Distributed optimisation method for multi-resource constrained scheduling in coal supply chains

We consider an integrated planning and scheduling problem motivated by the coal supply chains in Australia. The problem considers production planning of several independent mines. The mines need trains to complete delivery of coal by the arrival of ships at the terminal. The trains, on the other hand, are in limited supply and therefore the mines need to share this common resource. For this problem, we present a mixed integer programming formulation which minimises total weighted earliness, tardiness and operational costs. We also present a distributed algorithm based on the Lagrangian relaxation, which incorporates the volume and Wedelin algorithms. The strength of our distributed algorithm is demonstrated by an extensive computational experiment on several randomly generated instances.     

A constrained EPSAC approach to inventory control for a benchmark supply chain system

The design of an appropriate inventory control policy for a supply chain (SC) plays an essential role in tempering inventory instability and bullwhip effect. Several constraints are commonly encountered in actual operations so managers are required to take these physical restrictions into account when designing the inventory control policy. Model predictive control (MPC) appears as a promising solution to this issue, due to its capability of finding optimal control actions for a constrained SC system. Therefore, the inventory control problem for a benchmark SC is solved using the extended prediction self-adaptive control approach to MPC. To extend methodologies in our previous work, the control framework relies on generic process model and incorporates the physical constraints arising from practical operations to form the general constrained optimisation problems. The managers can choose from decentralised and centralised control structures according to specific informational and organisational factors of their SCs. The proposed control schemes in this study may be appropriate for industrial practice because the designed policy can bring a reduction of over 30% in operating cost and a significant increase of customer satisfaction level compared with that of the conventional policy.     

Open-pit coal mine production sequencing incorporating grade blending and stockpiling options: An application from an Indian mine

Production scheduling is a crucial aspect of the mining industry. An optimal and efficient production schedule can increase the profits manifold and reduce the amount of waste to be handled. Production scheduling for coal mines is necessary to maintain consistency in the quality and quantity parameters of coal supplied to power plants. Irregularity in the quality parameters of the coal can lead to heavy losses in coal-fired power plants. Moreover, the stockpiling of coal poses environmental and fire problems owing to low incubation periods. This article proposes a production scheduling formulation for open-pit coal mines including stockpiling and blending opportunities, which play a major role in maintaining the quality and quantity of supplied coal. The proposed formulation was applied to a large open-pit coal mine in India. This contribution provides an efficient production scheduling formulation for coal mines after utilizing the stockpile coal within the incubation periods with the maximization of discounted cash flows. At the same time, consistency is maintained in the quality and quantity of coal to power plants through blending and stockpiling options to ensure smooth functioning.     

Scheduling and co-ordination of multi-suppliers single-warehouse-operator single-manufacturer supply chains with variable production rates and storage costs

We study a supply chain scheduling and co-ordination problem comprising multiple suppliers, a single warehouse operator, a single manufacturer, and multiple retailers, where the supply chain has limited production capacity that can take only some of the orders from the retailers. For a decentralised supply chain, the manufacturer is a decision maker that selects the orders and aims to maximise its own profit, where the profit is a function of the order storage time and storage quantity, order sequence-dependent weighted storage costs, and idle time of the orders. On the other hand, for a centralised supply chain, a supply chain co-ordinator exists that aims to maximise the profit of the whole supply chain and allocates the profit among the supply chain members. We first formulate the problem as a two-machine common-due-window flow shop scheduling problem. We then develop a theorem and two algorithms to solve the optimal scheduling problems in both the decentralised and centralised supply chains. With these results, we develop a method that can achieve channel co-ordination based on a profit sharing rule, together with an increase in the production rates and a decrease in the storage costs.     

Quay crane scheduling in container terminals

The problem of scheduling identical quay cranes moving along a common linear rail to handle containers for a ship is studied. The ship has a number of container-stacking compartments called bays, and only one quay crane can work on a bay at the same time. The objective of the scheduling problem is to find the work schedule for each quay crane which minimizes the ship’s stay time in port. Finding the optimal solution of the scheduling problem is computationally intractable and a heuristic is proposed to solve it. The heuristic first decomposes the difficult multi-crane scheduling problem into easier subproblems by partitioning the ship into a set of non-overlapping zones. The resulting subproblems for each possible partition are solved optimally by a simple rule. An effective algorithm for finding tight lower bounds is developed by modifying and enhancing an effective lower-bounding procedure proposed in the literature. Computational experiments were carried out to evaluate the performance of the heuristic on a set of test problems randomly generated based on typical terminal operations data. The computational results show that the heuristic can indeed find effective solutions for the scheduling problem, with the heuristic solutions on average 4.8% above their lower bounds.     

