We are now living in the big data era, where firms can improve their decision makings by adopting big data technology to utilize mass information. To explore the effects of the big data technology, we build an analytical model to study the sustainable investment in a supply chain, consisting of one manufacturer and one retailer, by using Bayesian information updating approach. We derive the optimal sustainable investment level for the manufacturer and the optimal order quantity for the retailer. Comparing the results with and without the big data technology, we find that whether the manufacturer should make more sustainable investment when the retailer adopts the big data technology depends on the service level at the retailer side. Interestingly, it is not always optimal for the retailer to adopt the big data technology. We identify the conditions under which the manufacturer and retailer are better off with the big data technology. In addition, we investigate the impact of the number of observations regarding the market information and find that the optimal decisions and profits increase in the number of the observations, if and only if the service level is low.