The inventory replenishment policy in an uncertain production-inventory-routing system

<p style='text-indent:20px;'>This study introduces an uncertain programming model for the integrated production routing problem (PRP) in an uncertain production-inventory-routing system. Based on uncertainty theory, an uncertain programming model is proposed firstly and then transformed into a deterministic and equivalent model. The study further probes into different types of replenishment policies under the condition of uncertain demands, mainly the uncertain maximum level (UML) policy and the uncertain order-up to level (UOU) policy. Some inequalities are put forward to define the UML policy and the UOU policy under the uncertain environments, and the influences brought by uncertain demands are highlighted. The overall costs with optimal solution of the uncertain decision model grow with the increase of the confidence levels. And they are simultaneously affected by the variances of uncertain variables but rely on the value of confidence levels. Results show that when the confidence levels are not less than 0.5, the cost difference between the two policies begins to narrow along with the increase of the confidence levels and the variances of uncertain variables, eventually being trending to zero. When there are higher confidence levels and relatively large uncertainty in realistic applications, in which the solution scale is escalated, being conducive to its efficiency advantage, the comprehensive advantages of the UOU policy is obvious.</p>

An uncertain programming model for preventive maintenance scheduling

Purpose The purpose of this paper is to illustrate an uncertain programming model for scheduling of preventive maintenance (PM) actions. The PM scheduling, in which PM actions are performed under fixed intervals, is solved by grey systems theory. Design/methodology/approach The paper applied the grey evaluation method based on triangular whitenization weight functions which includes two classes: endpoint evaluation method and center-point evaluation method. Findings Two methods give the same results based on endpoint and center-point triangular whitenization weight functions. For validation, the results were compared by Cassady’s method. Originality/value The scheduling of PM is crucial in reliability and maintenance engineering. Hundreds of parts compose complex machines that require replacement and/or repairing. It is helpful to reduce the outage loss on frequent repair/replacement parts and avoid lack of maintenance of the equipment by controlling the equipment maintenance frequency.