A multi-objective model for risk mitigating in supply chain design

The goal of this study is to recognise various factors for responsive SCs that affect supply risk and model their impact on SC design and operation. We propose a conceptual model for SC responsiveness that encompasses practices such as flexibility, agility, internal integration, and visibility. This conceptual model is utilised to build up a multi-objective, multi-period SC design and operation model. A heuristic algorithm is developed to find the supplier, product, period, and production rate for the numerical problem. The improved genetic algorithm (GA) produces solutions with more accuracy in considerably less time than a traditional GA. Finally, an approach to prioritise the objective functions is developed that allows managers to focus on specific objective functions more than optimum values. This approach provides risk-averse, responsiveness-oriented, cost-effective managers the capability to set priorities based on their policies.     

An effective heuristic for scheduling a yard crane to handle jobs with different ready times

In land-constrained port container terminals, yard cranes are commonly used for handling containers in a container yard to load containers onto or unload containers from trucks. However, yard cranes are bulky, slow and need to move frequently between their work locations. As it is common that the container flow in a terminal is bottlenecked by yard crane operations, effective work schedules of yard cranes are needed to increase the terminal’s throughput. This article studies the problem of scheduling a yard crane to perform a given set of container handling jobs with different ready times. The objective is to minimize the sum of job waiting times. It is noted that the scheduling problem is NP-complete. This research develops a heuristic to solve the scheduling problem and an algorithm to find lower bounds for benchmarking the schedules found by the heuristic. The performance of the heuristic is evaluated by a set of test problems generated on the basis of real-life terminal operations data. Indeed, the computational results show that the proposed heuristic can find effective solutions for the scheduling problem.     

A multi-objective model for multi-project scheduling and multi-skilled staff assignment for IT product development considering competency evolution

We address a multi-skill project scheduling problem for IT product development in this article. The goal is for product development managers to be able to generate an initial schedule at an early stage of development activities. Due to the complexity of the product structure and functionality, an IT product development effort is divided into multiple projects. Each project includes several tasks, and each task must be completed by an employee who has mastered a certain skill to complete it. A pool of multi-skilled employees is available, and the employees’ skill efficiencies are influenced by both learning and forgetting phenomena. Based on the real-world demands of product development managers, three objectives are simultaneously considered: skill efficiency gain, product development cycle time and costs. To solve this problem, we propose a multi-objective non-linear mixed integer programming model. The Non-dominated Sorting Genetic Algorithm II (NSGA-II)is designed to generate an approximation to the optimal Pareto front of this NP-hard multi-objective optimisation problem. The algorithm produces feasible schedules for all the development projects using the serial schedule generation scheme. We adopt penalty values and individual employee adjustments to address resource conflicts and constraint violations. A weighted ideal point method is used to select the final solution from the approximate Pareto solution set. An application case of a new electrical energy saving product implementation in a leading electrical device company in China is used to illustrate the proposed model and algorithm.     

An approach to integrate production-transportation planning and scheduling in an aluminium supply chain network

This article is based on a real-life problem of a global aluminium supply chain network driven by an aluminium smelter. At each echelon of the aluminium supply chain network, several members are involved which are scattered around the world. Producing aluminium begins with bauxite mining. Next, aluminium oxide is made from bauxite and finally aluminium is produced from aluminium oxide. A novel type of mixed-integer decision-making model, including a time-continuous representation of the planning period, is presented. The model enables coordination of production quantities and times of all supply chain members in order to minimise production and transportation costs of the whole supply chain minus bonus payments for early deliveries which are stipulated between the supply chain network and its customers. Material flows can take place with or without temporary storage of intermediate products at supplying and/or receiving sites. Furthermore, relax-and-fix heuristics are presented. A number of randomly generated scenarios are presented to demonstrate that the heuristics can find nearly optimal solutions along with drastically reduced computation times. The relax-and-fix heuristic enables iterative planning between centralised and decentralised decision makers.     

Multi-period channel coordination in vendor-managed inventory for deteriorating goods

This study examines the problem of optimally dynamic joint decisions, including replenishment scheduling/quantity, retail price, wholesale price, and revenue-sharing allocation, in a vertically decentralised single-manufacturer Stackelberg and single-retailer channel over a multi-period planning horizon, subject to deteriorating goods and multivariate demand function. This study uses a calculus-based formulation combined with dynamic programming techniques to solve the channel coordination decision problem. Additionally, three arrangements, namely price-only contract, revenue-sharing contract, and revenue-sharing plus linear rebate and side-payment contract for channel coordination, are developed under retailer-managed inventory (RMI) and vendor-managed inventory (VMI) systems, respectively. The analysis reveals that the proposed policy under the VMI system with the revenue-sharing plus linear rebate and side-payment contract tends to obtain low retail prices and large demand quantity, and results in near-perfect coordination, including greater system efficiency and Pareto improvements, for the vertically decentralised dynamic channel.     

