Joint production and preventive maintenance scheduling for a single degraded machine by considering machine failures

Production scheduling and maintenance planning are two interdependent issues that most often have been investigated independently. Although both preventive maintenance (PM) and minimal repair affect availability and failure rate of a machine, only a few researchers have considered this interdependency in the literature. Furthermore, most of the existing joint production and preventive maintenance scheduling methods assume that machine is available during the planning horizon and consider only a possible level for PM. In this research, an integrated model is proposed that coordinates preventive maintenance planning with single-machine scheduling to minimize the weighted completion time of jobs and maintenance cost, simultaneously. This paper not only considers multiple PM levels with different costs, times and reductions in the hazard rate of the machine, but also assumes that a machine failure may occur at any time. To illustrate the effectiveness of the suggested method, it is compared to two situations of no PM and a single PM level. Eventually, to tackle the suggested problem, multi-objective particle swarm optimization and non-dominated sorting genetic algorithm (NSGA-II) are employed and their parameters are tuned Furthermore, their performances are compared in terms of three metrics criteria.     

Online scheduling with machine cost and rejection

In this paper we define and investigate a new scheduling model. In this new model the number of machines is not fixed; the algorithm has to purchase the used machines, moreover the jobs can be rejected. We show that the simple combinations of the algorithms used in the area of scheduling with rejections and the area of scheduling with machine cost are not constant competitive. We present a 2.618-competitive algorithm called OPTCOPY.     

Uniform parallel machine scheduling problems with fixed machine cost

This paper considers two uniform parallel machine scheduling problems with fixed machine cost under the background of cloud manufacturing. The goal is to minimize the makespan with a given budget of total cost, \(\hat{U}\). All the jobs are homogeneous, i.e., the processing times of the jobs are identical. Non-preemptive and preemptive problems are studied. For the non-preemptive problem, we give a \(2[1+1{/}(h-1)]\)-approximation algorithm, where h is the number of the machine which can not be selected the first time. For the preemptive problem, we give an algorithm whose worst-case bound equals to \(1+1{/}(h-1)\). Preliminary experimental results indicate that the proposed algorithms are reasonably accurate compared with the lower bounds.     

Parallel machine scheduling problems considering regular measures of performance and machine cost

This research considers a broad range of scheduling problems in the parallel machines environment. Schedules are evaluated according to two independent components of the objective function: (1) machine cost consisting of a fixed cost and a variable cost; and (2) a regular measure of performance. This study is only one of a few that take the selection of machines among those available as a decision variable. For machine cost with concave functions, we derive the general characteristics of optimal solutions with respect to decisions on the number of machines to use and the way to load the machines. Our analysis is not restricted to the machine cost criterion, but may be extended to other measures with concave functions. Furthermore, we provide a Pareto efficient perspective in understanding the tradeoff between machine cost and any regular measure of performance.     

DEA-based production planning considering influencing factors

When planning production in a centralized decision-making environment using data envelopment analysis (DEA), previous researches usually plan for units by selecting best-practice points within the entire production possibility set or adhering to their original abilities so that potentials may not be fully explored. In practice, there often exist factors that influence units’ production abilities. Difficulties may occur when improving inefficient units’ performances or they can only be improved in a limited room. This paper takes these influencing factors into account to avoid new plans beyond units’ abilities or not fully exploring their potentials. Depending on performance variability, two DEA-based production planning approaches are proposed to optimize the total resource utilization assuming demand changes in the next production season can be forecasted. When performances are improvable, units are grouped according to the influencing factors they face. Simple numerical examples and a real world data set are used to illustrate the proposed approaches.     

Multi-objective parallel machine scheduling problems by considering controllable processing times

This study examines parallel machine scheduling problems with controllable processing times. The processing time of each job can be between lower and upper bounds, and a cost is associated with the processing of a job on a machine. The processing time of a job can be decreased, which may lower the cycle time, although doing so would incur additional costs. This study develops two multi-objective mathematical models, which consist of two and three inconsistent objective functions, respectively. The first model minimizes the total manufacturing cost (TMC) and the total weighted tardiness (TWT) simultaneously, while the second uses makespan (C_max) as an additional objective function. In contrast to conventional mathematical models, efficient solutions are attained using the lexicographic weighted Tchebycheff method (LWT). Experimental results indicate that the LWT yields better-spread solutions and obtains more non-dominated solutions than its alternative, that is the weighted-sum method, which is a widely used yet promising approach to achieve multi-objective optimization. Results of this study also demonstrate that in purchasing machines, the variation in the fixed costs associated with the processing of jobs on machines is critical to reducing TWT. Moreover, using C_max as an additional objective function typically improves TWT and worsens TMC.     

