Applying the Lexicographic Maximum Solution of Min-Product Fuzzy Relational Inequalities for Finding the Optimal Pricing with a Fixed Priority in a Supply Chain System

Fuzzy relational inequalities composed by the min-product operation are established to model the optimal pricing with fixed priority in a single product supply chain system. The solution algorithm has been proposed for solving such an optimization problem and finding the optimal solution (is called lexicographic maximum solution). In this study, a novel approach is proposed to finding the optimal pricing with fixed priority in a single product supply chain system. This approach is based on new properties of solution set in a min-product fuzzy relational inequality. These new properties allow us directly determine the optimal value of variable without many duplicate checks in the solution procedure. A numerical example is provided to illustrate the procedure.

Excluding Parallel Execution to Improve Global Fixed Priority Response Time Analysis

Response Time Analysis (RTA) is an effective method for testing the schedulability of real-time tasks on multiprocessor platforms. Existing RTAs for global fixed priority scheduling calculate the upper bound of the worst case response time of each task. Given a target task, existing RTAs first calculate the workload upper bound of each higher priority task (than the target task), and then calculate the interference on the target task by each higher priority task according to the obtained workload upper bounds. The workload of a task consists of three parts: carry-in, body and carry-out. The interference from all these three parts may be overestimated in existing RTAs. However, although the overestimation of the interference from body is the major factor that causes the low accuracy of existing RTAs, all existing work only focuses on how to reduce the overestimation of the interference from carry-in, and there is no method to reduce the overestimation of the interference from body or carry-out. In this work, we propose a method to calculate the lower bound of the accumulative time in which the target task and higher priority tasks are executed in parallel. By excluding the parallel execution time from the interference, we derive a new RTA test that can reduce the overestimation of the interference from all three parts of the workload. Extensive experiments are conducted to verify the superior performance of the proposed RTA test.