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Certain inventory items are living organisms, for example livestock, and are therefore capable of growing during the replenishment cycle. These items often serve as various saleable food items downstream in supply chains. The purpose of this paper is to develop a lot sizing model for growing items if the supplier of the items offers incremental quantity discounts. A mathematical model is derived to determine the optimal inventory policy which minimises the total inventory cost in both the owned and rented facilities. A solution procedure for solving the model is developed and illustrated through a numerical example. Sensitivity analysis is performed to demonstrate the response of the order quantity and total costs to some key input parameters. Incremental quantity discounts result in reduced purchasing costs; however, ordering very large quantities has downsides as well. The biggest downsides include the increased holding costs, the risks of running out of storage capacity and item deterioration since the cycle time increases if larger quantities are purchased. Owing to the importance of growing items in the food supply chains, the model presented in this article can be used by procurement and inventory mangers when making purchasing decisions.

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Purpose The purpose of this paper is to formulate a coordinated inventory control model for growing items in a supply chain with farming, processing and retail operations. The farmer grows newborn items and then delivers them to a processor once the items mature. At the processing plant, the items are slaughtered, cut and packaged at a specified rate. The processor then delivers a certain number of equally sized shipments of processed items to a retailer who satisfies customer demand. Design/methodology/approach A cost minimisation inventory model describing the problem at hand is formulated with the number of shipments and the cycle time being the decision variables. A solution algorithm for solving the problem is presented and applied to a numerical example. Findings Opting for an integrated policy is favourable to all supply chain members. When the proposed model is compared to equivalent independent and equal-cycle time replenishment policies, the total cost savings amount to 3 and 14 per cent, respectively. Social implications The model can serve as a guideline for procurement managers dealing with growing items to better their inventory management practices. Considerable cost savings in food production chains can be achieved through improved inventory control, and these savings can be used to cushion consumers against rising food prices. Originality/value Most previously published models on inventory management for growing items were formulated under the assumption that the items are grown and then sold to consumers instantaneously. In real food production systems, the items need to be transformed and packaged into a consumable form before customer demand is met. The model presented in this paper accounts for this and is therefore more realistic.

Quality control is an important consideration in food production systems which often start with farming and processing operations and finish with consumption. This study develops an integrated inventory control model for a four-echelon supply chain (with farming, processing, screening and retail operations). The farmer grows newborn items and then delivers them to a processor once the items are mature enough. At the processing plant, the items are slaughtered, processed, packaged and screened for quality. The processor then delivers a certain number of equally sized batches of good quality processed inventory to the retailer who satisfies customer demand for good quality processed inventory. The processor sells the processed poorer quality inventory at a discounted price and as a single batch to secondary markets. The proposed supply chain inventory system is formulated as a profit maximisation problem with the number of batches of good quality processed inventory and the order quantity as the decision variables.

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