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Packing problems are classical optimization problems with wide-ranging applications. With the advancement of robotic manipulation, there are growing demands for the automation of packing tasks. However, the simultaneous optimization of packing and the robot’s motion planning is challenging because these two decisions are interconnected, and no previous study has addressed this optimization problem. This paper presents a framework to simultaneously determine the robot’s motion planning and packing decision to minimize the robot’s processing time and the container’s volume. This framework comprises three key components: solution encoding, surrogate modeling, and evolutionary computation. The sequence-triple representation encodes complex packing solutions by a sequence of integers. A surrogate model is trained to predict the processing time for a given packing solution to reduce the computational burden. Training data is generated by solving the motion planning problem for a set of packing solutions using the rapidly exploring random tree algorithm. The Non-Dominated Sorting Genetic Algorithm II searches for the Pareto solutions. Experimental evaluations are conducted using a 6-DOF robot manipulator. The experimental results suggest that implementing the surrogate model can reduce the computational time by 91.1%. The proposed surrogate-assisted optimization method can obtain significantly better solutions than the joint angular velocity-based estimation method.

The distributed optimization algorithms using consensus control are proposed for solving multi-agent optimization problems. The multi-agent optimization problem has discrete and continuous decision variables to minimize the sum of local cost functions with local and global constraints. The problem is formulated as a mixed integer programming problem. In this study, we propose two distributed optimization algorithms to solve the problem. A feasible solution is obtained by solving the continuous optimization problem using an existing distributed optimization method with consensus control and solving the discrete optimization problem by fixing 0-1 variables. In the proposed method 1, all possible combinations of a binary variables are searched. Since all combinations are searched, the exact optimal solution can be obtained. However, it is difficult to apply to large-scale problems. In the proposed method 2, we derive the solution of binary variables by using Lagrangian decomposition and coordination approach. The proposed method 2 can provide approximate solutions for more complex problems within a practical computation time. These methods are successfully implemented to obtain near-optimal solutions in a distributed environment for supply chain planning problems for multiple companies and multi-agent unit commitment problem. The number of information exchanges in the two proposed methods is evaluated. The information exchange for these methods can significantly reduce the data exchange compared with the conventional centralized optimization method. Computational experiments for the multi-agent unit commitment problems and supply chain planning problems for multiple companies demonstrate the effectiveness of the proposed methods.

The workforce scheduling problem for cell production lines has been recognized as one of the significant issues in manufacturing systems. In most of previous studies, complex workers’ operations in a cell such as traveling times of multi-skilled operators in another cell to their workplaces, have not been considered in the workforce optimization model. In this paper, we consider the simultaneous optimization of the product input sequence and workforce assignment scheduling problem for multi-stage multi-item cell production lines. The problem is formulated as a resource-constrained project scheduling problem (RCPSP). We propose an RCPSP formulation of the scheduling problem for multi-product cell production lines where the traveling time of operators and products are considered. The exact solution of the RCPSP formulation is derived by using a general-purpose solver, Gurobi. The validity of the RCPSP model is verified by comparing it with a genetic algorithm (GA) using a commercial simulation software (Siemens Plant Simulation). Experimental results show that the derived exact solution of RCPSP is better than that of the solutions derived by the GA algorithm in the Siemens Plant Simulation.

Abstract Supply chain digital twin has emerged as a powerful tool in studying the behavior of an actual supply chain. However, most studies in the field of supply chain digital twin have only focused on what-if analysis that compares several different scenarios. This study proposes a data-driven evolutionary algorithm to efficiently solve the service constrained inventory optimization problem using historical data that generated by supply chain digital twins. The objective is to minimize the total costs while satisfying the required service level for a supply chain. The random forest algorithm is used to build surrogate models which can be used to estimate the total costs and service level in a supply chain. The surrogate models are optimized by an ensemble approach-based differential evolution algorithm which can adaptively use different search strategies to improve the performance during the computation process. A three-echelon supply chain digital twin on the geographic information system (GIS) map in real-time is used to examine the efficiency of the proposed method. The experimental results indicate that the data-driven evolutionary algorithm can reduce the total costs and maintain the required service level. The finding suggests that our proposed method can learn from the historical data and generate better inventory policies for a supply chain digital twin.

