考虑货架存放期的经济批量排产问题的求解

在化工、造纸、制药、钢铁等工业生产中，一台设备或一条生产线可以生产多种产品的情况很常见。在生产中，如何安排各类产品的生产顺序以及生产数量显得十分重要。这类问题通常称作经济批量排产问题，这类问题是生产库存中的经典问题。本文研究的经济批量排产问题考虑了产品货架存放期因素，针对以往研究的不足，本文提出用批量变动方法求解该类问题，由计算结果显示，按照这种排产方法花费的成本要低于其他两种经济批量排产问题常用的方法。     

经济批量排产问题的改进算法:设定最高允许高度

经济批量排产问题是指在生产准备费用与库存费用最低的情况下,协调地、周期性地生产多种产品的问题.由于此问题是NP-hard的,人们一种致力于寻找快速地求解高质量的近似最优解的方法.在将生产次数舍入为2的幂次后,误差小,获得可行解的速度快.研究的经济批量排产问题考虑了产品货架存放期因素.指出了Dobson算法的不足,并提出了基于2的幂次条件的改进算法.改进算法设定了最高允许高度,首先给部分箱进行装箱.由于能获得高质量的生产排产,因此,算法能获得2的幂次条件下的高质量解.给出一个算例,计算结果显示,算法结果更优.     

A search heuristic for the sequence-dependent economic lot scheduling problem

Almost all of the research on the economic lot scheduling problem (ELSP) has assumed that setup times are sequence-independent even though sequence-dependent problems are common in practice. Furthermore, most of the solution approaches that have been developed solve for a single optimal schedule when in practice it is more important to provide managers with a range of schedules of different length and complexity. In this paper, we develop a heuristic procedure to solve the ELSP problem with sequence-dependent setups. The heuristic provides a range of solutions from which a manager can choose, which should prove useful in an actual stochastic production environment. We show that our heuristic can outperform Dobson's heuristic when the utilization is high and the sequence-dependent setup times and costs are significant.     

多种变质性物品的经济批量问题

本文考虑了多种变质性物品在同一台设备上生产的最优基本生产周期问题。本文采用了基本周期法,给出了问题的数学模型,分析了模型最优解的存在性,并给出了求解该模型的算法和算例,从算例的结果说明基本周期法比公共周期法解决经济批量问题更优。     

Economic lot scheduling problem with imperfect production processes

In this paper, we model the effects of imperfect production processes on the economic lot scheduling problem (ELSP). It is assumed that the production facility starts in the in-control state producing items of high or perfect quality. However the facility may deteriorate with time and shifts at a random time to an out of control state and begins to produce nonconforming items. A mathematical model is developed for ELSP taking into account the effect of imperfect quality and process restoration. Numerical examples are presented to illustrate important issues related to the developed model.     

Crossdocking— Just in Time scheduling: an alternative solution approach

In this paper, a scheduling problem which allows a warehouse to function as a crossdock where transit storage time for cargo is minimized according to Just in Time scheduling is studied. A model that uses the machine scheduling notation to describe the problem is written. As the problem is NP-hard, a solution approach based on a combination of two metaheuristics, Reactive GRASP and Tabu Search (RGTS), is provided. Experiments are carried out to determine the usefulness of this approach. The results obtained from the exact method that uses the ILOG CPLEX 9.1 solver for 16 problem instances and the results obtained from the RGTS metaheuristic scheduling algorithm and two other algorithms proposed by other authors for the same problem instances are discussed. Analysis and comparisons are made.     

Determining a common production cycle time for an economic lot scheduling problem with deteriorating items

This paper considers the economic lot scheduling problem (ELSP) for a production-inventory system where items produced are subject to continuous deterioration. The problem is to schedule multiple products to be manufactured on a single machine repetitively over an infinite planning horizon. Each product is assumed to have a significant rate of deterioration. Only one product can be manufactured at a time. The demand rate for each product is constant, but an exponential distribution is used to represent the distribution of the time to deterioration. A common cycle time policy is assumed in the production process. A near optimal production cycle time is derived under conditions of continuous review, deterministic demand, and no shortage.     

