Incorporating planned backorders in a family production context with shelf-life considerations

This paper considers the problem of determining the optimal production rate for each item and the optimal cycle time for the family of items in a family production context with restrictions on the shelf-life of various items in the family. We investigate the impact of incorporating planned backorders into the system. We show that the model with planned backorders reduces to a model without backorders with modified holding costs and shelf-life. Therefore, the model with planned backorders can be analysed using the earlier model developed by Viswanathan and Goyal. We also present several examples to demonstrate how incorporating planned backorders can reduce the total costs.