A four-echelon supply chain inventory model for growing items with imperfect quality and errors in quality inspection

To safeguard the livelihood of consumers, food producers are required, either by law or regulatory bodies, to inspect their products for quality before selling the products to consumers. This is because food processing, as is the case with most production systems, is not perfect and there is a possibility that some of the processed products do not meet the required quality standard. Likewise, the inspection process is seldom perfect, meaning that it is subject to errors and thus, some of the processed products might be incorrectly classified. In light of this, an inventory model for a four-echelon food processing supply chain is developed. The supply chain has a farming echelon where live items are grown with the possibility that some of them might not survive; a processing echelon where the live items are transformed into processed inventory; an inspection echelon where the processed inventory is classified into good and poorer quality classes under the assumption that the inspection process is subject to type I and type II errors; and a retail echelon where the processed inventory of good quality is sold to consumers. The supply chain is modelled as a profit maximisation problem and a solution procedure for solving the model is proposed. The problem is studied under both centralised and decentralised supply chain structures and from the analysis, the centralised supply chain with a profit-sharing agreement performs better in terms of profit maximisation.