Dynamic product innovation and production decisions under quality authorization

We consider the joint product innovation and production decisions of a manufacturing firm under the existence of quality authorization from a 3rd party, which has gained growing popularity in recent years. A dynamic control model is developed to analyse the effects of quality authorization. Combining the techniques of Pontryagin maximum principle and backward induction, the optimal decisions on production and investment in product innovation before and after attaining the quality authorization is analysed. The analytical solution of the optimal investment and production decisions is derived providing that the time for the firm to obtain the quality authorization is known. To fully solve the firm's optimization problem, an iterative algorithm is then introduced to calculate the best time of attaining the quality authorization. We find that although the firm should have a continuous and incremental improvements in product quality, there can be jumps in the optimal production and investment levels. While the investment in product innovation is higher before obtaining the quality authorization than that after obtaining the quality authorization, the production is lower before obtaining the quality authorization. Moreover, the firm should attain the quality authorization sooner under a less costly the product innovation investment, a lower depreciation rate due to ageing of technology, a smaller production cost, and a lower interest rate. Finally, we compare our results with existing studies and discuss the managerial implications.