A continuous review production–inventory system in fuzzy random environment: Minmax distribution free procedure

• Continuous review economic production quantity model with reordering strategy.
• Uncertain demand is prescribed as a fuzzy random variable.
• Minmax distribution free procedure is extended for fuzzy random variable.
• Fuzzy random cost function is scalarized by fuzzy expectation and signed distance method.

In many manufacturing systems, the production process may take some time to start the initial phase due to various reasons such as delay in installation of machines, short supply of raw materials, unavailability of workers, etc. Thus, the organization should plan accordingly so that the manufacturing process can start at the desired time. In an economic production quantity (EPQ) model, lead-time plays a significant role in ensuring that the manufacturing process starts on time. As we know, when both lead-time and demand rate are deterministic and constant, then demand during the lead-time is constant, and is referred to as zero lead-time. Moreover, when either or both of them are random variables, then lead-time demand (LTD) is a random variable. In such a case, a crucial question is: “when should the order be placed?” On the other hand, the distributional information on demand may not always be available or there may be many distribution functions in the practice, which have same mean and variance, but their frequencies are different. In this study, we develop an EPQ model in stochastic framework, wherein the distribution function of demand is unknown, but the mean and variance are known. The inventory level is continuously reviewed, and an order is placed when it reaches the reorder level. The real-life business situations are so sophisticated and floating in nature that the consideration of ‘impreciseness’ along with ‘statistical variability’ in demand parameter is more preferable. To be a part of this contingency, we further extend the model in the fuzzy random environment by considering demand rate as a fuzzy random variable (FRV). Furthermore, we mathematically analyze the cost function and propose a heuristic procedure to find the global optimum. Numerical examples with sensitivity analysis are also provided for illustration purpose.