A Genetic Algorithm for the Allocation of Buffer Storage Capacities in a Production Line with Unreliable Machines

In this paper, we consider a flow-line manufacturing system organized as a series of workstations separated by finite buffers. The failure and repair times of machines are supposed to be exponentially distributed. The production rate of each machine is deterministic, and different machines may have different production rates. The buffer allocation problem consists in determining the buffer capacities with respect to a given optimality criterion, which depends on the average production rate of the line, the buffer acquisition and installation cost, and the inventory cost. For this problem we propose a genetic algorithm where the tentative solutions are evaluated with an approximate method based on the Markov-model aggregation approach.     

Complexity of flow shop scheduling problems with transportation constraints

In most manufacturing and distribution systems, semi-finished jobs are transferred from one processing facility to another by transporters such as Automated Guided Vehicles, robots and conveyors, and finished jobs are delivered to warehouses or customers by vehicles such as trucks.This paper investigates two-machine flow shop scheduling problems taking transportation into account. The finished jobs are transferred from the processing facility and delivered to customers by truck. Both transportation capacity and transportation times are explicitly taken into account in these models. We study the class of flow shop problems by analysing their complexity. For the makespan objective function, we prove that this problem is strongly NP-hard when the capacity of a truck is limited to two or three parts with an unlimited buffer at the output of the each machine. This problem with additional constraints, such as blocking, is also proven to be strongly NP-hard.     

Profit maximization in flexible serial queueing networks

We analyze the tradeoff between efficiency and service quality in tandem systems with flexible servers and finite buffers. We reward efficiency by assuming that a revenue is earned each time a job is completed, and penalize poor service quality by incorporating positive holding costs. We study the dynamic assignment of servers to tasks with the objective of maximizing the long-run average profit. For systems of arbitrary size, structured service rates, and linear or nonlinear holding costs, we determine the server assignment policy that maximizes the profit. For systems with two stations, two servers with arbitrary service rates, and linear holding costs, we show that the optimal server assignment policy is of threshold type and determine the value of this threshold as a function of the revenue and holding cost. The threshold can be interpreted as the best possible buffer size, and hence our results prove the equivalence of addressing service quality via a holding cost and via limiting the buffer size. Furthermore, we identify the optimal buffer size when each buffer space comes at a cost. We provide numerical results that suggest that the optimal policy also has a threshold structure for nonlinear holding costs. Finally, for larger systems with arbitrary service rates, we propose effective server assignment heuristics.     

Multiple bottleneck assignment problem

We consider the multiple bottleneck assignment problem which subsumes the well known min-sum and bottleneck assignment problems. The problem arises in the context of flexible manufacturing systems, where the objective is to maximize the throughput of a production system with several flow shops, running in parallel, to produce a product. The problem is known to be strongly NP-hard. We propose a new algorithm for obtaining sharp lower bounds to the optimal objective value. Computational experiments are conducted to show the improvement over existing methods.     

Mathematical programming formulations for approximate simulation of multistage production systems

Mathematical programming representation has been recently used to describe the behavior of discrete event systems as well as their formal properties. This new way of representing discrete event systems paves the way to the creation of simpler mathematical programming models that reduce the complexity of the system analysis. The paper proposes an approximate representation for a class of production systems characterized by several stages, limited buffer capacities and stochastic production times. The approximation exploits the concept of a time buffer, modeled as a constraint that put into a temporal relationship the completion times of two customers in a sample path. The main advantage of the proposed formulation is that it preserves its linearity even when used for optimization and, for such a reason, it can be adopted in simulation–optimization problems to reduce the initial solution space. The approximate formulation is applied to relevant problems such as buffer capacity allocation in manufacturing systems and control parameters setting in pull systems.     

