An EOQ model with substitutions between products

This paper presents an economic order quantity (EOQ) model when two products are required, and one can be substituted for the other, if necessary, at a given unit cost. It considers three cases: (i) when there is no substitution between the products, (ii) when there is full substitution between the products, and (iii) when there is partial substitution between the products. In a deterministic setting with proportional substitution costs, one would expect to find full substitution or no substitution being optimal, depending on the cost parameters. However, it is observed that full substitution is never optimal; only partial substitution or no substitution may be optimal. This result can best be explained due to the non-linearity of the decision variables in the total cost expression. Finally, the paper presents an algorithm to compute the optimal order quantities.