dynamic programming

In this research, we study an optimal overhaul–replacement policy of a multi-degraded repairable system sold with a free replacement warranty. In the proposed replacement policy, a maintenance action and failure are dependent on a system degradation level and the system age, and hence the replacement model will provide more effective maintenance decisions. Failure of the system is modeled using a rate of occurrence of failure for the system, which is as a function of a degradation level of the system and its age. We develop the optimal replacement policy for a multi-degraded repairable system from the buyer’s point of view, who plans to use the system for a horizon planning T. The buyer conducts a periodic evaluation and selects an appropriate maintenance option based on the revealed system condition together with the system operational age. At each evaluation point, three alternative decisions are available, i.e., keep running the system, overhaul, or replace it with a new one. We formulate the sequential decision (keep, overhaul, or replace) problem as a dynamic programming model and obtain an optimal policy that minimizes total cost over T. Numerical examples are presented using several hypothetical data sets to illustrate the structure of optimal solution and its sensitivity against the change in parameter values. The main contribution of the paper is to offer a decision tool that will help in deciding the overhaul–replacement action based on the degradation level and the operational age of the system.

Investment problem is one of the most important and interesting optimization problems. This problem becomes more difficult when we deal with it in an uncertain and vague environment with chaos data. This paper attempts to study the investment problem with uncertain return data. These data are represented as chaos numbers. Dynamic programming is applied to obtain the optimal policy and the corresponding best return. Finally, a numerical example is given to illustrate the utility, effectiveness, and applicability of the approach to the problem.

Supplier selection is one of the critical issues in the supply chain. Green supplier selection is performed based on the assessment of quantitative and qualitative criteria in two fields, including economic, environmental attributes. In this study, a two-level supply chain model has been proposed for green supplier selection and order allocation in a multi-period and single-product environment. In the first phase, the analytic hierarchical process (AHP) method is used to rank the suppliers and in the second phase, a model is designed based on constraints such as demand, capacity, and allowed level of inventory and shortage to maximize the total value of purchase (TVP) and total profit of purchase (TPP). Demand is assumed to be stochastic in different periods. Thus random demand leads to create the various scenarios in the planning horizon. A new integrated approach is presented based on stochastic programming and dynamic programming to solve the problem. The incorporation of stochastic demand condition and application of dynamic programming is a novel idea. Finally, a Numerical example is provided to investigate the procedure in details.

In this article, we present a sequential sampling plan for a three-state machine replacement problem using dynamic programming model. We consider an application of the Bayesian Inferences in a machine replacement problem. The machine was studied at different states of good, medium and bad. Discount dynamic programming (DDP) was applied to solve the three-state machine replacement problem, mainly to provide a policy for maintenance by considering item quality and to determine an optimal threshold policy for maintenance in the finite time horizon.  A decision tree based on the sequential sampling which included the decisions of renew, repair and do-nothing was implemented in order to achieve a threshold for making an optimized decision minimizing expected final cost. According to condition-based maintenance, where the point of defective item is placed in continuing sampling area, we decided to repair the machine or to continue sampling. A sensitivity analysis technique shows that the optimal policy can be very sensitive.