The rapid growth of cloud computing has brought new challenges in Parallel Batch Machine Scheduling (PBMS), particularly when incorporating malleability and rejection constraints. This has led to the Parallel Batch Machine Scheduling with Malleability and Rejection problem (PBMSMR), which involves malleable jobs whose widths can be adjusted during execution within specified limits and incorporates job rejection subject to a penalty threshold. Based on an analysis of key properties of batch scheduling with job rejection, we develop an approximation algorithm for PBMSMR by employing a greedy approach that reorders and iteratively refines job sets to minimize the objective while respecting rejection constraints. The algorithm achieves a time complexity of \(O(n^2 \log n)\) and an approximation ratio of \((4-\frac{2}{Km})\) , where K and m denote the capacities and the number of the machines, respectively. For jobs with identical release times, we fine-tune the algorithm to achieve an approximation ratio of \((3 + \frac{2(K-1)}{Km})\) . Additionally, for PBMS with two machines of non-identical capacities and fixed-width jobs, we achieve a ratio of \(\frac{17}{5}\) with \(O(n \log n)\) , improving upon the previous state-of-the-art approximation ratio of \(5\) with a runtime of \(O(n^2)\) .