A column generation based heuristic for the capacitated vehicle routing problem with three-dimensional loading constraints

This paper addresses an integrated problem of vehicle routing and three-dimensional loading with additional practical constraints such as stability, fragility and LIFO. A column generation (CG) technique-based heuristic is proposed to handle this problem. To generate new columns in CG technique, first, an elementary shortest path problem is solved to find routes with negative reduced cost. Then an extreme point-based heuristic method is employed to verify feasibility of obtained routes in terms of loading and other constraints. To speed up the CG technique, fast column generation is also performed by applying an efficient heuristic pricing method. The CG technique, tested on the benchmark instances, outperforms the efficient tabu search method developed in the literature in terms of solution quality and computation time.     

Optimizing the landside operation of a container terminal

This paper concerns the problem of operating a landside container exchange area that is serviced by multiple semi-automated rail mounted gantry cranes (RMGs) that are moving on a single bi-directional traveling lane. Such a facility is being built by Patrick Corporation at the Port Botany terminal in Sydney. The gantry cranes are a scarce resource and handle the bulk of container movements. Thus, they require a sophisticated analysis to achieve near optimal utilization. We present a three-stage algorithm to manage the container exchange facility, including the scheduling of cranes, the control of associated short-term container stacking, and the allocation of delivery locations for trucks and other container transporters. The key components of our approach are a time scale decomposition, whereby an integer program controls decisions across a long time horizon to produce a balanced plan that is fed to a series of short time scale online subproblems, and a highly efficient space-time divisioning of short-term storage areas. A computational evaluation shows that our heuristic can find effective solutions for the planning problem; on real-world data it yields a solution at most 8% above a lower bound on optimal RMG utilization. Research supported by Patrick Technology and Systems, the Australian Research Council Centre of Excellence for Mathematics and Statistics of Complex Systems (MASCOS), and the German Research Foundation Research Center Mathematics for key technologies: Modelling, simulation, and optimization of real-world processes (Matheon).     

Multi-resource routing with flexible tasks: an application in drayage operations

This paper introduces an application of a Multi-Resource Routing Problem (MRRP) in drayage operations. Drayage involves the movement of loaded and empty equipment between rail yards, shippers, consignees, and equipment yards. The problem of routing and scheduling drayage movements is modeled as an MRRP with flexible tasks, since the origins and destinations of some movements can be chosen from a set of possible nodes. The complexities added by routing choice are studied, along with the impact of these complexities on problem formulation. The solution approach developed to solve this problem includes column generation embedded in a branch-and-bound framework. Using this approach, efficient operating plans are designed to coordinate independent drayage operations in the Chicago region.     

A Phase Estimation Algorithm for Quantum Speed-Up Multi-Party Computing

Security and privacy issues have attracted the attention of researchers in the field of IoT as the information processing scale grows in sensor networks. Quantum computing, theoretically known as an absolutely secure way to store and transmit information as well as a speed-up way to accelerate local or distributed classical algorithms that are hard to solve with polynomial complexity in computation or communication. In this paper, we focus on the phase estimation method that is crucial to the realization of a general multi-party computing model, which is able to be accelerated by quantum algorithms. A novel multi-party phase estimation algorithm and the related quantum circuit are proposed by using a distributed Oracle operator with iterations. The proved theoretical communication complexity of this algorithm shows it can give the phase estimation before applying multi-party computing efficiently without increasing any additional complexity. Moreover, a practical problem of multi-party dating investigated shows it can make a successful estimation of the number of solution in advance with zero communication complexity by utilizing its special statistic feature. Sufficient simulations present the correctness, validity and efficiency of the proposed estimation method.     

Optimisation of online retailer pricing and carrier capacity expansion during low-price promotions with coordination of a decentralised supply chain

In recent years, many online retailers in China set low prices on 11 November, which stimulates huge delivery demand and results in many problems although carriers make an effort to increase their delivery capacities temporarily. To circumvent this difficulty, we consider a supply chain consisting of an online retailer, who can set price to influence the demand, and a capacitated carrier, whose capacity can be expanded at a high cost. We derive the optimal decisions in the centralised and decentralised decision systems, and compare the performances of the two systems. We find that the optimal decisions, and which system has lower price, larger capacity increment, and more late delivered goods depends on the model parameters (the market scale, the late delivery costs, the capacity expansion cost, the delivery fee, and the demand uncertainty). Specially, we show that, contrary to the traditional channel, the online retailer in the decentralised system may set lower price and the carrier has less incentive to expand capacity in the decentralised system in some situations, which underlines the need for coordination. In addition, we propose coordination contracts to improve the overall performance of the supply chain under deterministic and random demands.     