Integrated cellular manufacturing systems design with production planning and dynamic system reconfiguration

This paper presents and analyzes a comprehensive model for the design of cellular manufacturing systems (CMS). A recurring theme in research is a piecemeal approach when formulating CMS models. In this paper, the proposed model, to the best of the authors’ knowledge, is the most comprehensive one to date with a more integrated approach to CMS design, where production planning and system reconfiguration decisions are incorporated. Such a CMS model has not been proposed before and it features the presence of alternate process routings, operation sequence, duplicate machines, machine capacity and lot splitting. The developed model is a mixed integer non-linear program. Linearization procedures are proposed to convert it into a linearized mixed integer programming formulation. Computational results are presented by solving some numerical examples, extracted from the existing literature, with the linearized formulation.     

An integrated production and preventive maintenance planning model

We are given a set of items that must be produced in lots on a capacitated production system throughout a specified finite planning horizon. We assume that the production system is subject to random failures, and that any maintenance action carried out on the system, in a period, reduces the system’s available production capacity during that period. The objective is to find an integrated lot-sizing and preventive maintenance strategy of the system that satisfies the demand for all items over the entire horizon without backlogging, and which minimizes the expected sum of production and maintenance costs. We show how this problem can be formulated and solved as a multi-item capacitated lot-sizing problem on a system that is periodically renewed and minimally repaired at failure. We also provide an illustrative example that shows the steps to obtain an optimal integrated production and maintenance strategy.     

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.     

Optimal production time and number of maintenance actions for an imperfect production system under equal-interval maintenance policy

This paper deals with the optimal production/maintenance (PM) policy for a deteriorating production system which may shift from the in-control state to the out-of-control state while producing items. The process is assumed to have a general shift distribution. Under the commonly used maintenance policy, equal-interval maintenance, the joint optimizations of the PM policy are derived such that the expected total cost per unit time is minimized. Different conditions for optimality, lower and upper bounds and uniqueness properties on the optimal PM policy are provided. The implications of another commonly used policy, to perform a maintenance action only at the end of the production run, are also discussed. Structural properties for the optimal policy are established so that an efficient solution procedure is obtained. In the exponential case, some extensions of the results obtained previously in the literature are presented. A numerical example is provided to illustrate the solution procedure for the optimal production and maintenance policy.     

Minimizing maximum cost on a single machine with two competing agents and job rejection

The classical Lawler’s Algorithm provides an optimal solution to the single-machine scheduling problem, where the objective is minimizing maximum cost, given general non-decreasing, job-dependent cost functions, and general precedence constraints. First, we extend this algorithm to allow job rejection, where the scheduler may decide to process only a subset of the jobs. Then, we further extend the model to a setting of two competing agents, sharing the same processor. Both extensions are shown to be solved in polynomial time.     

Economic production lot-sizing for an unreliable machine under imperfect age-based maintenance policy

This paper is concerned with the joint determination of both economic production quantity and preventive maintenance (PM) schedules under the realistic assumption that the production facility is subject to random failure and the maintenance is imperfect. The manufacturing system is assumed to deteriorate while in operation, with an increasing failure rate. The system undergoes PM either upon failure or after having reached a predetermined age, whichever of them occurs first. As is often the case in real manufacturing applications, maintenance activities are imperfect and unable to restore the system to its original healthy state. In this work, we propose a model that could be used to determine the optimal number of production runs and the sequence of PM schedules that minimizes the long-term average cost. Some useful properties of the cost function are developed to characterize the optimal policy. An algorithm is also proposed to find the optimal solutions to the problem at hand. Numerical results are provided to illustrate both the use of the algorithm in the study of the optimal cost function and the latter’s sensitivity to different changes in cost factors.     

