is proposed for the problem configuration under consideration. Focusing on minimizing the total weighted tardiness of orders, the efficiency of the heuristic approach is evaluated using comprehensive test data. Further, we show the importance of the considered order-related objective by using qualitative analysis.

A Genetic Hyper-Heuristic for an Order Scheduling Problem with Two Scenario-Dependent Parameters in a Parallel-Machine Environment

Studies on the customer order scheduling problem have been attracting increasing attention. Most current approaches consider that either component processing times for customer orders on each machine are constant or all customer orders are available at the outset of production planning. However, these assumptions do not hold in real-world applications. Uncertainty may be caused by multiple issues including a machine breakdown, the working environment changing, and workers’ instability. On the basis of these factors, we introduced a parallel-machine customer order scheduling problem with two scenario-dependent component processing times, due dates, and ready times. The objective was to identify an appropriate and robust schedule for minimizing the maximum of the sum of weighted numbers of tardy orders among the considered scenarios. To solve this difficult problem, we derived a few dominant properties and a lower bound for determining an optimal solution. Subsequently, we considered three variants of Moore’s algorithm, a genetic algorithm, and a genetic-algorithm-based hyper-heuristic that incorporated the proposed seven low-level heuristics to solve this problem. Finally, the performances of all proposed algorithms were evaluated.

Improved discrete imperialist competition algorithm for order scheduling of automated warehouses

An improved discrete imperial competition algorithm (DICA) is proposed for the multi-objective order scheduling problems of automated warehouses. The aim is to minimize the completion time of all orders and the total tardiness of outbound orders. The priority value, influenced by the importance and relative cut-off time of the orders, as well as the number of tasks, is designed to sort the orders. Similar to the genetic algorithm (GA), the assimilation process of the improved DICA is constructed by crossover and mutation. Meanwhile, Hamming distance is introduced to verify the quality of assimilation. Taking a practical case as an example, the improved DICA is used to solve two scheduling strategies: outbound order priority scheduling and compound order scheduling. The main results show that the compound order scheduling can be performed effectively, especially when the number of orders is large, the completion time and total tardiness can be greatly reduced. In addition, compared with GA, the solution quality of the improved DICA is better, but its convergence speed is slower.

Scheduling a cellular manufacturing system based on price elasticity of demand and time-dependent energy prices

Cellular manufacturing system (CMS) is a novel production system adaptable to the make-to-order production. The present study focuses on scheduling CMS aimed at maximizing total profits as a function of the revenues earned from sales as well as energy consumption cost and order tardiness penalties. The components to be considered in the problem in hand include the time-dependency of energy price, price elasticity of demand, and speed-based power consumption of machines. Two linearization approaches are used to determine order quantities. The first chooses lot sizes from a continuous range while the second chooses them among prespecified discrete levels. Especially developed mathematical models are used to solve the problem in either approach. For the second linearization approach, a constraint programming model, and a hybrid algorithm based on the fix-and-optimize and variable neighborhood search metaheuristic (FOVNS, for short) are additionally developed. Changing the branching procedure as a technique and three dominance rules are also proposed to improve the performance of the CP and FOVNS models while their effectiveness is examined using the full factorial design of experiments. Also, the parameters of the FOVNS are tuned using the Taguchi method. Exact methods are found capable of optimizing medium-size problems in less than an hour while FOVNS is able to optimize large-size ones in 822 seconds on average with a deviation of 1.8% from the optimal solution. Statistical analysis show that considering a time-dependent energy price in the scheduling decreases the energy cost by about 40%.

Solving the online batching problem using deep reinforcement learning

In e-commerce markets, on-time delivery is of great importance to customer satisfaction. In this paper, we present a Deep Reinforcement Learning (DRL) approach, together with a heuristic, for deciding how and when arrived orders should be batched and picked in a warehouse to minimize the number of tardy orders. In particular, the technique facilitates making decisions on whether an order should be picked individually (pick-by-order) or picked in a batch with other orders (pick-by-batch), and if so, with which other orders. We approach the problem by formulating it as a semi-Markov decision process and developing a vector-based state representation that includes the characteristics of the warehouse system. This allows us to create a deep reinforcement learning solution that learns a strategy by interacting with the environment and solve the problem with a proximal policy optimization algorithm. We evaluate the performance of the proposed DRL approach by comparing it with several batching and sequencing heuristics in different problem settings. The results show that the DRL approach can develop a strategy that produces consistent, good solutions and performs better than the proposed heuristics in most of the tested cases. We show that the strategy learned by DRL is different from the hand-crafted heuristics.In this paper, we demonstrate that the benefits from recent advancements of Deep Reinforcement Learning can be transferred to solve sequential decision-making problems in warehousing operations.