Production planning for hybrid remanufacturing and manufacturing system with component recovery

In this paper, we address component recovery under the condition of limited resources from the OEM's (Original Equipment Manufacturer's) standpoint. We develop a linear programming model for a hybrid remanufacturing and manufacturing system for production planning problems with deterministic returns. In this paper, a data set from an OEM that both remanufactures and manufactures the products is used to demonstrate the performance of the proposed model. Subsequently, an analysis of the impact of the remanufactured product’s price and the quantity of returns on revenue and total cost will be discussed. We have found that uncertain factors of manufacturing influence the profit and uncertain factors of remanufacturing influence the production planning, such as the rate of the yield on component remanufacturing and the quantity of returns.     

带缓冲串行生产系统预防性维护建模及运行参数优化研究

为了保证串行生产系统的产能和提高系统可靠性,提出了带缓冲区的串行生产系统预防性维护决策模型。首先,分析了生产线各执行单元可靠性和运行参数之间的关系,建立了考虑执行单元运行参数和缓冲库存的维护模型。在此基础上,结合串行生产线的特点,建立综合考虑维护成本、有效运行速度和缓冲库存的多目标优化函数。最后,构建启发式算法求解目标函数,并以串行包装生产线为例进行仿真实验分析,结果表明本文所建模型是有效且实用的。     

Human resources scheduling to improve the product quality according to exhaustion limit

The role of human resources in manufacturing systems is very significant, and without efficient human resources we encounter high-price products with low quality. To improve the efficiency of human resources, we need to provide an optimal working schedule for each worker in production period. In this paper, we proposed a mixed-integer nonlinear model to find the best working schedule based on product quality cost and workers reliability. In this model, if the worker’s exhaustion level reaches a specific limit, the worker can rest to increase his reliability level and an accommodator should work instead of him. Since the proposed model is NP-hard, we used an artificial immune system to provide the best working schedule. The results indicate that this model can provide efficient and effective human resources schedule in manufacturing systems.     

A polyhedral approach to a production planning problem

Production planning in manufacturing industries is concerned with the determination of the production quantities (lot sizes) of some items over a time horizon, in order to satisfy the demand with minimum cost, subject to some production constraints. In general, production planning problems become harder when different types of constraints are present, such as capacity constraints, minimum lot sizes, changeover times, among others. Models incorporating some of these constraints yield, in general, NP-hard problems. We consider a single-machine, multi-item lot-sizing problem, with those difficult characteristics. There is a natural mixed integer programming formulation for this problem. However, the bounds given by linear relaxation are in general weak, so solving this problem by LP based branch and bound is inefficient. In order to improve the LP bounds, we strengthen the formulation by adding cutting planes. Several families of valid inequalities for the set of feasible solutions are derived, and the corresponding separation problems are addressed. The result is a branch and cut algorithm, which is able to solve some real life instances with 5 items and up to 36 periods. This revised version was published online in June 2006 with corrections to the Cover Date.     

Network flow problems with pricing decisions

This paper considers a class of network flow problems in which the demand levels of the nodes are determined through pricing decisions representing the revenue received per unit demand at the nodes. We must simultaneously determine the pricing decisions and the network flow decisions in order to maximize profits, i.e., the revenues received from the pricing decisions minus the cost of the network flow decisions. Specializations of this class of problems have numerous applications in supply chain management. We show that the class of problems with a single pricing decision throughout the network can be solved in polynomial time under both continuous pricing restrictions and integer pricing restrictions. For the class of problems with customer-specific pricing decisions, we provide conditions under which the problem can be solved in polynomial-time for continuous pricing restrictions and prove that the problem is NP-hard for integer pricing restrictions.     

Balancing U-lines in a multiple U-line facility

U-shaped production lines and facilities consisting of many such lines are important parts of modem manufacturing systems. The problem of balancing and rebalancing U-line facilities is studied in this paper. Like the traditional line balancing problem this problem is NP-hard. The objective is to assign tasks to a minimum number of regular, crossover, and multiline stations while satisfying cycle time, precedence, location, and station-type constraints. A secondary objective is to concentrate the idle time in one station so that improvement efforts can be focused there in accordance with modern just-in-time principles. A reaching dynamic programming algorithm is presented for determining optimal balances. It is effective for balancing and rebalancing facilities with any number of U-lines, provided that individual U-lines do not have more than 22 tasks and do not have wide, sparse precedence graphs.     

