The maintenance problem with safety-critical components is significant for the economical benefit of companies. Motivated by a practical asset maintenance project, a new joint replacement maintenance problem is introduced in this paper. The dynamics of the problem are modelled as a Markov decision process, whose action space increases exponentially with the number of safety-critical components in the asset. To deal with the curse of dimensionality, we identify a key property of the optimal solution: the optimal performance can always be achieved in a class of policies which satisfy the so-called shortest-remaininglifetime- first (SRLF) rule. It reduces the action space from O(2n ) to (On ), where is the number of safety-critical components. To further speed up the optimization procedure, some interesting properties of the optimal policy are derived. Combining the SRLF rule and the neuro-dynamic programming (NDP) methodology, we develop an efficient on-line algorithm to optimize this maintenance problem. This algorithm can handle the difficulties of large state space and large action space. Besides the theoretical proof, the optimality and efficiency of the SRLF rule and the properties of the optimal policy are also illustrated by numerical examples. This work can shed some insights to the maintenance problems in a more general situation.

Finite-Stage Markov Decision Process (MDP) supplies a general framework for many practical problems when only the performance in a finite duration is of interest. Dynamic programming (DP) supplies a general way to find the optimal policies but is usually practically infeasible, due to the exponentially increasing policy space. Approximating the finitestage MDP by an infinite-stage MDP reduces the search space but usually does not find the optimal stationary policy, due to the approximation error. We develop a method that finds the optimal stationary policies for the finite-stage MDP. The method is based on performance potentials, which can be estimated through sample paths and thus suits practical application.

The pervasive application of digital computer in control and optimization techniques forces us to consider the constraint of limited memory space when dealing with large scale practical systems. As an example, we consider the famous Witsenhausen counterexample with the new constraint of limited memory space in this paper. The main difficulty is how to sample strategies that can be stored in the given memory space efficiently. The concept of Kolmogorov complexity measures the minimal memory space to store a strategy (i.e., simple strategies), but is incomputable. To overcome this difficulty, we propose a method based on ordered binary decision diagram to sample only simple strategies. Besides the high sampling efficiency which is demonstrated by numerical testing, the proposed sampling method can be easily combined with optimization algorithms and performance evaluation techniques. As an example, we show how to combine ordinal optimization, numerical integration, and the proposed sampling method to solve the Witsenhausen problem with the constraint of limited memory space. We hope this work can shed some insights to computer-based optimization problems with memory space constraint in a more general situation.

Due to the abundant application background, the optimization of maintenance problem has been extensively studied in the past decades. Besides the well-known difficulty of large state space and large action space, the pervasive application of digital computers forces us to consider the new constraint of limited memory space. The given memory space restricts what strategies can be explored during the optimization procedure. By explicitly quantifying the minimal memory space to store a strategy using support vector machine, we propose to describe simple strategies exactly and only approximate complex strategies. This selective approximation can best utilize the given memory space for any description mechanism. We use numerical results on illustrative examples to show how the selective approximation improves the solution quality. We hope this work sheds some insights to best utilize the memory space for practical engine maintenance strategy optimization problems.

Planning for a complex remanufacturing systems is often an NP-hard problem in terms of computational complexity and simulation is usually the only available but very time-consuming approach in many cases. Ordinal optimization offers an efficient framework for simulation based optimization approaches. In this paper, a new constrained ordinal optimization method is presented for solving remanufacturing planning problems. The scheme of "Horse Race" with Feasibility Model (HRFM) is developed to select the set of good enough plans. The rough set method in machine learning and knowledge discovery is applied to generate rules for feasibility determination. This method is compared with the Blind Picking with Feasibility Model (BPFM) method. Numerical testing of a practical remanufacturing system shows that the HRFM method presented in this paper is more efficient to meet the same required alignment probability.

usually very time consuming. Optimizing the system performance becomes even more computationally infeasible. Ordinal optimization (OO) is a technique introduced to attack this difficulty in system design by looking at “order” in performances among designs instead of “value” and providing a probability guarantee for a good enough solution instead of the best for sure. The selection rule, known as the rule to decide which subset of designs to select as the OO solution, is a key step in applying the OO method. Pairwise elimination and round robin comparison are two selection rule examples. Many other selection rules are also frequently used in the ordinal optimization literature. To compare selection rules, we first identify some general facts about selection rules. Then we use regression functions to quantify the efficiency of a group of selection rules, including some frequently used rules. A procedure to predict good selection rules is proposed and verified by simulation and by examples. Selection rules that work well most of the time are recommended.

The balance between the supply and demand of some kind of resource is critical for the functionality and security of many complex networks. Local contingencies that break this balance can cause a global collapse. These contingencies are usually dealt with by spare capacity, which is costly especially when the network capacity (the total amount of the resource generated/consumed in the network) grows. This paper studies the relationship between the spare capacity and the collapse probability under separation contingencies when the network capacity grows. Our results are obtained based on the analysis of the existence probability of balanced partitions, which is a measure of network security when network splitting is unavoidable. We find that a network with growing capacity will inevitably collapse after a separation contingency if the spare capacity in each island increases slower than a linear function of the network capacity and there is no suitable global coordinator.

Electric power network is a fundamental facility in modern society. The importance to ensure and enhance the security of the power network can never be over emphasized. In this paper, we study how the topology of a power network restricts the security. By focusing on the power balanced condition which is necessary for the security after line outage contingencies, we show that a practical power network cannot avoid collapse. Using a method based on ordered binary decision diagram (OBDD) that fast enumerates the line outages causing network collapses, we obtain an upper bound for power network security, and indicate the transmission lines that are critical to power network security. This method is demonstrated on an IEEE 30-bus network. We hope this work brings insights to the understanding of why power networks cannot avoid collapse and how to enhance the security of an electric power network.

Coordinating supply chains has been a major issue in supply chain management research. This paper focuses on the coordination of supply chains with downside-risk-averse agents. Motivating by the revenue sharing contract, we developed the sufficient conditions for the coordination of the supply chain with one downside-risk-averse agent. Following the sufficient conditions, the downside protection contract thus developed also allows arbitrary allocation of the profit between the supplier and the retailer. We also develop the necessary condition for the coordination of the supply chain when both the supplier and the retailer are downside-risk averse. We hope this work sheds some insights to the study of the coordination of supply chains with downside-risk-averse agents in more general situations.