A Service Production Planning Model Integrating Human Risk Factors

Most models of production planning based on mathematical programming tend to assume constant technical coefficients. This assumption is realistic when the production is based on machines as it is the case in manufacturing. On the other hand, production planning in the service sector involves humans instead of machines. Consequently, the assumption that all technical coefficient of the mathematical program are constant cannot hold anymore. This is especially the case for productivity parameters related to human activity. It is well known for instance that in the service sector when administrative tasks are repetitive and boring, working overload has a direct impact on the employee productivity. We have adapted a manufacturing planning model producing industrial goods into a service production planning model. In this service model, employees with different job status (junior, senior and expert) are handling cases of specific difficulties (simple, standard, personal and special). Then, we have introduced a variable productivity formula into the mathematical program that takes into account "plateau" levels assuming diminishing productivities. To do so the mathematical program includes integer variables as well as non-linearity and thus becomes a NLMIP (Non Linear Mixed Integer Program). A fictitious case study is presented. The initial service production planning model with constant technical coefficient leads to solutions involving job specialization. On the other hand the model version with the variable productivity formula offers a better workload balance and more possibilities of job polyvalence reducing thus human risks such as burn-outs.