Maximizing the profit in customer’s order acceptance and scheduling problem with weighted tardiness penalty

The customer’s order acceptance and scheduling problem in a single machine environment has long been an appealing research subject. In this paper, a situation where a pool of customers exists and each customer tends to place all his orders to a single company is addressed. Hence, the customer’s orders will be entirely either accepted or rejected. In this work, decisions on rejection or acceptance of customers and sequencing of the accepted orders are simultaneously considered. The goal is to maximize the total net profit obtained from accepted orders revenues contributed by tardiness penalty. In response to the computational complexity of the problem, a heuristic algorithm and two optimal branch and bound procedures with upper bound, lower bound, and dominance rules are developed. Computational results demonstrate that the proposed methods perform well in a timely manner.     

Column generation heuristics for multiple machine, multiple orders per job scheduling problems

Front opening unified pods (FOUPs) are used to store and transport silicon wafers in 300-mm semiconductor wafer fabs. To achieve production efficiencies, wafers are grouped together in FOUPs without regard to the originating customer placing the order. In the resulting multiple orders per job (moj) scheduling problem, scheduling is performed at the FOUP (i.e., aggregated order) level, while scheduling performance is assessed per individual customer order. Column generation heuristics are presented for single and parallel machine moj scheduling problems to minimize total weighted order completion time. The proposed heuristics obtain near-optimal solutions very quickly, outperforming competing approaches in the literature.     

订单带多工类工件时的极小迟后范围问题

本文考虑下述由多工类工件组成的订单的单机排序问题：每一个客户提供一个由若干工件组成的订单,总共n个工件又分成k个类．当机器从加工某类中的工件转向加工不同于它的第i类工件时,需一调整时间si．每一订单有一给定的应交工时间,订单的完工时间定义为该定单所含全部工件完工时的时间．我们希望适当排列这n个工件,使得订单的迟后范围最小．相应这一排序问题,文中依不同的背景给出了以下二种模式：同类工件一起连续加工,工件的完工时间为其所属类中全部工件完工时的时间,用GT,Ba来表示；同类工件一起连续加工,工件的完工时间为其本身的完工时间,用GT,Ja来表示．对于这两种模式的排序同题,我们均证明了其NP-hard性并给出了对应的分枝定界算法．     

Supply chain scheduling with receiving deadlines and non-linear penalty

We study the operations scheduling problem with delivery deadlines in a three-stage supply chain process consisting of (1) heterogeneous suppliers, (2) capacitated processing centres (PCs), and (3) a network of business customers. The suppliers make and ship semi-finished products to the PCs where products are finalized and packaged before they are shipped to customers. Each business customer has an order quantity to fulfil and a specified delivery date, and the customer network has a required service level so that if the total quantity delivered to the network falls below a given targeted fill rate, a non-linear penalty will apply. Since the PCs are capacitated and both shipping and production operations are non-instantaneous, not all the customer orders may be fulfilled on time. The optimization problem is therefore to select a subset of customers whose orders can be fulfilled on time and a subset of suppliers to ensure the supplies to minimize the total cost, which includes processing cost, shipping cost, cost of unfilled orders (if any), and a non-linear penalty if the target service level is not met. The general version of this problem is difficult because of its combinatorial nature. In this paper, we solve a special case of this problem when the number of PCs equals one, and develop a dynamic programming-based algorithm that identifies the optimal subset of customer orders to be fulfilled under each given utilization level of the PC capacity. We then construct a cost function of a recursive form, and prove that the resulting search algorithm always converges to the optimal solution within pseudo-polynomial time. Two numerical examples are presented to test the computational performance of the proposed algorithm.     

Order acceptance and due-date quotation in low machine rates

In real manufacturing environments, some customer orders include multiple jobs. However, a single due-date should be assigned to each order. Further, machine processing rate is not constant at all times. In effect, in many manufacturing operations, the machine processing rate decreases to a subnormal level during time and needs a special type of maintenance to bring the normal state back. Due to this reduction in capacity, production schedulers may decide to reject some orders. In this paper, the novel extensive problem of selecting a subset of orders, assigning due-dates to selected orders, scheduling the selected orders and jobs within each one, and scheduling the rate-modifying maintenance is studied. The objective function is minimizing total cost of lost-sales of rejected orders together with due-date length and maximum of earliness and tardiness of selected orders. The problem is proved polynomial and an optimal approach is developed.     

