Forecasting and maintenance problem under subcontracting constraint with transportation delay

Abstract

In this paper, a forecasting production/maintenance optimization problem has been proposed with a random demand and single machine M₁ on a finite horizon. The function rate of the machine M₁ is depending on the production rate for each period of the forecasting horizon. In order to satisfy the customer, a subcontracting assures the rest of the production through machine M₂ with transportation delay. An analytic formulation of the problem has been proposed using a sequential computation of the optimal production plan for which an optimal preventive maintenance policy has been calculated based on minimal repair. Firstly, we find, the optimal production plans of principal and subcontracting machines, which minimises the total production and inventory cost for the cases without and with returned products under service level and subcontracting transportation delay. Secondly, we determine a joint effective maintenance policy with the optimal production plan, which integrates the various constraints for the production rates, the transportation delay and the returned production deadline. Numerical results are presented to highlight the application of the developed approach and sensitivity analysis shows the robustness of the model.

Keywords:

• production plan
• maintenance policy
• subcontractor
• transportation delay
• random demand and service level