Optimal control of production and remanufacturing for a recovery system with perishable items

In this paper, a recovery system for perishable items is introduced and developed considering production and remanufacturing capacity constraints. The system consists of two inventories, one for serviceable items and the other for returned and recoverable items. Taking the production cost, remanufacturing cost, disposal cost, and the loss caused by deterioration into account, the optimal control model is established to minimise the total cost. The continuous-time dynamic optimal production, remanufacturing and disposal rates that minimise the total cost are obtained using Pontryagin's maximum principle. Additionally, to highlight the advantage of the dynamic optimal policy, the case of the static optimal policy that does not vary with time is investigated and compared with the dynamic policy. It is shown that the dynamic optimal policy is significantly better than the static optimal policy. A numerical example is provided to illustrate the proposed methods.