Network Data Envelopment Analysis (NDEA) models assess the processes of the underlying system at a certain moment and disregard the dynamic effects inside the production process. Hence, distorted efficiency evaluation is gained that might give misleading information to Decision-Making Units (DMUs). However, the dynamic DEA model discusses the repetition of a single-period form over a long-term period, and it appears as a shape of time series one which includes a particular construction in each period. Malmquist Productivity Index (MPI) assesses efficiency changes over time which are measured as the product of recovery and frontier-shift terms, both coming from the DEA framework. In this study, a form of MPI involving network structure for evaluating DMUs in the presence of uncertainty and undesirable outputs in two periods of time is presented. To cope with the uncertainty, we use the stochastic p-robust approach, and the weak disposability of Kuosmanen (2005) is utilized to take care of undesirable outputs. The proposed fractional models are linearized applying the Charnes and Cooper transformation, and they are applied to evaluate the efficiency of 11 oilfields to identify the main factors determining their productivity, utilizing the data from the 2020 to 2021 period. The results show that the management of resource usage, especially forces and equipment, is inappropriate and investment is not sufficient. This specific attribute highlights the necessity to enhance the rate of investment to substitute the depreciated funds.