A bi-objective inventory optimization model under inflation and discount using tuned Pareto-based algorithms

•A multi-product multi-period inventory control problem under budget constraint is developed.•The shortages in combination of backorders and lost sales are considered for each product.•The ordered quantities of products are delivered in batch sizes of known number of boxes.•All unit discount policy is considered to purchase the products.•Three meta-heuristic algorithms i.e. NSGA-II, NRGA and MOPSO are applied to solve the problem.