The Economic Lot Scheduling Problem without Capacity Constraints

This study presents a comprehensive analysis on the Economic Lot Scheduling Problem (ELSP) without capacity constraints. We explore the optimality structure of the ELSP without capacity constraints and discover that the curve for the optimal objective values is piecewise convex with repsect to B, i.e., the values of basic period. The theoretical properties of the junction points on the piecewise convex curve not only provides us the information on “which product i” to modify, but also on “where on the B-axis” to change the set of optimal multpliers in the search process. By making use of the junction points, we propose an effective search algorithm to secure a global optimal solution for the ELSP without capacity constraints. Also, we use random experiments to verify that the proposed algorithm is efficient. The results in this paper lay important foundation for deriving an efficient heuristic to solve the conventional ELSP with capacity constraints.     

阻塞混流生产机器人制造单元调度问题可行解性质研究

针对阻塞混流生产机器人制造单元调度问题的可行解性质进行研究。首先,定义了机器人活动,将机器人运行排序和工件加工排序转化为机器人活动调度,将二维调度问题转化为一维调度问题;其次,提出了可行机器人活动调度概念,给出了几个等价定义;最后,给出了可行机器人活动调度经过一定变换,仍然是可行调度的条件。这些性质为优化算法的设计提供了理论基础。     

A truck scheduling problem arising in intermodal container transportation

We address a truck scheduling problem that arises in intermodal container transportation, where containers need to be transported between customers (shippers or receivers) and container terminals (rail or maritime) and vice versa. The transportation requests are handled by a trucking company which operates several depots and a fleet of homogeneous trucks that must be routed and scheduled to minimize the total truck operating time under hard time window constraints imposed by the customers and terminals. Empty containers are considered as transportation resources and are provided by the trucking company for freight transportation. The truck scheduling problem at hand is formulated as Full-Truckload Pickup and Delivery Problem with Time Windows (FTPDPTW) and is solved by a 2-stage heuristic solution approach. This solution method was specially designed for the truck scheduling problem but can be applied to other problems as well. We assess the quality of our solution approach on several computational experiments.     

The use of genetic algorithms to solve the economic lot size scheduling problem

The purpose of this paper is to investigate the use genetic algorithms (GAs) for solving the Economic Lot Size Scheduling Problem (ELSP). The ELSP is formulated using the Basic Period (BP) approach which results in a problem having one continuous decision variable and a number of integer decision variables equal to the number of products being produced. This formulation is ideally suited for using GAs. The GA is tested on Bomberger's classical problem. The resulting solutions were better than those obtained using an iterative dynamic programming (DP) approach. The total cost of GA solutions to the problem with utilization up to 65% were within 3.4% of the lower bound. The GA also performed well for higher utilization yielding solutions within 13.87% of the lower bound for utilization up to 86%. The GA was tested on a 30-item problem and good solutions were obtained. The results of the GA under different binary representations, crossover methods, and initialization methods are compared to identify the best settings. The results indicate that for this particular problem, binary representation works better than Gray coding, 2-point crossover is best, and an infeasible starting population is better than feasible.     

Economic lot scheduling with uncontrolled co-production

The aim of this paper is to analyze the effects of uncontrolled co-production on the production planning and lot scheduling of multiple products. Co-production occurs when a proportion of a certain production comes out as another product. This is typical in the process industry where quality and process specifications can lead to diversified products. We assume that there is no demand substitution and each product has its own market. Furthermore, we assume that co-production cannot be controlled due to technical and/or cost considerations. We introduce two models that extend the common cycle economic lot scheduling (ELSP) setting to include uncontrolled co-production. In the first model we do not allow for shortages and derive the optimal cycle time expression. In the second model, we allow for planned backorders and characterize the optimal solution in closed form. We provide a numerical study to gain insight about co-production. It seems that the cycle time increases with co-production rate and utilization of the system. The effect of co-production on long-term average cost does not exhibit a certain characteristic.     