Pharmaceuticals play a critical role in the eradication of infectious diseases. Effective pharmaceutical inventory management is important for controlling epidemics since medical resources such as pharmaceuticals, medical staff, and hospitals are limited. In this study, a novel epidemiological model is proposed to evaluate the resource requirements for pharmaceuticals and is applied to analyze different pharmaceutical inventory management strategies. We formulate the relationship between the number of infected individuals and the risk of infection to account for virus mutation. Evolutionary game theory is integrated into an epidemiological model to represent human behavioral choices. The proposed model can be developed to forecast the demand for pharmaceuticals and analyze how human behavior affects the demand of pharmaceuticals. This study found that making people aware of the risk of disease has a positive impact on both reducing the number of infections and managing the pharmaceutical inventory. The main contribution of this study is to enhance areas of research in pharmaceutical inventory management. This study revealed that the correct recognition of the risk of disease leads to appropriate pharmaceutical management. There are a few studies on the application of infectious disease models to inventory control problems. This study provides clues toward proper pharmaceutical management.

Mass customization is an important strategy to improve production systems to satisfy customers’ preferences while maintaining production efficiency for mass production. Module production is one of the ways to achieve mass customization, and products are produced by combining modules. In the module production, it becomes much more important for manufacturing companies to reflect customers’ preferences for selling products. The manufacturer can increase its total profit by providing customized products that satisfy customers’ preferences by increasing customers’ satisfaction. In conventional production planning, there are some cases where module production is conducted by the demands from customers’ preferences. However, the customer decision-making model has not been employed in the production planning model. In this paper, a production planning model incorporating customers’ preferences is developed. The customers’ purchasing behavior is generated by using a machine learning model. Customer segmentation is conducted by clustering data that uses the purchase data of multiple customers. The resulting production planning model is a bilevel production planning problem consisting of a single company and multiple customers. Each company can sell products that combine modules that customers require in each segment. We show that the proposed model can obtain higher customers’ satisfaction with greater profits than the model that does not employ the customers’ purchasing model.

This paper proposes an adaptive heterogeneous particle swarm optimization with a comprehensive learning strategy for solving single-objective constrained optimization problems. In this algorithm, particles can use an exploration strategy and an exploitation strategy to update their positions. The historical success rates of the two strategies are used to adaptively control the adoption rates of strategies in the next iteration. The search strategy in the canonical particle swarm optimization algorithm is based on elite solutions. As a result, when no particles can discover better solutions for several generations, this algorithm is likely to fall into stagnation. To respond to this challenge, a new strategy is proposed to explore the neighbors of the elite solutions in this study. Finally, a constraint handling method is equipped to the proposed algorithm to make it be able to solve constrained optimization problems. The proposed algorithm is compared with the canonical particle swarm optimization, differential evolution, and several recently proposed algorithms on the benchmark test suite. The Wilcoxon signed-rank test results show that the proposed algorithm is significantly better on most of the benchmark problems compared with the competitors. The proposed algorithm is also applied to solve two real-world mechanical engineering problems. The experimental results show that the proposed algorithm performs consistently well on these problems.

Energy usage in robotic applications is rapidly increasing as industrial robot installations grow. This research introduces a novel approach, using the rapidly exploring random tree (RRT)-based scheme for optimizing the robot’s motion planning and minimizing energy consumption. Sampling-based algorithms for path planning, such as RRT and its many other variants, are widely used in robotic motion planning due to their efficiency in solving complex high-dimensional problems efficiently. However, standard versions of these algorithms cannot guarantee that the generated trajectories are always optimum and mostly ignore the energy consumption in robotic applications. This paper proposes an energy-efficient industrial robotics motion planning approach using the novel flight cost-based RRT (FC-RRT*) algorithm in pick-and-place operation to generate nodes in a predetermined direction and then calculate energy consumption using the circle point method. After optimizing the motion trajectory, power consumption is computed for the rotary axes of a six degree of freedom (6DOF) serial type of industrial robot using the work–energy hypothesis for the rotational motion of a rigid body. The results are compared to the traditional RRT and RRT* (RRT-star) algorithm as well as the kinematic solutions. The experimental results of axis indexing tests indicate that by employing the sampling-based FC-RRT* algorithm, the robot joints consume less energy (1.6% to 16.5% less) compared to both the kinematic solution and the conventional RRT* algorithm.

The use of multiple mobile robots has grown significantly over the past few years in logistics, manufacturing and public services. Conflict–free route planning is one of the major research challenges for such mobile robots. Optimization methods such as graph search algorithms are used extensively to solve route planning problems. Those methods can assure the quality of solutions, however, they are not flexible to deal with unexpected situations. In this article, we propose a flexible route planning method that combines the reinforcement learning algorithm and a graph search algorithm for conflict–free route planning problems for multiple robots. In the proposed method, Q–learning, a reinforcement algorithm, is applied to avoid collisions using off–line learning with a limited state space to reduce the total learning time. Each vehicle independently finds the shortest route using the A* algorithm, and Q–learning is used to avoid collisions. The effectiveness of the proposed method is examined by comparing it with conventional methods in terms of computation time and the quality of solutions. Computational results show that for dynamic transportation problems, the proposed method can generate the solutions with approximately 10% of the computation time compared to the conventional Q–learning approach. We found that the required computation time is linearly increased with respect to the number of vehicles and nodes in the problems.