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.

Spatial and temporal optimization for smart warehouses with fast turnover

With the rapid development of e-commerce and the new retail, the same-day or even same-half day delivery service is provided to compete for market share. Recently, an increased number of e-commerce companies implement the unmanned smart warehouses to improve the logistics efficiency. In order to further reduce the demand response time, a novel picking strategy is designed to firstly split the orders, and then assign the partial orders to different pickers. After all the order segments have been collected, it is shipped to the customer. Due to the inherent complexity of the problem, a two stage optimization model is introduced. In the first stage, an order splitting and batching strategy based on spatial measure is proposed. And a MIP model is constructed to minimize the total picking distance, which is then solved via a column generation based algorithm. In the second stage, the newly formed batches are considered as a priori inputs, which are then assigned to automatic pickers. The picking process is modeled as a special parallel machine scheduling problem with multiple due dates for a single item, which could reduce to a customer order scheduling problem on parallel machines, and it is unary NP-complete. A heuristic method is proposed to obtain an approximate solution. Although the order splitting technique is not new in the logistics industry, the split orders are picked according to a vehicle routing problem, which fails to address the kitting issue for fast turnovers. In the numerical analysis section, the proposed algorithm is validated through extensive testing on various scales of instances. It is observed that the optimality gap for our algorithm is within 9%, and the computation time is around 5 min. Also, the average turnover rate increases by approximately 50% in comparison with the no-splitting policy. In most cases, the average order tardiness decreases by 90% compared with order splitting and no-kitting policy.

Lot scheduling on a single machine to minimize the (weighted) number of tardy orders

We consider a single machine lot scheduling problem. A number of customer orders of different sizes may be processed in the same lot. We consider first the setting that splitting orders between consecutive lots is allowed. We focus on minimizing the number of tardy orders. A polynomial time solution algorithm is introduced for this problem. We then study the extension to minimizing the weighted number of tardy orders. This problem is NP-hard, and a pseudo-polynomial dynamic programming is provided and tested. We also study the setting of no-split. The problem of minimizing the number of tardy orders in this context is proved to be strongly NP-hard, and an efficient heuristic is introduced.

Stochastic internal task scheduling in cross docking using chance-constrained programming

ABSTRACT A novel mathematical model of stochastic internal task scheduling in cross docking is proposed herein for minimizing the total tardiness of customer orders. The model aims to simultaneously assign internal cross-dock working teams and transportation equipment to obtain the optimal internal task schedule in a single unloading activity. Stochastic parameters are considered to yield a more realistic problem. In this problem, the processing times of breaking down incoming containers and building up customer orders, and the due dates of customer orders are assumed as random variables subjected to normal and uniform distributions, respectively. The problem was formulated using chance-constrained programming to minimize the total tardiness. An experiment was performed for comparing solutions between stochastic and deterministic scheduling environments. Computational experiment using a LINGO optimization solver showed that the total tardiness obtained from the stochastic model with chance-constraint programming was higher than that from the deterministic model because of uncertainties in terms of processing times and due dates. However, the internal task scheduling problem in cross docking is NP-hard. The exact method provides an optimal solution within a reasonable time for small problems. Therefore, future research should consider metaheuristic approaches to addressing complexities in real-world practices.

Dominance Conditions for Optimal Order-Lot Matching in the Make-To-Order Production System

Order-lot matching is the process of assigning items in lots being processed in the make-to-order production system to meet the due dates of the orders. In this study, an order-lot matching problem (OLMP) is considered to minimize the total tardiness of orders with different due dates. In the OLMP considered in this study, we need to not only determine the allocation of items to lots in the production facility but also generate a lot release plan for the given time horizon. We show that the OLMP can be considered as a special type of machine scheduling problem with many similarities to the single machine total tardiness scheduling problem ( 1 | | ∑ T i ). We suggest dominance conditions for the OLMP by modifying those for 1 | | ∑ T i and a dynamic programming (DP) model based on the dominance conditions. With two example problems, we show that the DP model can solve small-sized OLMPs optimally.

