A sustainable lot-sizing model with partial backordering

Due to the competitive nature of business, accompanied by social and environmental awareness, a great necessity to incorporate additional non-classical criteria into traditional inventory models is comprehended. Sustainable lot-sizing model is considered to be a powerful response to this necessity. In this paper a novel sustainable lot-sizing model is developed which converts all emission types of inventory management life-cycle into tangible economic metrics. In order to develop the model in a more practical manner, partial backordering consideration is embedded into the model. A pretty simple procedure is developed to determine the optimal solutions of the proposed model. Finally the formulated model is illustrated with a numerical example. A comprehensive sensitivity analysis has been accomplished on model parameters as well. According to the sensitivity analysis the results show that the decision variables are highly sensitive respect to the selling price and purchasing cost and are moderately sensitive to the demand rate, fixed ordering cost, annual average inventory obsolescence rate, weight of an obsolete unit stored and also partial backordering rate. In the other hand the changes of other parameters have slight effects on the decision variables.

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