Multi-objective imperfect maintenance optimization for production system with an intermediate buffer

In several production systems, buffer stocks are built between consecutive machines to ensure the continuity of supply during interruptions of service caused by breakdowns or planned maintenance actions. However, in previous research, maintenance planning is performed individually without considering buffer stocks. In order to balance the trade-offs between them, in this study, an integrated model of buffer stocks and imperfective preventive maintenance for a production system is proposed. This paper considers a repairable machine subject to random failure for a production system by considering buffer stocks. First, the random failure rate of a machine becomes larger with the increase of the number of random failures. Thus, the renewal process is used to describe the number of random failures. Then, by considering the imperfect maintenance action reduced the age of the machine partially, a mathematical model is developed in order to determine the optimal values of the two decision variables which characterize the proposed maintenance strategy and which are: the size of the buffer stock and the maintenance interval. The optimal values are those which minimize the average total cost per time unit including maintenance cost, inventory holding cost and shortage cost, and satisfy the availability constraint. Finally, a heuristic procedure is used to solve the proposed model, and one experiment is used to evaluate the performance of the proposed methods for joint optimization between buffer stocks and maintenance policy. The results show that the proposed methods have a better performance for the joint optimization problem and can be able to obtain a relatively good solution in a short computation time.     

Integrated production-inventory models for imperfect production processes under inspection schedules

This paper deals with inventory models that unify the inventory problems of raw materials and finished products for a single product imperfect manufacturing system. The product is manufactured in batches, and raw materials are jointly replenished from outside suppliers. The system is assumed to deteriorate during the production process. As a result, some proportion of defective items is produced. The defective items are reworked at some cost either before or after a sale. Periodic inspections at equally spaced times and restorations of the production process are used to operate the system. The objective is to minimize the expected total cost for the system. A solution procedure is developed to find a near optimal solution for the basic model. The analysis is extended to various cases where the defect rate is a function of the setup cost, the proportion of defective items is not constant, or the inventory system has a limited capacity for raw materials.     

An artificial neural network based decision support system for solving the buffer allocation problem in reliable production lines

One of the major design problems in the context of manufacturing systems is the well-known Buffer Allocation Problem (BAP). This problem arises from the cost involved in terms of space requirements on the production floor and the need to keep in mind the decoupling impact of buffers in increasing the throughput of the line. Production line designers often need to solve the Buffer Allocation Problem (BAP), but this can be difficult, especially for large production lines, because the task is currently highly time consuming. Designers would be interested in a tool that would rapidly provide the solution to the BAP, even if only a near optimal solution is found, especially when they have to make their decisions at an operational level (e.g. hours). For decisions at a strategic level (e.g. years), such a tool would provide preliminary results that would be useful, before attempting to find the optimal solution with a specific search algorithm.     

Value set iteration for Markov decision processes

This communique presents an algorithm called “value set iteration” (VSI) for solving infinite horizon discounted Markov decision processes with finite state and action spaces as a simple generalization of value iteration (VI) and as a counterpart to Chang’s policy set iteration. A sequence of value functions is generated by VSI based on manipulating a set of value functions at each iteration and it converges to the optimal value function. VSI preserves convergence properties of VI while converging no slower than VI and in particular, if the set used in VSI contains the value functions of independently generated sample-policies from a given distribution and a properly defined policy switching policy, a probabilistic exponential convergence rate of VSI can be established. Because the set used in VSI can contain the value functions of any policies generated by other existing algorithms, VSI is also a general framework of combining multiple solution methods.     

Maintenance interval decision models for a system with failure interaction

Based on the three types of failure interactions, two periodical maintenance cost models were presented for a two-state series system and a three-state series system respectively, which all subjected to failure interactions between units. Consider any unit fails would cause damages to other units. The failure interaction influences included instantaneous damages and continuous damages between units. The result indicated that failure interactions will shorten system preventive maintenance interval, if the preventive maintenance strategy is based on the cost.     

Multiple lot-sizing decisions with an interrupted geometric yield and variable production time

This study examines a multiple lot-sizing problem for a single-stage production system with an interrupted geometric distribution, which is distinguished in involving variable production lead-time. In a finite number of setups, this study determined the optimal lot-size for each period that minimizes total expected cost. The following cost items are considered in optimum lot-sizing decisions: setup cost, variable production cost, inventory holding cost, and shortage cost. A dynamic programming model is formulated in which the duration between current time and due date is a stage variable, and remaining demand and work-in-process status are state variables. This study then presents an algorithm for solving the dynamic programming problem. Additionally, this study examines how total expected costs of optimal lot-sizing decisions vary when parameters are changed. Numerical results show that the optimum lot-size as a function of demand is not always monotonic.     

