Production control of unreliable manufacturing systems with perishable inventory

Manufacturing systems with perishable products appears in several industrial branches such as food production, chemical and radioactive material manufacturing, and pharmaceutical industry. Product perishability often results in the disposal of the fraction of products that do not meet the final specifications, after being kept too long within serviceable inventory. The disposal of perishables raises several environmental issues and its minimization together with reduction of other costs related to perishable inventories are most often studied within inventory management framework. The production control problem for the systems with perishable products, especially in case of failure-prone manufacturing facilities, is an important and challenging topic that was only sparsely addressed in the scientific literature. The main difficulty consists in resolving the trade-off between having an inventory level sufficient to fill the demand in case of machine failure, and potential deterioration of products kept too long within inventory. The paper proposes an approach to resolve this trade-off. First, a mathematical model describing the stochastic behavior of such systems is developed. Next, an analytical study of the system is performed, and finally, an optimal production policy that takes the product perishability into account is determined. This policy is shown to be a hedging point-type policy; thus the well-known result about the optimality of hedging point policy (in nonperishable case) is generalized to the class of perishable products with fixed shelf-life. It is shown that under conventional conditions (limited production capacity, Markovian failure/repair processes, constant demand rate), the optimal hedging level does not exceed the cumulative demand along the product shelf-life, and that leads to no disposal of products, known as a zero-waste policy. Numerical simulations allowed to perform the sensitivity analysis and a comparative study of the costs incurred in the systems with and without perishability.