A study on periodic deteriorating linguistic fuzzy inventory model with natural idle time and imprecise demand using GSA

The modern global economy is becoming more challenging and it is hardly possible to minimize the inventory cost for inventory practitioners in the coming days. Basically, most of the enterprises deal with deteriorating items having flexible demand rate and follow natural idle time in the entire inventory process. Moreover, traditionally most of the research articles have been made under non-stop time frame, but in reality, in a day–night scenario there exists a natural idle time and hence the time consumed for inventory run time may be viewed as single shift or periodic model. Here we formulate an economic order quantity (EOQ) inventory model considering natural idle time and deterioration under some constraints and minimize the average inventory cost. Then, the model is converted into an equivalent fuzzy model, taking the demand and all the cost parameters as linguistic polynomial fuzzy set (LPFS). To defuzzify the model, we have adopted indexing method as well as \(\alpha \)-cut method. To validate the novelty, numerical experimentations have also been analyzed with the help of metaheuristic and evolutionary algorithms like goat search algorithm (GSA) and particle swarm optimization (PSO). Comparative analysis reveals that GSA approach can give finer optimum (− 10 % cost reduction) than other approaches. The main findings of this research give a new technique of (linguistic term) fuzzification–defuzzification of the proposed model and a new solution procedure to optimize the periodic deteriorating inventory model under GSA. To justify this model, sensitivity analysis and graphical illustration have been done. Scopes of future work have been discussed for further improvement of research on optimization problems using metaheuristic algorithms.