An exact iterative search algorithm for constrained Markov decision processes

This communique provides an exact iterative search algorithm for the NP-hard problem of obtaining an optimal feasible stationary Markovian pure policy that achieves the maximum value averaged over an initial state distribution in finite constrained Markov decision processes. It is based on a novel characterization of the entire feasible policy space and takes the spirit of policy iteration (PI) in that a sequence of monotonically improving feasible policies is generated and converges to an optimal policy in iterations of the size of the policy space at the worst case. Unlike PI, an unconstrained MDP needs to be solved at iterations involved with feasible policies and the current best policy improves all feasible policies included in the union of the policy spaces associated with the unconstrained MDPs.     

Average cost optimal policies for Markov control processes with Borel state space and unbounded costs

We show the existence of average cost optimal stationary policies for Markov control processes with Borel state space and unbounded costs per stage, under a set of assumptions recently introduced by L.I. Sennott (1989) for control processes with countable state space and finite control sets.     

An optimal production and inspection strategy with preventive maintenance error and rework

This study considers the integrated problem of production, preventive maintenance (PM), inspection, and inventory for an imperfect production process where rework and PM error exist. PM is performed when the process is in a controlled state. The correct implementation of PM results in a lower system failure rate, whereas a PM error results in the system shifting to the out-of-control state with a certain probability. The age of the system after PM is correlated with the level of PM performed. When the process in an out-of-control state produces a certain percentage of non-conforming items, we assume that a certain proportion of the non-conforming items can be reworked into conforming items. In a deteriorating production system, we determine the optimal inspection interval, inspection frequency, and production quantity that will yield the maximal unit expected profit. Numerical analyses are used to investigate the effectiveness of imperfect PM and to explore the effect of rework and PM error on profit.     

Combining a maintenance center M/M/c/m queue into the economic production quantity model with stochastic machine breakdowns and repair

This article considers a production system in which “m” identical machines produce nonidentical products at production rates. Products made by each machine are on the other hand consumed at a specific demand rate. Machines may be affected by unwanted breakdowns. Machines break down according to a Poisson distribution with equal rates and the failed machines are sent to maintenance center for repair which is consisted of “c” servers or servicemen. However, Number of machines is greater than number of servicemen (m > c). Hence, if the number of failed machines is greater than that of servicemen, the machines have to be put in a queue. Machines are put in one queue with the order of queue being FCFS. The queue has a typical M/M/c/m system. If machines are broken down during production, shortage will occur. This problem has been considered to obtain a single production cycle for the machines and an optimum number of the servers such that costs are minimized. For this purpose, distribution of waiting time for machines in repair center is calculated and a cost function is formed. Steepest descent and direct search methods are applied in this work to obtain optimal production cycle and maintenance servers, respectively. The proposed methods are studied using a comprehensive example.     

Integrated production scheduling and maintenance policy for robustness in a single machine

This paper addresses the problem of finding robust production and maintenance schedules for a single machine with failure uncertainty. Both production and maintenance activities occupy the machine׳s capacity, while production depletes the machine׳s reliability and maintenance restores its reliability. Thus, we propose a proactive joint model which simultaneously determines the production scheduling and maintenance policy to optimize the robustness of schedules. Then, a three-Phase heuristic algorithm is devised to solve the mathematic model. Computational results indicate that the performance of solution can be significantly improved using our algorithm compared with the solutions by the traditional way. Furthermore, the balance of quality robustness and solution robustness and the impact of jobs׳ due dates are explored in detail.     

Determination of optimal size of the de-jitter buffer of a receiving router

The influence of the size of the de-jitter buffer of a receiving router and of the network load on the transmission quality of voice traffic is investigated by means of simulation modeling. The optimal size of the de-jitter buffer that supports an acceptable level of loss of voice packets and a propagation time of the voice signal that corresponds to accepted standards is determined.     

A dynamic programming algorithm for the Knapsack Problem with Setup

The Knapsack Problem with Setup (KPS) is a generalization of the classical Knapsack problem (KP), where items are divided into families. An individual item can be selected only if a setup is incurred for the family to which it belongs. This paper provides a dynamic programming (DP) algorithm for the KPS that produces optimal solutions in pseudo-polynomial time. In order to reduce the storage requirements of the algorithm, we adopt a new technique that consists in converting a KPS solution to an integer index. Computational experiments on randomly generated test problems show the efficiency of the DP algorithm compared to the ILOG׳s commercial product CPLEX 12.5.     

On a system of first-order quasi-variational inequalities connected with the optimal switching problem

In this paper we prove the existence of the maximum bounded Lipschitz continuous solution to a system of first-order quasi-variational inequalities. The method is to discretize by an Euler scheme the characteristic lines of the differential operator appearing in the system and to solve by iteration the corresponding approximate problem. The solution is interpreted as the value function of a deterministic optimal switching problem.     