In recent years, scheduling optimization has been utilized in production systems. To construct a suitable mathematical model of a production scheduling problem, modeling techniques that can automatically select an appropriate objective function from historical data are necessary. This paper presents two methods to estimate weighting factors of the objective function in the scheduling problem from historical data, given the information of operation time and setup costs. We propose a machine learning-based method, and an inverse optimization-based method using the input/output data of the scheduling problems when the weighting factors of the objective function are unknown. These two methods are applied to a multi-objective parallel machine scheduling problem and a real-world chemical batch plant scheduling problem. The results of the estimation accuracy evaluation show that the proposed methods for estimating the weighting factors of the objective function are effective.

Many researchers have focused on the comparison between the JIT model and the EOQ model. However, few of them studied this problem from an evolutionary perspective. In this paper, a JIT purchasing with the single-setup-multi-delivery model is introduced to compare the total costs of the JIT model and the EOQ model. Also, we extend the classical JIT-EOQ models to a two-echelon supply chain which consists of one manufacturer and one supplier. Considering the bounded rationality of players and the quickly changing market, an evolutionary game model is proposed to discuss how these factors impact the strategy selection of the companies. And the evolutionarily stable strategy of the proposed model is analyzed. Based on the analysis, we derive the conditions when the supply chain system will choose the JIT strategy and propose a contract method to ensure that the system converges to the JIT strategy. Several numerical experiments are provided to observe the JIT and EOQ purchasing strategy selection of the manufacturer and the supplier. The results suggest that, in most situations, the JIT strategy is preferred. However, the EOQ strategy remains competitive when the supplier’s inventory cost level is high or the demand is low. Supply chain members can choose the EOQ strategy even when the JIT strategy is more profitable. In some situations, strategy selection also depends on the market situation. The JIT policy with low investment costs and high supply chain performance is preferred for the companies.

The implementation of Industry 5.0 necessitates a decrease in the energy consumption of industrial robots. This research investigates energy optimization for optimal motion planning for a dual-arm industrial robot. The objective function for the energy minimization problem is stated based on the execution time and total energy consumption of the robot arm configurations in its workspace for pick-and-place operation. Firstly, the PID controller is being used to achieve the optimal parameters. The parameters of PID are then fine-tuned using metaheuristic algorithms such as Genetic Algorithms and Particle Swarm Optimization methods to create a more precise robot motion trajectory, resulting in an energy-efficient robot configuration. The results for different robot configurations were compared with both motion planning algorithms, which shows better compatibility in terms of both execution time and energy efficiency. The feasibility of the algorithms is demonstrated by conducting experiments on a dual-arm robot, named as duAro. In terms of energy efficiency, the results show that dual-arm motions can save more energy than single-arm motions for an industrial robot. Furthermore, combining the robot configuration problem with metaheuristic approaches saves energy consumption and robot execution time when compared to motion planning with PID controllers alone.

The analysis of the quantity discount of the decentralized supply chain has been studied only for single-period planning models. This article presents the design of an optimal quantity discounts for multi-period bilevel production planning for two-echelon supply chains under demand uncertainty. In order to derive an optimal contract for multi-period production planning, the cumulative order quantity and production quantity are introduced. From our proposed model, a Stackelberg equilibrium is analytically derived for the supply chain when the supplier is the leader and the retailer is the follower. An optimal discount contract is analytically designed through the optimal solution of the centralized problem. Computational results show the effectiveness of the proposed discount contract under demand uncertainty.

The paper aims to study a multi-period maximal covering location problem with the configuration of different types of facilities, as an extension of the classical maximal covering location problem (MCLP). The proposed model can have applications such as locating disaster relief facilities, hospitals, and chain supermarkets. The facilities are supposed to be comprised of various units, called the modules. The modules have different sizes and can transfer between facilities during the planning horizon according to demand variation. Both the facilities and modules are capacitated as a real-life fact. To solve the problem, two upper bounds—(LR1) and (LR2)—and Lagrangian decomposition (LD) are developed. Two lower bounds are computed from feasible solutions obtained from (LR1), (LR2), and (LD) and a novel heuristic algorithm. The results demonstrate that the LD method combined with the lower bound obtained from the developed heuristic method (LD-HLB) shows better performance and is preferred to solve both small- and large-scale problems in terms of bound tightness and efficiency especially for solving large-scale problems. The upper bounds and lower bounds generated by the solution procedures can be used as the profit approximation by the managerial executives in their decision-making process.

