Stochastic models and numerical solutions for manufacturing/remanufacturing systems with applications to the printer cartridge industry

• We consider a manufacturing factory with degradation according to its production rate.
• We develop a stochastic optimization model with two decision and two state variables.
• We obtain a control policy for the system through the implementation of numerical methods.
• We show through a sensitivity analysis that the parameters of the control policy move as expected, from a practical perspective.

This paper investigates the production rates control of a hybrid manufacturing/remanufacturing system in a closed-loop environment, with application to the printer cartridge industrial sector. The system studied comprises manufacturing and remanufacturing factories working in parallel, and subject to random failures and repairs. The failure rate of the manufacturing factory depends on its production rate, while the failure rate is constant for the remanufacturing factory. Given the dependence of the failure rate on the production rate of the manufacturing factory, a non-homogeneous Markov process is used to describe the dynamics of the overall production system. The objective of the control problem concerns the minimization of a cost function which penalizes the presence of waiting customers, the inventory of finished parts, and the inventory of parts returned from customers upon reaching the end of their lives. Using a real business case study adapted from a leading European company producing printer cartridges, we obtain the optimal production policies for the both factories. Sensitivity analyses are conducted to illustrate the usefulness of the proposed approach and its applicability to other cases.