Inventory models for growing items in the presence of price-sensitive demandi ncorporating imperfect quality, inspection errors, carbon emissions, and planned backorders

Abstract

Recently, growing items have increasingly come to the forefront within inventory modeling. Unlike conventional items, these items can grow in the cycle of replenishment. They are of paramount importance for human consumption, primarily as a source of high-quality proteins, essential vitamins, and minerals for a balanced diet. Examples of such items include farm animals, plants, and more. Just like any living organism, they require food or nutrients to grow. They are nourished during a growth period and are subsequently sacrificed once they reach a pre-defined target weight, marking the beginning of a timeframe for consumption. The sacrificed products are then stored in inventory and depleted constantly at a specific rate of demand. Throughout the cycle, expenses are incurred for feeding the growing products, while conservation costs are accrued to maintain the sacrificed products in inventory during the consumption period, as well as to sustain the live products for the subsequent cycle. Inventory models have evolved over the years to incorporate features aimed at making them more realistic and robust while addressing specific needs in the field. The concept of imperfect quality is a characteristic assumed to exist in any process due to machine breakdowns and, mong other reasons, inspection errors that are inevitably linked to human error. Inventory shortages do occur in reality, so a company that is prepared for such situations can ensure customer confidence and loyalty. Carbon emissions have gained significance as well. Their reduction is a means of contributing to the fight against climate change and minimizing the environmental impact of corporate operations. Additionally, this reduction can lead to significant cost savings. In short, a reduction in carbon emissions is beneficial both for Mother nature and the long- term success and sustainability of businesses. Another important aspect is models of inventory with price that fluctuates based on demand, which are utilized in specific situations. This occurs when consumers are price-sensitive, and a decrease in price can boost demand. Furthermore, it considers aspects such as item mortality. The relevance of these conditions, combined with the presence of growing items, provides a valuable contribution to the understanding of this relatively new and essential area within inventory theory. In this context, this thesis’ objective is to progressively develop inventory models for growing items incorporating these features. Specifically, 1) to develop an inventory model for growing items with imperfect quality when the demand is price sensitive under carbon emissions and shortages; 2) to generate an inventory model in a three-echelon supply chain for growing items with imperfect quality, mortality, and shortages under carbon emissions when the demand is price sensitive; and 3) to formulate an inventory model for growing items when the demand is price sensitive with imperfect quality, inspection errors, carbon emissions, and planned backorders. The developed inventory models determine the optimal solutions for selling price, backordering quantity, order quantity, and number of shipments to maximize expected total profit per unit of time. Sensitivity analyses and numerical examples are utilized to describe the applicability of the proposed inventory models with the aim of guiding procurement and inventory managers working in industries that store growing items in making informed decisions.