A hybrid of adaptive large neighborhood search and tabu search for the order-batching problem

Given a set of customer orders and a routing policy, the goal of the order-batching problem?(OBP) is to group customer orders to picking orders (batches) such that the total length of all tours through a rectangular warehouse is minimized. Because order picking is considered the most labor-intensive process in warehousing, effectively batching customer orders can result in considerable savings. The OBP is NP-hard if the number of orders per batch is greater than two, and the exact solution methods proposed in the literature are not able to consistently solve larger instances. To address larger instances, we develop a metaheuristic hybrid based on adaptive large neighborhood search and tabu search, called ALNS/TS. In numerical studies, we conduct an extensive comparison of ALNS/TS to all previously published OBP methods that have used standard benchmark sets to investigate their performance. ALNS/TS outperforms all comparison methods with respect to both average solution quality and run-time. Compared to the state-of-the-art, ALNS/TS shows the clearest advantages on the larger instances of the existing benchmark sets, which assume a higher number of customer orders and higher capacities of the picking device. Finally, ALNS/TS is able to solve newly generated large-scale instances with up to 600 customer orders and six articles per customer order with reasonable run-times and convincing scaling behavior and robustness.     

Integrated scheduling of production and distribution for manufacturers with parallel batching facilities

We consider a class of integrated scheduling problems for manufacturers. The manufacturer processes job orders and delivers products to the customer. The objective is to minimize the service span, that is, the period lasting from the time when the order is received to the time when all the products have been delivered to the customer. In the production phase, parallel batch-processing facilities are used to process the jobs. Jobs have arbitrary sizes and processing times. Each facility has a fixed capacity and jobs are processed in batches with the restriction that the total size of jobs in a batch does not exceed the facility capacity. When all the jobs in a batch are completed, the batch is completed. In the distribution phase, the manufacturer uses a vehicle with a fixed capacity to deliver products. The transportation time from the manufacturer to the customer is a constant. Completed products can be delivered in one transfer if the total size does not exceed the vehicle capacity. We first consider the problem where jobs have the same size and arbitrary processing times. We propose approximation algorithms for the problem and we show that a worst-case ratio performance guarantee is respectively 2–1/m. Then we consider the problem where jobs have the same processing time and arbitrary sizes. An approximation algorithm is proposed with an absolute worst-case ratio of 13/7 and an asymptotic worst-case ratio of 11/9. Both the proposed algorithms can be executed in polynomial time.     

一种改进的多模式项目反应性调度问题

既有的项目反应性调度问题只关注了基准调度方案的稳定性,而忽略了项目调度目标的最优实现。本文提出了一种两阶段多模式资源受限项目反应性调度问题。第一阶段,在新的项目执行环境下,对项目进行完全重调度,得到新的最优调度目标值。第二阶段,以新的最优调度目标值为约束,以最大化调度稳定性为目标,求得新的最优调度方案。针对问题特点,基于IBM ILOG优化编程语言OPL和CPLEX V12.8.0,设计出该问题的求解程序。最后,基于标准算例,对本文提出的反应性调度方法、既有的反应性调度方法、完全重调度方法进行了充分的比较测试,结果表明本文提出的反应性调度方法在缩短项目工期、保护基准方案的稳定性方面具有明显优势。     

具有学习效应的三层供应链排序问题

研究了具有学习效应的三层供应链排序问题. 多个客户分布在不同位置,每个客户都有订 单需要制造商进行生产. 制造商需要针对每一个不同订单的客户从不同的地方进购对应的原材料进行生产,生产完工后需要利用有限的车辆将工件运输到相应客户处. 要求每辆运输车装载尽可 能多的货物才开始运输. 利用动态规划算法研究了最大流程时间、总流程时间以及最大延迟三个目标函数.     