Short-term production scheduling with non-triangular sequence-dependent setup times and shifting production bottlenecks

A novel mathematical model is introduced that allows solving real-life scheduling problems in complex multi-stage machine environment with (i) non-triangular sequence-dependent setup times and (ii) shifting production bottlenecks, both of which are important aspects appearing in varying manufacturing industries. The primary goal is to minimise the tardiness of customer orders, which may consist of multiple production orders each in turn composed of several batches. A secondary objective is to maximise the production capacity utilization as measured by the makespan. The model is elaborated for general animal-feed plants which have to deal with the particular production scheduling problem on a daily basis. Dispatching rules are introduced to enhance the optimization progress. Numerical experiments show that optimising the model leads to schedules that meet the due dates. Moreover, by reducing the mean idle time of production lines with 35.6%, the optimization leads to a makespan reduction of 6.5% on average compared to real-life applied schedules.

POLCA Control in Two-Stage Production Systems

POLCA (Paired-cell Overlapping Loops of Cards with Authorization) is a decision support system for material flow control under Quick Response Manufacturing. It operates in the context of low-volume, high-mix, and cellular manufacturing. While there is an increasing literature on POLCA performance, current studies usually assume full availability of components (or parts) at assembly stations, neglecting parts manufacturing and feeding. Therefore, this study uses simulation to assess POLCA performance in a two-stage production system, where at the first stage parts are manufactured and at the second, they are assembled into end-products. The study demonstrates that using POLCA to control both production stages, manufacturing and assembly, significantly outperforms the use of POLCA at the assembly stage only, leading to important reductions of the total throughput time of orders and on the percentage of tardy orders. Statistical analysis of our results was conducted using ANOVA.

An Agent-Based Model Driven Decision Support System for Reactive Aggregate Production Scheduling in the Green Coffee Supply Chain

The aim of this paper is to contribute to the thread of research regarding the need for logistic systems for planning and scheduling/rescheduling within the agro-industry. To this end, an agent-based model driven decision support system for the agri-food supply chain is presented. Inputs in this research are taken from a case example of a Mexican green coffee supply chain. In this context, the decision support agent serves the purposes of deriving useful knowledge to accomplish (i) the decision regarding the estimation of Cherry coffee yield obtained at the coffee plantation, and the Parchment coffee sample verification decision, using fuzzy logic involving an inference engine with IF-THEN type rules; (ii) the production plan establishment decision, using a decision-making rule approach based upon the coupling of IF-THEN fuzzy inference rules and equation-based representation by means of mixed integer programming with the aim to maximize customer service level; and (iii) the production plan update decision using mathematical equations once the customer service level falls below the expected level. Three scenarios of demand patterns were considered to conduct the experiments: increasing, unimodal and decreasing. We found that the input inventory and output inventory vary similar over time for the unimodal demand pattern, not the case for both the increasing and decreasing demand patterns. For the decreasing demand pattern, ten tardy orders for the initial production schedule, an 88% service level, and nineteen tardy orders from the estimated production results, a 77% service level. This value falls below the expected level. Consequently, the updated aggregate production schedule resulted in ten tardy orders and an 88% service level.

Multi-agent supply chain scheduling problem by considering resource allocation and transportation

Today in the global market competition, integration issue in supply chain is considered as an important principle. In this study, for the first time, different requirements of the customers and different aims of the manufacturer are simultaneously addressed in an integrated problem of production scheduling, transportation, and resource allocation. The problem consists of two types of customers, considered as the agents. The first agent accepts tardiness in delivery of orders provided that the manufacturer pays the tardiness penalty; whereas, the second agent does not accept the tardy orders. The purpose is to minimize the sum of batch delivery cost, resource allocation, tardiness penalty cost, and lost sale cost (the total number of tardy orders). To solve the problem, two mathematical programming models, including a Mixed Integer Non-Linear Programming (MINLP) and a Mixed Integer Linear Programming (MILP) are proposed. Also, due to NP-hard nature of the problem, two meta-heuristic algorithms of Adaptive Genetic Algorithm (AGA) and Ant Lion Optimization (ALO), as well as a heuristic algorithm are proposed. To assess the merits of the solution methods, small and large-scale tests are designed. The results indicate the superiority of adaptive genetic algorithm in comparison with other algorithms.