Evaluating strategic issues in supply chain scheduling using game theory

This paper deals with the problem of scheduling and batch delivery of orders in a supply chain (SC) including a supplier, a manufacturer and a final customer. First, the individual decisions of partners in the SC and their behaviours are analysed through mathematical models. Second, the best policy is obtained assuming that the SC is vertically integrated and the partners fully cooperate (this is called SC scheduling in the relevant literature). Since this strategy is usually against a partner, it might not be implemented in practice as the authors have observed this condition in real world. Hence, a fair sharing mechanism based on game theory concepts is also introduced which can motivate the partners to cooperate and adopt the best policy of the SC. The numerical examples show the superiority of integrated decisions over independent actions and also the importance of the sharing mechanism.     

Non-Cooperative Game of Coordinated Scheduling of Parallel Machine Production and Transportation in Shared Manufacturing

Given the challenges of manufacturing resource sharing and competition in the modern manufacturing industry, the coordinated scheduling problem of parallel machine production and transportation is investigated. The problem takes into account the coordination of production and transportation before production as well as the disparities in machine spatial position and performance. A non-cooperative game model is established, considering the competition and self-interest behavior of jobs from different customers for machine resources. The job from different customers is mapped to the players in the game model, the corresponding optional processing machine and location are mapped to the strategy set, and the makespan of the job is mapped to the payoff. Then the solution of the scheduling model is transformed into the Nash equilibrium of the non-cooperative game model. A Nash equilibrium solution algorithm based on the genetic algorithm (NE-GA) is designed, and the effective solution of approximate Nash equilibrium for the game model is realized. The fitness function, single-point crossover operator, and mutation operator are derived from the non-cooperative game model’s characteristics and the definition of Nash equilibrium. Rules are also designed to avoid the generation of invalid offspring chromosomes. The effectiveness of the proposed algorithm is demonstrated through numerical experiments of various sizes. Compared with other algorithms such as heuristic algorithms (FCFS, SPT, and LPT), the simulated annealing algorithm (SA), and the particle swarm optimization algorithm (PSO), experimental results show that the proposed NE-GA algorithm has obvious performance advantages.     

吸附处理煤层气中去除二氧化碳的数值模拟

煤矿开采过程中排放出大量低浓度煤层气,提纯利用这部分煤层气对我国能源开发利用和环境保护意义重大,其难点是经济高效地分离CH4和CO2.本文针对煤层气的沸石分子筛柱吸附床建立了控制方程与定解条件,只考虑甲烷和二氧化碳二元组成采用控制体积法对控制方程进行离散处理,采用TDMA算法编制程序对控制方程进行求解,通过对模拟结果的...     

A robust scheduling for the multi-mode project scheduling problem with a given deadline under uncertainty of activity duration

The problem of this paper deals with the multi-mode project scheduling problem under uncertainty of activity duration where only the renewable resources are taken into account and a given deadline has to be met at the cost of recruiting additional resources. A heuristic algorithm is employed to solve this problem, and to maintain the robustness of the baseline schedule, the concept of critical chain project management (CCPM) is applied in which a new definition to resource buffer is considered. A simulation methodology is used to determine the size and location of resource buffers in the schedules in which three different buffer sizes and three different uncertainty levels are considered. Results and analysis of the simulation outcomes illustrate that resource buffers are useful and should be simulated by the CCPM schedules, as they help to decrease the total duration of the project during implementation and meet the deadline of the project with more assurance.     

Decentralizing semiconductor capacity planning via internal market coordination

Semiconductor capacity planning is a cross-functional decision that requires coordination between the marketing and manufacturing divisions. We examine the main issues of a decentralized coordination scheme in a setting observed at a major US semiconductor manufacturer: marketing managers reserve capacity from manufacturing based on product demands, while attempting to maximize profit; manufacturing managers allocate capacity to competing marketing managers so as to minimize operating costs while ensuring efficient resource utilization. This cross-functional planning problem has two important characteristics: (i) both demands and capacity are subject to uncertainty; and (ii) all decision entities own private information while being self-interested. To study the issues of coordination we first formulate the local marketing and the manufacturing decision problem as separate stochastic programs. We then formulate a centralized stochastic programming model (JCA), which maximizes the firm's overall profit. JCA establishes a theoretical benchmark for performance, but is only achievable when all planning information is public. If local decision entities are to keep their planning information private, we submit that the best achievable coordination corresponds to an alternative stochastic model (DCA). We analyze the relationship and the theoretical gap between (JCA) and )DCA), thereby establishing the price of decentralization. Next, we examine two mechanisms that coordinate the marketing and manufacturing decisions to achieve (DCA) using different degrees of information exchange. Using insights from the Auxiliary Problem Principle (APP), we show that under both coordination mechanisms the divisional proposals converge to the global optimal solution of (DCA). We illustrate the theoretic insights using numerical examples as well as a real world case.