Modeling and optimization of multi-item multi-constrained EOQ model for growing items

In this paper, a new mathematical model is presented, for the first time, for multi-item economic order quantity for growing items considering various operational constraints. The model aims to maximize company’s total profit by determining the optimal values of the decision variables including: number of ordered items from each type and the time period needed to grow each type of items. To propose a realistic model which can be implemented in variety of real-world problems, different operational constraints are considered including: on-hand budget, warehouse capacity, and total allowable holding cost constraints. To solve the problem in small sizes a well-known exact solution methodology called Sequential Quadratic Programming is utilized. To solve the problem in medium and large sizes two novel hybrid metaheuristics called Sine Cosine Crow Search Algorithm and Water Cycle Moth–Flame Optimization algorithm are utilized due to sub-optimal results of the exact solution method. This is due to existence of enormous number of local optima and non-linearity of the proposed model. The performance of the algorithms is evaluated using different measures such as relative percentage deviation, percentage relative error, and CPU-Time. By solving various test problems in different sizes performance of the algorithms is evaluated and the best solution method for the problem is determined using statistical analyses.