Two models of inventory system with stochastic demand and deteriorating items: case study of a local cheese factory

This paper formulates two production-inventory system models, the Markov decision process (MDP) and chance-constraint programming (CCP). Three strategies of production, with and without lost sales, were developed for a local cheese factory. The target is to introduce a practical production plan to minimize the weekly cost of a system where the models used have to deal with stochastic demand, deteriorating items, lost sales, and the normal production rate. The problem of uncertain demand requires the use of specific methods to find a solution and MDP and CCP are definitely both effective methods to deal with this problem. CCP converts to a deterministic problem with a specific error probability that represents constraint un-achievement probability. Stored items are classified into groups depending on storage period length. So, the weekly deterioration rate takes into account the shelf life of stored items for every group. Our results showed the MDP model was better than the CCP model based on the weekly cost, whereas, the CCP model achieved a better level for safety stock. The effects of both the storage period length and the cost of lost sales on the results were considered.