Recursive operation time maximization model for the maintenance of power generation equipment

Repairable equipment requires preventive maintenance (PM) to maintain proper function. An appropriate PM strategy can extend the life of equipment and reduce variable costs. A power generation company in Taiwan that has a fixed-period PM strategy is studied. However, a fixed-period PM strategy is usually not an optimal solution for maintaining equipment those ages gradually. An age-related dynamical model is designed for creating a timely maintenance schedule that extends the life of equipment and improves its efficiency. A recursive mathematical programming model that considers regular maintenance, emergent maintenance, and maintenance improvement factors is used to obtain the optimal equipment PM schedule. An empirical experiment with the nonperiodic PM schedule computed using the proposed method was conducted. Results show a significant reduction in the PM cost and an extension of the life of equipment.     

L-class enumeration algorithms for a discrete production planning problem with interval resource quantities

A discrete production planning problem which may be formulated as the multidimensional knapsack problem is considered, while resource quantities of the problem are supposed to be given as intervals. An approach for solving this problem based on using its relaxation set is suggested. Some L-class enumeration algorithms for the problem are described. Results of computational experiments are presented.     

An efficient algorithm for optimal control of PWA systems with polyhedral performance indices

We present an algorithm for the computation of explicit optimal control laws for piecewise affine (PWA) systems with polyhedral performance indices. The algorithm is based on dynamic programming (DP) and represents an extension of ideas initially proposed in Kerrigan and Mayne [(2003). Optimal control of constrained, piecewise affine systems with bounded disturbances. In Proceedings of the 41st IEEE conference on decision and control, Las Vegas, Nevada, USA, December], and Baoti? et al. [(2003). A new algorithm for constrained finite time optimal control of hybrid systems with a linear performance index. In Proceedings of European control conference, Cambridge, UK, September]. Specifically, we show how to exploit the underlying geometric structure of the optimization problem in order to significantly improve the efficiency of the off-line computations. An extensive case study is provided, which clearly indicates that the algorithm proposed in this paper may be preferable to other schemes published in the literature.     

Approximations for optimal stopping of a piecewise-deterministic process

This paper deals with approximation techniques for the optimal stopping of a piecewise-deterministic Markov process (P.D.P.). Such processes consist of a mixture of deterministic motion and random jumps. In the first part of the paper (Section 3) we study the optimal stopping problem with lower semianalytic gain function; our main result is the construction of ε-optimal stopping times. In the second part (Section 4) we consider a P.D.P. satisfying some smoothness conditions, and forN integer we construct a discretized P.D.P. which retains the main characteristics of the original process. By iterations of the single jump operator from ℝ ^N to ℝ ^N , each iteration consisting ofN one-dimensional minimizations, we can calculate the payoff function of the discretized process. We demonstrate the convergence of the payoff functions, and for the case when the state space is compact we construct ε-optimal stopping times for the original problem using the payoff function of the discretized problem. A numerical example is presented.     

Joint production,inspection and maintenance control policies for deteriorating system under quality constraint

This paper studies the integration of production, sampling inspection and age-based maintenance planning for an unreliable production system subject to gradual deterioration. The deterioration process of the production unit has a twofold effect on its reliability and product quality. To mitigate the effects of such deterioration, an age-based major maintenance can be conducted, which denotes a perfect repair that restores the production unit to initial conditions. The quality control is performed through a sampling plan that inspects a fraction of the parts produced. The problem further considers that the optimal decision must be determined under a constraint on the outgoing quality required by the final customer. In this domain, standard sampling procedures are applicable only to production process that are statistically stable and under control. Nevertheless, such sampling plans disregard the interaction with production management and maintenance issues and they do not consider the effects of deterioration. In this paper a new joint control policy considering the interactions between production-quality and maintenance is proposed. A stochastic mathematical model is developed through specialized optimization techniques to solve such quality constrained problem. Numerical examples are provided to illustrate the usefulness of the proposed approach and to study the interactions between production-quality and maintenance strategies. An extensive sensitivity analysis and a comparative study are conducted to illustrate the effectiveness of the obtained joint control policy.     

On the value function for nonautonomous optimal control problems with infinite horizon

In this paper we consider nonautonomous optimal control problems of infinite horizon type, whose control actions are given by L¹-functions. We verify that the value function is locally Lipschitz. The equivalence between dynamic programming inequalities and Hamilton–Jacobi–Bellman (HJB) inequalities for proximal sub (super) gradients is proven. Using this result we show that the value function is a Dini solution of the HJB equation. We obtain a verification result for the class of Dini sub-solutions of the HJB equation and also prove a minimax property of the value function with respect to the sets of Dini semi-solutions of the HJB equation. We introduce the concept of viscosity solutions of the HJB equation in infinite horizon and prove the equivalence between this and the concept of Dini solutions. In the Appendix we provide an existence theorem.