Order acceptance and scheduling on two identical parallel machines

We study the order acceptance and scheduling problem on two identical parallel machines. At the beginning of the planning horizon, a firm receives a set of customer orders, each of which has a revenue value, processing time, due date, and tardiness weight. The firm needs to select orders to accept and schedule the accepted orders on two identical parallel machines so as to maximize the total profit. The problem is intractable, so we develop two heuristics and an exact algorithm based on some optimal properties and the Lagrangian relaxation technique. We evaluate the performance of the proposed solution methods via computational experiments. The computational results show that the heuristics are efficient and effective in approximately solving large-sized instances of the problem, while the exact algorithm can only solve small-sized instances.     

Real-time production planning and control system for job-shop manufacturing: A system dynamics analysis

Much attention has been paid to production planning and control (PPC) in job-shop manufacturing systems. However, there is a remaining gap between theory and practice, in the ability of PPC systems to capture the dynamic disturbances in manufacturing process. Since most job-shop manufacturing systems operate in a stochastic environment, the need for sound PPC systems has emerged, to identify the discrepancy between planned and actual activities in real-time and also to provide corrective measures. By integrating production ordering and batch sizing control mechanisms into a dynamic model, we propose a comprehensive real-time PPC system for arbitrary capacitated job-shop manufacturing. We adopt a system dynamics (SD) approach which is proved to be appropriate for studying the dynamic behavior of complex manufacturing systems. We study the system’s response, under different arrival patterns for customer orders and the existence of various types real-time events related to customer orders and machine failures. We determine the near-optimal values of control variables, which improve the shop performance in terms of average backlogged orders, work in process inventories and tardy jobs. The results of extensive numerical investigation are statistically examined by using analysis of variance (ANOVA). The examination reveals an insensitivity of near-optimal values to real-time events and to arrival pattern and variability of customer orders. In addition, it reveals a positive impact of the proposed real-time PPC system on the shop performance. The efficiency of PPC system is further examined by implementing data from a real-world manufacturer.     

Cane Railway Scheduling via Constraint Logic Programming: Labelling Order and Constraints in a Real-Life Application

In Australia, cane transport is the largest unit cost in the manufacturing of raw sugar, making up around 35% of the total manufacturing costs. Producing efficient schedules for the cane railways can result in significant cost savings. This paper presents a study using Constraint Logic Programming (CLP) to solve the cane transport scheduling problem. Tailored heuristic labelling order and constraints strategies are proposed and encouraging results of application to several test problems and one real-life case are presented. The preliminary results demonstrate that CLP can be used as an effective tool for solving the cane transport scheduling problem, with a potential decrease in development costs of the scheduling system. It can also be used as an efficient tool for rescheduling tasks which the existing cane transport scheduling system cannot perform well.     

Scheduling multiple orders per job in a single machine to minimize total completion time

This paper deals with a single-machine scheduling problem with multiple orders per job (MOJ) considerations. Both lot processing machines and item processing machines are also examined. There are two primary decisions that must be made in the proposed problem: (1) how to group the orders together, and (2) how to schedule the jobs once they are formed. In order to obtain the optimal solution to a scheduling problem, these two decisions should be made simultaneously. The performance measure is the total completion time of all orders. Two mixed binary integer programming models are developed to optimally solve this problem. Also, two efficient heuristics are proposed for solving large-sized problems. Computational results are provided to demonstrate the efficiency of the models and the effectiveness of the heuristics.     

A lexicographic approach to bi-objective scheduling of single-period orders in make-to-order manufacturing

This paper presents a lexicographic approach and integer programming formulations for a dual-objective, long-term production scheduling in make-to-order manufacturing environment. The problem objective is to assign single-period customer orders for various product types to planning periods to complete all the orders with minimum number of tardy orders as a primary criterion and to level the aggregate production or the total capacity utilization over a planning horizon as a secondary criterion. Each order must be completed during one planning period. The basic integer programming formulation has been strengthened by the addition of some cutting constraints derived by relating the demand on required capacity to available capacity for each subset of orders with the same due date. The approach has been applied to optimize production schedules in a flexible flowshop made up of several processing stages in series, with identical, parallel machines, and an output buffer of limited capacity for holding completed products before delivery to the customers. Numerical examples modeled after a real-world make-to-order flexible assembly line in the electronics industry are provided and some computational results are reported.     

