Productivity is defined as the ratio of total output produced vs total input supplied.
Efficiency is defined as the ratio of total output produced vs actual efforts spent to produce this output.
In the software application management world output can be measured as number of incidents/queries/bugs resolved, number of standard changes delivered, number of batch jobs scheduled or monitored, number of small/medium/large enhancements delivered etc. Application development work output can be measured as number of Function Points delivered, number of objects (screens, reports, batch scripts, etc.) delivered, total LOCs delivered, total LOCs migrated, etc. Input is typically person efforts (hrs, mandays, etc.).
Efficiency of an individual or a team to resolve say an incident would typically involve actual efforts spent to resolve an incident. Whereas productivity of an individual may also involve waiting time for clarification resolution and other overheads which are not directly adding any value to incident resolution.
So efficiency is required to track real efforts required to produce a unit of output and productivity is required to track what additional efforts are required for other non value added activities or inefficiencies due to waiting for work, infrastructure, no clean order, etc. Highly efficient is the one who produces best output by consuming minimum possible resources.
Organisations need to measure both productivity and efficiency to create a baseline, to monitor performance against baseline and have plan in place for continuous improvement of these important KPIs. They need to focus on getting productivity of individuals/groups in their organisation closer to the efficiency by doing right things to work towards the purpose.
Suresh Dhamapurkar's Blog 