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Optimal lot-sizing policy in supply chain (SC) has an important role in companies applying SC management to their system. An excellent lot-sizing policy will control and manage the inventory costs of SCs. By managing lot sizes in the SCs, companies become capable of bringing down additional costs and delivering extra value to the consumers. In this paper, a multi-product, multi-wholesaler, multi-level, and integrated SC under the shortage and the limited warehouse space is modelled. In this model, there are some real stochastic constraints. The objectives are both, to determine the optimum number of lots and the optimum lot volumes in order to minimise the total cost of SC, while the stochastic constraints are satisfied. All of the products are single-stage and the shortage is allowed for products in each one of the chain levels. Resources follow normal distributions with known means and variances. The model is mixed integer nonlinear programming (MINLP) type, large-scale and hard to solve. In this regard, generalised outer approximation based on decomposition principles, outer-approximation, and relaxation is utilised to optimise the MINLP model of research. The results and analyses demonstrate that proposed algorithm has excellence and acceptable performance.
Shekarabi et al. (Fri,) studied this question.