This paper presents an extension of the covering location problem as a hybrid covering model that utilizes the set covering and maximal covering location problems. The developed model is a multi-period model that considers strategic and tactical planning decisions. Hybrid covering location problem (HCLP) determines the location of the capacitated facilities by using dynamic set covering location problem as strategic decisions and assigns the constructive units of facilities and allocates the demand points by using dynamic modular capacitated maximal covering location problem as tactical decisions. One of the applications of the proposed model is locating first aid centers in humanitarian logistic services that have been addressed by studying a threat case study in Japan. In addition to validating the developed model, it has been compared to other possible combined problems, and several randomly generated examples have been solved. The results of the case study and model validation tests approve that the main hybrid developed model (HCLP) is capable of providing better coverage percentage compared to conventional covering models and other hybrid variants.

In this article, a dynamic maximal hub location covering problem for a freight transportation system is studied, in which the model has the possibility of having expansion scenarios for future according to the forecasts of increasing demands. Two expansion scenarios are to add up the number of hubs in the network and to add up more carriers. As the markets are involved in the pricing procedure, the model is a bi-level problem which needs more effort to deal with, for which in this work two reformulations based on Karush–Kuhn–Tucker conditions and duality theory are utilized to reformulate the bi-level problem to a single-level one. To solve the model efficiently, a decomposition method is applied and numerical examples are solved to verify the accuracy of the proposed model.

Cluster tools are widely used for semiconductor manufacturing. A multi-cluster tool consists of several single cluster tools which are interconnected with each other. The multi-cluster tool causes a deadlock due to non-existence of intermediate buffer. Deadlock is a serious problem leading decrease of throughput and deterioration of wafers. In this paper, the optimal supervisor proposed by Chen et al. (2011) is applied to a Petri net model of the multi-cluster tools. From the comparison of performance with the conventional deadlock prevention policies, we find that the maximally permissive supervisor does not always produce a better scheduling performance. We propose a design method of a Petri net supervisor to improve the scheduling performance. Our main idea is to eliminate legal markings that may eventually cause the increase of makespan. The proposed method is applied to the two-connected multi-cluster tool. The results indicate that the scheduling performance can be improved by the proposed method without lowering maximal permissivity.

We address a game theoretical analysis of the leadership structure of two-echelon supply chains with a single supplier and a single retailer involving a risky supplier under demand uncertainty. The risky supplier has a risk of unavailability of delivering the product to the retailer. The equilibrium solutions for different leadership structures are analytically derived. The influence of the probability of risky supplier availability on the optimal leadership structure is investigated. The model is extended to consider a two-echelon supply chain with two risky suppliers. The total profits for each leadership structure are evaluated from the perspective of the entire supply chain. The analytical results show that the leadership structure with the risky supplier as a leader can maximize the total profit. Numerical examples are provided to show the validity of the proposed analysis.

In this paper, we consider the production planning problem for a single manufacturer with the investment to improve the market impact under demand uncertainty. In the mathematical model, the average demand increases if the investment of market impact is increased for each product. The objective is to maximize the total profit with a piecewise linear investment cost and a budget constraint. The problem is formulated as a mixed integer nonlinear programming problem. A solution procedure based on Lagrangian relaxation is developed to solve the problem efficiently. In the proposed method, an analytical solution of the newsboy problem is effectively used to derive the lower and upper bounds. The condition of the concavity of the profit function is derived. The effectiveness of the proposed method is confirmed through computational experiments.

Cluster tools are used for semiconductor wafer fabrication. A cluster tool consists of several loadlock modules, processing modules, and material handling armed robots to transfer wafers between loadlocks and processing modules. Most conventional scheduling methods consider a cyclic schedule to minimize makespan. We consider noncyclic scheduling of dual-armed cluster tools. In practice, it is important to minimize wafer residency time in processing modules to maintain the surface quality of wafers. In the noncyclic operations, the cluster tool causes deadlock which may lead to excessive loss in the wafer fabrication process. We propose an efficient deadlock-free scheduling method for the noncyclic scheduling problem of a dual-armed cluster tool to minimize the residency time and makespan. The proposed method is applied to a dual-armed cluster tool with a non-revisiting process and a revisiting process. Computational results demonstrate the effectiveness of the proposed method.