可转包的双目标单机排序问题（英文）

Scheduling with outsourcing is studied in this paper. It is assumed that both manufacturer and subcontractor have a single machine to process n jobs. The manufacturer needs to determine simultaneously a set of outsourced jobs and the schedule of the jobs in-house such that two criterias, i.e., outsourcing cost and production cost, are minimized.The production cost is measured by the number of tardy jobs or the total tardiness of jobs in-house, and the outsourcing cost is proportional to the total processing time of jobs outsourced. Two kinds of problems with different criterias are considered. We analyze the computational complexity and provide pseudo-polynomial time optimization algorithms for the NP-hard version of the problems.     

Cyclic scheduling for F.M.S.: Modelling and evolutionary solving approach

This paper concerns the domain of flexible manufacturing systems (FMS) and focuses on the scheduling problems encountered in these systems. We have chosen the cyclic behaviour to study this problem, to reduce its complexity. This cyclic scheduling problem, whose complexity is NP-hard in the general case, aims to minimise the work in process (WIP) to satisfy economic constraints. We first recall and discuss the best known cyclic scheduling heuristics. Then, we present a two-step resolution approach. In the first step, a performance analysis is carried out; it is based on the Petri net modelling of the production process. This analysis resolves some indeterminism due to the system’s flexibility and allows a lower bound of the WIP to be obtained. In the second step, after a formal model of the scheduling problem has been given, we describe a genetic algorithm approach to find a schedule which can reach the optimal production speed while minimizing the WIP. Finally, our genetic approach is validated and compared with known heuristics on a set of test problems.     

Min–max and min–max (relative) regret approaches to representatives selection problem

The following optimization problem is studied. There are several sets of integer positive numbers whose values are uncertain. The problem is to select one representative of each set such that the sum of the selected numbers is minimum. The uncertainty is modeled by discrete and interval scenarios, and the min?Cmax and min?Cmax (relative) regret approaches are used for making a selection decision. The arising min?Cmax, min?Cmax regret and min?Cmax relative regret optimization problems are shown to be polynomially solvable for interval scenarios. For discrete scenarios, they are proved to be NP-hard in the strong sense if the number of scenarios is part of the input. If it is part of the problem type, then they are NP-hard in the ordinary sense, pseudo-polynomially solvable by a dynamic programming algorithm and possess an FPTAS. This study is motivated by the problem of selecting tools of minimum total cost in the design of a production line.     

Statistical search methods for lotsizing problems

This paper reports on our experiments with statistical search methods for solving lotsizing problems in production planning. In lotsizing problems the main objective is to generate a minimum cost production and inventory schedule, such that (i) customer demand is satisfied, and (ii) capacity restrictions imposed on production resources are not violated. We discuss our experiences in solving these, in general NP-hard, lotsizing problems with popular statistical search techniques like simulated annealing and tabu search. The paper concludes with some critical remarks on the use of statistical search methods for solving lotsizing problems.     

Supporting offshoring and nearshoring decisions for mass customization manufacturing processes

Offshore countries attract companies for a possible relocation of production processes through extremely low worker wages. Particularly, mass production processes seem to be highly appropriate for a relocation. However, while the impact of wage reductions can be directly estimated, an appropriate determination of additional cost consequences proves to be a complex task. For instance, on account of lower education standards and higher fluctuation rates, the average worker skills in offshore countries are often significantly lower than in high-wage countries like the United States. In order to appropriately analyze and evaluate the resulting tradeoff between wages and worker skills for mass customization manufacturing systems, this paper introduces a new approach that comprises a detailed mixed-model assembly line balancing. This approach provides a direct comparison of the estimated variable manufacturing costs by generating a country-dependent line layout for all competing locations. In order to validate the efficiency of the balancing approach and, in particular, derive general implications for management, several test series with various country configurations were executed. First, by attaining improvement rates of up to 40%, the capability of a generated Tabu Search procedure for finding appropriate line layouts was proven. Second, as the main result, the complexity of the variant program was identified as a crucial factor for offshoring decisions since it substantially affects variable manufacturing costs. This was particularly proven for countries with low worker skills, which attract offshoring/nearshoring through exceptionally low labor costs. Hence, companies that consider outsourcing production systems to those countries are strongly hold to examine these decisive effects thoroughly. Regarding this, offshoring becomes very promising for manufacturing processes characterized by a moderate variant complexity level.     