Tabu search heuristics for the order batching problem in manual order picking systems

In a manual order picking system, order pickers walk or ride through a distribution warehouse in order to collect items requested by (internal or external) customers. In order to perform these operations efficiently, it is usually required that customer orders be combined into (more substantial) picking orders that are limited in size. The order batching problem considered in this paper deals with the question of how a given set of customer orders should be combined into picking orders such that the total length of all picker tours necessary for all of the requested items to be collected is minimized. For the solution of this problem the authors suggest two approaches based on the tabu search principle. The first is a (classic) tabu search (TS), and the second is the attribute-based hill climber (ABHC). In a series of extensive numerical experiments, these approaches are benchmarked against other solution methods put forward in the current literature. It is demonstrated that the proposed methods are superior to the existing methods and provide solutions which may allow distribution warehouses to operate more efficiently.     

A Branch and Bound Algorithm to Minimize the Total Weighed Number of Tardy Jobs and Delivery Costs

This paper addresses the production and delivery scheduling integration problem; a manufacturer receives ₋ orders from one customer while the orders need to be processed on one or two machines and be sent to the customer in batches. Sending several jobs in batches will reduce the transportation cost but it may increase the number of tardy jobs. The objective is to minimize the sum of the total weighted number of tardy jobs and the delivery costs. The structural properties of the problem for a single machine and special cases of the two-machine flow shop problem are investigated and used to set up a new branch and bound algorithm. A heuristic algorithm for upper bound calculation and two approaches for lower bound calculation are also introduced. Results of computational tests show significant improvement over an existing dynamic programming method.     

Rescheduling problems with deteriorating jobs under disruptions

In this paper, we consider two single-machine rescheduling problems with linear deteriorating jobs under disruption. By a deteriorating jobs, we mean that the actual processing time of the job is an increasing function of its starting time. The two problems correspond to two different increasing linear function. Rescheduling means a set of original jobs has already been scheduled to minimize some classical objective, then a new set of jobs arrives and creates a disruption. We consider the rescheduling problem to minimize the total completion time under a limit of the disruption from the original scheduling. For each problem, we consider two versions. For each version, the polynomial algorithms are proposed, respectively.     

Vehicle-scheduling Problems with Uncertainty and Omitted Customers

The standard vehicle-scheduling problem is deterministic, assuming all factors are known with certainty in advance of scheduling. In practice there are several areas which might contain uncertainty. This paper suggests ways of tackling these, but concentrates on problems where some customers do not need deliveries during a scheduling period. If the number of such customers is small, semi-fixed routes may be acceptable. As the number of customers omitted rises, there comes a point when rescheduling becomes preferable. The potential savings made by semi-fixed or variable routes over fixed routes are estimated for standard problems. The implications of these savings are then evaluated for a wholesale distributor.     

Customer Service vs Trim Waste in Corrugated Box Manufacture

Many approaches to the problem of arranging customer orders for cutting or corrugation have focused on the minimization of trim waste. This views the corrugator more or less in isolation. When downstream machines or customer due-dates exist, however, customer service may suffer from the desire to keep scrap at a low level. Thus, if slightly higher levels of waste were accepted, the production scheduler might be able to improve performance regarding due dates.We developed a simulation model, for Domtar Packaging Ltd, of a corrugated cardboard box factory, which included the corrugation process and four finishing machines. Customer orders were generated via empirical and theoretical probability distributions, then sent through the model according to one of several scheduling rules. This allowed the relationship between various levels of trim waste and customer service to be viewed. Results of the simulation experiments, as well as a discussion of the model itself, are given. Comments and conclusions regarding both our model and corrugator algorithms in general are presented in the light of the role of the human scheduler in plants of this type.     

行驶时间延迟下物流配送干扰管理模型——基于客户终身价值的视角

物流配送过程中干扰事件导致行驶时间延迟后,初始配送方案将不再最优甚至根本不可行,此时如何生成副作用最小的调整方案,快速恢复配送的正常运行,是当前研究的难点。本文首先将客户为企业当前(及潜在)贡献价值考虑在内,基于客户终身价值对系统扰动进行度量。进而兼顾偏离成本和初始目标,构建干扰管理模型并提出相应的启发式算法。算例结果表明:与其他重调度方法相比,本文方法的实用性更强。