We propose an application of a two-phase decomposition algorithm for a practical airline crew rostering problem for fair working time. The problem is to find an optimal assignment of duties to individual crew members such that various hard constraints such as rest days, rules and regulations are satisfied. The objective is to minimize the total deviation of the average working time from the standard working time for crew members. A two-phase decomposition algorithm is successfully applied to solve the problem. The proposed method decomposes the original problem into the master problem and the subproblem. The master problem is solved by an exact algorithm with a generalized set partitioning formulation if all possible rosters are enumerated by an efficient enumeration algorithm. The upper bound is improved by a metaheuristic algorithm. The effectiveness of the proposed method for a large scale rostering problem is shown from computational experiments.

In this paper, we propose a heuristic algorithm to solve a practical ship scheduling problem for international crude oil transportation. The problem is considered as a vehicle routing problem with split deliveries. The objective of this paper is to find an optimal assignment of tankers, a sequence of visiting and loading volume simultaneously in order to minimize the total distance satisfying the capacity of tankers. A savings-based meta-heuristic algorithm with lot sizing parameters and volume assignment heuristic is developed. The proposed method is applied to solve a case study with real data. Computational results demonstrate the effectiveness of the heuristic algorithm compared with that of human operators.

In this paper, we propose Petri net decomposition approach for bi-objective optimization of conflict-free routing for AGV systems. The objective is minimizing total traveling time and equalizing delivery time simultaneously. The dispatching and conflict-free routing problem for AGVs is represented as a bi-objective optimal firing sequence problem for Petri Net. A Petri net decomposition approach is proposed to solve the bi-objective optimization problem efficiently. The convergence of the proposed algorithm is improved reducing search region by the proposed coordination method. The effectiveness of the proposed method is compared with that of a nearest neighborhood dispatching method. Computational results are provided to show the effectiveness of the proposed method.

In this paper, we propose an application of Petri Net decomposition approach for the simultaneous optimization of dispatching and conflict-free routing for automated guided vehicles in the dynamic situation where transport requests are given in real time. The objective is to maximize the total throughput of the AGV transport system during the time horizon. In order to solve the dynamic problem, static problems are periodically solved when the transport requests are given to the AGV system. The dispatching and conflict-free routing are simultaneously optimized by the Petri Net decomposition approach. In the proposed method, the Petri Net is decomposed into several subnets for task subproblems and AGV subproblems that can be solved by the shortest path algorithm on the reachability graph. The local solutions for the subnets are coordinated by a penalty function algorithm. To ensure the generation of conflict-free routing, a new deadlock avoidance strategy is incorporated in the optimization algorithm. The effects of simultaneous optimization of dispatching and conflict-free routing are investigated for routing problems in dynamic environments.

Considering the need to develop general scheduling problem solver, the recent integration of Petri Nets as modeling tools into effective optimization methods for scheduling problems is very promising. The paper addresses a Petri Net modeling and decomposition method for solving a wide variety of scheduling problems. The scheduling problems are represented as the optimal transition firing sequence problems for timed Petri Nets. The Petri Net is decomposed into several subnets in which each subproblem can be easily solved by Dijkstra' algorithm. The approach is applied to a flowshop scheduling problem. The performance of the proposed algorithm is compared with that of a simulated annealing method.

Raw materials for industrial steel-making plants need to be stored in material yards in order to satisfy various production requirements. The stored materials are supplied to production plants by belt-conveyors with multiple alternative transportation routes. The simultaneous optimization of the storage allocation and transportation routing for the raw materials yard is required for achieving production that is flexible to changes in demand. In this paper, we propose a Lagrangian decomposition and coordination approach for storage allocation and routing for a belt-conveyor transportation system to handle demand changes. The overall problem is decomposed into an allocation planning subproblem and a transportation routing subproblem. A near-optimal solution for allocation planning and transportation routing is derived by repeating each optimization of subproblems and multiplier updates. The effectiveness of the proposed approach is confirmed in numerical experiments.

We consider an optimization of conflict-free routing problems for automated guided vehicles (AGV) with acceleration and deceleration. A continuous time model is developed to represent the dynamics of vehicles. In the proposed model, the transportation model is discretized into several regions. A network model is created by taking into account the acceleration and deceleration motions. The acceleration and deceleration are represented at curve locations. Column generation heuristic is used to find a near-optimal solution. In this algorithm, we construct a heuristic rule to generate a feasible solution with acceleration and deceleration of vehicles after the column generation. The pricing problem is represented by a resource constrained shortest path problem, which is effectively solved by a labeling algorithm. The dominance relation for acceleration and deceleration is addressed. In the proposed model, the dynamics of real speed AGV model are reflected into the routing problems. By comparing the performance of the conventional method, the effectiveness of the proposed method is demonstrated.