Integrated production and quality model under various preventive maintenance policies

In this paper, we investigate the effect of various preventive maintenance policies on the joint optimisation of the economic production quantity (EPQ) and the economic design of control chart. This has been done for a deteriorating process where the in-control period follows a general probability distribution with increasing hazard rate. In the proposed model, preventive maintenance (PM) activities reduce the shift rate of the system to the out-of-control state proportional to the PM level. For each policy, the model determines the EPQ, the optimal design of the control chart and the optimal preventive maintenance level. The effects of the three PM policies on EPQ and quality costs are illustrated using an example of a Weibull shock model with an increasing hazard rate.     

Coordination mechanisms for parallel machine scheduling

We consider coordination mechanisms for the distributed scheduling of n jobs on m parallel machines, where each agent holding a job selects a machine to process his/her own job. Without a central authority to construct a schedule, each agent acts selfishly to minimize his/her own disutility, which is either the completion time of the job or the congestion time (defined as the load of the machine on which the job is scheduled). However, the overall system performance is measured by a central objective which is quite different from the agents’ objective. In the literature, makespan is often considered as the central objective. We, however, investigate problems with other central objectives that minimize the total congestion time, the total completion time, the maximum tardiness, the total tardiness, and the number of tardy jobs. The performance deterioration of the central objective by a lack of central coordination, referred to as the price of anarchy, is typically measured by the maximum ratio of the objective function value of a Nash equilibrium schedule versus that of an optimal, coordinated schedule. In this paper we give bounds for the price of anarchy for the above objectives. For problems with due date related objectives, the price of anarchy may not be defined since the optimal value may be zero. In this case, we consider the maximum difference between the objective function value of an equilibrium schedule and the optimal value. We refer to this metric as the absolute price of anarchy and analyze its lower and upper bounds.     

Integrated market selection and production planning: complexity and solution approaches

Emphasis on effective demand management is becoming increasingly recognized as an important factor in operations performance. Operations models that account for supply costs and constraints as well as a supplier’s ability to influence demand characteristics can lead to an improved match between supply and demand. This paper presents a class of optimization models that allow a supplier to select, from a set of potential markets, those markets that provide maximum profit when production/procurement economies of scale exist in the supply process. The resulting optimization problem we study possesses an interesting structure and we show that although the general problem is ${\mathcal{NP}}$ -complete, a number of relevant and practical special cases can be solved in polynomial time. We also provide a computationally very efficient and intuitively attractive heuristic solution procedure that performs extremely well on a large number of test instances.     

Single-site strategic capacity planning considering renewal,maintenance, inventory,taxes and cash flow management

This paper deals with strategic capacity planning of a single-site manufacturing system. We propose a MILP model that includes relevant business aspects and possibilities, some of which are only partially or not at all found in the literature. Specifically, we consider decisions on expansion, reduction and renewal of production capacity, and acquisition of storage capacity. In addition, we model aspects such as (a) maintenance costs and unit variable costs depending, respectively, on age and characteristics of facilities, (b) seasonality of the demand and (c) cash flow management, including taxes and, therefore, depreciation of assets. The model maximises the after-tax cash balance at the end of the planning horizon. We also present a computational experiment with 54 instances to show that the model can be solved for a wide range of sizes in a reasonable computing time using comercial software.     

Resource allocation and target setting for parallel production system based on DEA

The paper proposes methodology for resource allocation and target setting based on DEA (data envelopment analysis). It deals with organization can be modeled as consisting of several production units, each of which has parallel production lines. The previous studies in the DEA literature only deal with reallocating/allocating organizational resources to production units and set targets for them. In their researches, the production unit is treated as a black box. In such circumstances, how to arrange the production at production unit level is not clear. This paper serves to generate resource allocation and target setting plan for each production unit by opening the black box. The proposed model exploits production information of production lines in generating production plans. The resulting plan has following characteristics: (1) the performance of each production lines are evaluated under common weights; (2) the weights chose for evaluation keep the efficiency of the entire unit not worse off; (3) the worst behaved production line in the production unit under evaluation are improved as much as possible. Finally, the real data of a production system extracted from extant literature are used to demonstrate the proposed method.     

Optimal system design considering warranty,periodic preventive maintenance,and minimal repair

This paper presents a cost minimisation model for an optimal design of a mixed series-parallel system with deteriorating components. The model incorporates warranty, periodic preventive maintenance, and minimal repair in the design of system configuration. Imperfect repair is adopted to model the effect of preventive maintenance. Both free and pro-rata warranty policies are considered. A numerical example is given to demonstrate the application of this model.     

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.