Constructive and composite heuristic solutions to the P//∑Ci scheduling problem

In this paper, we study the permutation flowshop scheduling problem with the criterion of minimising the total flow time. We propose a new constructive heuristic procedure to solve the problem. This procedure is flexible in the computational effort required, as it can be adjusted to the requirements of the problem. We combine this procedure with local search methods, whose computational requirements can also be varied, to study the efficiency and effectiveness of different ways of forming composite solution methods. Computational experiments on standard benchmark problems are carried out. The results show that the new heuristic performs significantly better than previous ones and that combining constructive and search heuristics not only further improves the solution quality but also saves computation time. Discussions on the results are provided and future research is suggested.     

Makespan minimization in machine dominated flowshop

In a flowshop scheduling problem, a set of jobs is processed by a set of machines. The jobs follow the same sequence in all machines. We study the flowshop scheduling problem under a new case of machine dominance that is often found in the manufacturing of computers and electronic devices. We provide a formula for makespan value for a given sequence, show that the makespan value depends only on certain jobs in the sequence, and present an algorithm that finds a sequence with minimum makespan. Numerical examples of the solution approaches are provided.     

Economic lot scheduling problem with imperfect production processes and setup times

Deteriorating production processes are common in reality. Although every production process starts in an ‘in-control’ state to produce items of acceptable quality, it may shift to an ‘out-of-control’ state, owing to ageing, at any random time and produce defective items. In the present article, we study the Economic Lot Scheduling Problem (ELSP) with imperfect production processes having significant changeovers between the products. The mathematical models are developed for the ELSP using both the common cycle approach and the time-varying lot sizes approach, taking into account the effects of imperfect quality and process restoration. Numerical examples are cited to illustrate the solution procedures and to compare the performances of the solution methodologies adopted to solve the ELSP.     

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.     

Shipment planning at oil refineries using column generation and valid inequalities

In this paper we suggest an optimization model and a solution method for a shipment planning problem. This problem concerns the simultaneous planning of how to route a fleet of ships and the planning of which products to transport in these ships. The ships are used for moving products from oil refineries to storage depots. There are inventory levels to consider both at the refineries and at the depots. The inventory levels are affected by the process scheduling at the refineries and demand at the depots. The problem is formulated using an optimization model including an aggregated representation of the process scheduling at the refineries. Hence, we integrate the shipment planning and the process scheduling at the refineries. We suggest a solution method based on column generation, valid inequalities, and constraint branching. The solution method is tested on data provided by the Nynas oil refinery company and solutions are obtained within 4 hours, for problem instances of up to 3 refineries, 15 depots, and 4 products when considering a time horizon of 42 days.     

Single-machine batch scheduling minimizing weighted flow times and delivery costs

This paper addresses scheduling a set of jobs on a single machine for delivery in batches to one customer or to another machine for further processing. The problem is a natural extension of that of minimising the sum of weighted flow times, considering the possibility of delivering jobs in batches and introducing batch delivery costs. The scheduling objective adopted is that of minimising the sum of weighted flow times and delivery costs. The extended problem arises in the context of coordination between machine scheduling and a distribution system in a supply chain network. Structural properties of the problem are investigated and used to devise a branch-and-bound solution method. For the special case, when the maximum number of batches is fixed, the branch-and-bound scheme provided shows significant improvements over an existing dynamic-programming algorithm.     

Routing and scheduling in a liquefied natural gas shipping problem with inventory and berth constraints

Liquefied natural gas (LNG) is natural gas that has been transformed to liquid form for the purpose of transportation, which is mainly done by specially built LNG vessels travelling from the production site to the consumers. We describe a real-life ship routing and scheduling problem from the LNG business, with both inventory and berth capacity constraints at the liquefaction port. We propose a solution method where the routing and scheduling decisions are decomposed. The routing decisions consist of deciding which vessels should service which cargoes and in what sequence. The scheduling decisions are then to decide when to start servicing the cargoes while satisfying inventory and berth capacity constraints. The proposed solution method has been tested on several problem instances based on the real-life problem. The results show that the proposed solution method is well suited to solve this LNG shipping problem.