Proposing an Economic Order Quantity (EOQ) model for imperfect quality growing goods with stochastic demand

The main aim of inventory control and production planning problems is to optimize the economic quantity of the order or determine the size of the production batch according to the capacities and limitations to minimize the total costs related to the order, purchase, maintenance, and delivery. The Economic Order Quantity (EOQ) model has been widely used to determine the order size or purchase of parts in production systems. Simultaneous consideration of the time and amount of ordering goods and minimizing system and customer costs is the main concern of inventory management. The assumptions of the classical EOQ model do not cover all inventory control systems in real terms. Leaving aside some of the assumptions, this paper aims to optimize and develop the EOQ model. The inventory system of this paper includes products that are capable of growing during the replenishment period, such as livestock. Also, it is assumed that the products of this system have a stochastic demand and a certain part of them has a lower desired quality. Newborn items are also ordered live and fed until slaughtered to the customer's desired weight and then slaughtered. Before all slaughtered items are sold, these products are screened to distinguish high-quality items from lower-quality items. To determine the optimal inventory policy, a model is proposed in this paper to maximize the expected total profit.

Design/methodology/approach: 

The studied inventory system examined the situation in which a company orders a certain number of items, e.g., chickens, that are in stochastic demand and are capable of growing over time. To maximize its total profit, the company should determine the number of goods that can be ordered at the beginning of a growth cycle. Total profit was defined as the difference between total revenue and total cost. Total revenue included revenue from the sale of items of good and lower quality, and the total cost included the total cost of purchasing, feeding, maintaining, setup and screening. The proposed model addressed two questions related to the order quantity and the order time. The objective function of the model was the expected total profit, while the decision variables were the batch size and cycle time, given the constraint that the total growth period and the facility setup time must be less than the consumption period.

In this study, a model of growing economic order quantity was proposed, which was expressed using a hypothetical numerical example. It was assumed that there is a company that buys day-old chicks, feeds and breeds them until they reach the desired weight, and sells them after checking the quality. Given sample quantities, the company should order 175 newborn items at the beginning of each cycle. Newborn items should grow in a period equivalent to 0.0941 years (34 days) and a period of consumption equivalent to 0.1928 years (70 days). The order must be registered every 0.1928 years (70 days) and the company expects to earn 42.2460 monetary units, annually. Quality screening should begin immediately upon consumption and occur over a period equivalent to 0.0499 years (18 days), after which imperfect quality items should be sold in a single batch.

Research limitations/implications: 

The proposed model can be extended by adding variables such as inflation, trade credit financing, allowable shortages, breakdowns, and quantitative discounts. Also, in the inventory system of this study, it was assumed that the screening process was 100% effective in separating items of good and lower quality. This issue, together with the learning effects on the screening process, suggest other potential areas for further model development.

Originality/value: 

In this paper, the assumptions of the classical model about the non-growth of items, good quality and equal to all products, and deterministic demand were discarded. Also, due to advances in technology and the existence of competitive markets, it was not possible to determine the exact amount of demand for firms. Considering stochastic demand as a way to deal with this uncertainty was inevitable. Therefore, it seems necessary to study this issue and propose a solution to remove the existing barriers in a way that in addition to providing the right amount of order, the profits of companies become maximized. The results of this study can be useful for all cases and units that have growing items and help to issue the right amount of orders, resulting in lower costs and higher profits.