This research work deals with an imperfect production system considering the purchasing of raw materials in order to study the economic production quantity (EPQ). This manufacturing system produces perfect and defective finished products; defectives are considered as scrap. A single product is manufactured from multiple raw materials which are purchased from outside suppliers. In the integrated procurement-production-inventory (IPPI) model, one of the principal decisions, in addition to determining the optimal lot size to produce, is to define the number of optimal orders of each raw material with respect to rate of consumption in the manufacturing of finished product. Two cases are considered: without shortage (first model) and with shortage (backordering, second model). In the first model, the purpose is to determine jointly the optimal lot size to manufacture and the optimal number orders of each raw material in order to minimize the total cost. The second model obtains the optimal number of orders of each raw material, the optimal lot size to manufacture and the optimal shortage level with aim to minimize the total cost. This research also shows that both of the proposed inventory models are a convex programming problem, so exact algorithms to solve these inventory problems are proposed.
The amount of global ammonia (NH3) emissions is growing continuously, similar to the damage to the environment, particularly humans and animals, caused by those emissions. Various problems derived from pollution by ammonia emissions have attracted increasing attention in recent years. In particular, accumulation of ammonia in poultry farms is a concern for the poultry industry as it can lead to possible damage due to reduced bird performance, damage to the respiratory tract and skin of birds, and thus loss of customers. As birds age, ammonia production increases due to factors such as feeding and mobility, requiring the application of solutions to reduce it such as the use of fans, feed supplements, and temperature adjustments to improve bird health. These solutions impose additional costs on poultry farms to combat ammonia emissions. This study presents a general economic growing quantity (EGQ) model that includes the cost of inhibition of ammonia production during the growing period. In addition, the model is formulated under an all-units discount policy, where the price of newborn items is related to the size of the order purchased from the supplier. Furthermore, the model assumed that some newborn items are dead when the lot is received because of stress experiences and incidents during the catching, loading, transportation, and unloading. Finally, two versions of the proposed general EGQ model are presented: EGQ with no discount and EGQ with known slaughter age.
Determining the optimal slaughter age of fast-growing animals regarding the mortality rates and breeding costs plays an important and major role for companies that benefit from their meat. Additionally, the effects of carbon dioxide (CO2) emissions during the growth cycle of animals are a significant concern for governments. This study proposes an economic order quantity (EOQ) for growing items with a mortality function under a sustainable green breeding policy. It assumes that CO2 production is a practical polynomial function that depends on the age of the animals as well as the mortality function. The aim of the model is to determine the optimal slaughter age and the optimal number of newborn chicks, purchased from the supplier, to minimize the total costs. We propose an analytical approach, with five simple steps, to find the optimal solutions. Finally, we provide a numerical example and some model management insights to help practitioners in this area.
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