基于产品生命周期的闭环供应链定价和协调策略研究

研究产品生命周期条件下一个制造商、一个零售商组成的闭环供应链的定价和协调策略:制造商第一周期只生产新品,从第二周期开始生产再制造品,并负责回收。建立了两周期、多周期和无限周期下的分散决策模型和多周期下的集中决策模型,得到最优定价和生产策略。结果表明:两周期中,制造商和零售商应根据不同的成本节约额制定不同的批发价、零售价和生产量。多周期中,当成本节约额比较小时,除第一和最后一个周期外,制造商和零售商应采取相同的定价和生产策略;当成本节约额比较大时,除第一和最后两个周期外,制造商和零售商应采取相同的定价和生产策略。无限周期中,除第一周期以外,制造商和零售商都应该采取相同的定价和生产策略。在有限周期情况下,制造商和零售商应通过在前期制定比较低的批发价和零售价,以提高生产量和销售量,使得后期的回收量增大,达到降低成本的目的。通过引入收益共享契约制定合适的批发价和销售收入及再制造收益共享比率可以协调整个闭环供应链。算例验证了上述结论。     

Workstage repair policies for sequential manufacturing systems

Dynamic stage repair policies where the stage repair probabilities are determined by the number of items in the buffer are examined through a model of a manufacturing system with two unreliable workstages connected by a minimal intermediate storage buffer. Definitions for workstage availability and line balance are extended for sequential manufacturing systems with dynamic repair policies. A measure for stage repair inputs and a general form of dynamic stage repair policies are presented. The steady-state probabilities of the resultant state-inhomogeneous Markov chain are computed by an efficient solution procedure. Insights obtained from extensive numerical studies are illustrated and discussed.     

A Hybrid Meta-Heuristic for the Batching Problem in Just-In-Time Flow Shops

This paper is concerned with a batching problem encountered in the context of production smoothing in just-in-time manufacturing systems. The manufacturing system of interest is a multi-level system with a flow-shop at the final level. We develop a hybrid meta-heuristic method to solve the batching problem, which is known to be NP-hard. We hybridize strategic oscillation (SO) and path re-linking (PR) methods and compare the hybrid method's performance to two benchmark methods: a bounded dynamic programming method developed for the problem earlier and an implementation of robust tabu search (RTS) meta-heuristic. Through a computational study, we show that the proposed hybrid method is effective in solving the problem within several minutes of computer time and yielding near-optimal results.     

A Petri Net based algorithm for minimizing total tardiness in flexible manufacturing systems

Petri Nets have been extensively used for modeling and simulating of the dynamics of flexible manufacturing systems. Petri Nets can capture features such as parallel machines, alternative routings, batch sizes, multiplicity of resources, to name but a few. However, Petri Nets have not been very popular for scheduling in manufacturing due to the Petri Net “state explosion” combined with the NP-hard nature of many of such problems. A promising approach for scheduling consists of generating only portions of the Petri Net state space with heuristic search methods. Thus far, most of this scheduling work with Petri Nets has been oriented to minimize makespan. The problem of minimizing total tardiness and other due date-related criteria has received little attention. In this paper, we extend the Beam A^* Search algorithm presented in a previous work with capability to handle the total tardiness criterion. Computational tests were conducted on Petri Net models of both flexible job shop and flexible manufacturing systems. The results suggest that the Petri Net approach is also valid to minimize due date related criteria in flexible systems.