A great number of models have been proposed to investigate the deterioration inventory. However, most of models assume that a fixed physical quantity of items deteriorates over time, the quality of items does not decay before their expiration dates. In practice, the quality and physical quantity of many products, including fresh produce and foods, often deteriorate over time. The quality of an item usually plays an important role in influencing the demand for products. In this paper, we consider the pricing and lot-sizing problem for products with quality and physical quantity deteriorating simultaneously. The deterioration rate of quality and physical quantity is taken to be time proportional. The demand rate is assumed to be deterministic and dependent on the quality of an item, the selling price per unit and the on-display stock level. The theory for finding the optimal solution of problem is discussed and numerical examples are used to illustrate the model and the solution procedure. Finally, sensitivity analysis of the optimal solution with respect to price sensitive parameter and values of different deterioration functions is carried out.
Due to advance in postharvest science and technological innovation in produce handling, agricultural produce grown in diverse climates that are continents apart can be purchased in top quality condition elsewhere in the world, and with the rising influence of multinational firms in the globalization of fresh produce supply chain, and increasing epidemiological evidence which positively link high consumption of fruits and vegetables with a reduced incidence of cardiovascular and other chronic diseases. The market for fresh produce has continued to expand during the past decade (Florkowski et al., 2009). On the other hand, fresh produce can easily spoil or deteriorate, which often results in product loss. Kantor et al. (1997) estimated the U.S. total retail, foodservice, and consumer food losses in 1995 to be 23% of fruits and 25% of vegetables. Fresh fruits and vegetables accounted for nearly 20% of consumer and foodservice losses. In the European grocery sector, products that are not purchased before their sell-by-date are estimated to cause costs running into billions of dollars each year (Karkkainen, 2003). Thus, how to design an inventory system for fresh produce and foods to decrease cost and meet customer requirements is a current managerial concern as well as an important research issue.
Fresh produce is a living entity. Even after harvest, fresh produce continues its metabolic activity and undergoes further biochemical and physiological changes. These changes are influenced by biological factors (respiration rate, ethylene production and action, rates of compositional changes, mechanical injuries, physiological disorders, and pathological breakdown) and environmental factors (temperature, relative humidity, air velocity, atmospheric composition, and sanitation procedures). The rate of biological deterioration depends on environmental factors. For example, transpiration or water loss is a main cause of deterioration because it results not only in direct quantitative losses (loss of salable weight), but also in losses in appearance (wilting and shriveling), textural quality (softening flaccidity limpness, loss of crispness and juiciness), and nutritional quality. Although all five environmental factors are important, temperature has the most profound affect on the deterioration rate of fresh produce placed in storage. For each increase of View the MathML source10°C(18°F) above optimum, the rate of deterioration increases by two to threefold.
The biochemical and physiological changes lead to the qualitative and quantitative deterioration in fresh produce. Quality is defined by the International Organization for standardization (ISO) as the totality of features and characteristics of a product that bear on its ability to satisfy stated or implied needs. This means quality is a term defined by the consumer, buyer, grader, or any other client based on a number of subjective and objective measurements of the food product. These may include measures of sensory, nutrition, safety, wholesomeness, or any other attribute or characteristic of the product. In some cases, quality degradation leads to a discarded product whereas in others it reduces consumer acceptability. In order to improve quality management in fresh produce, it is necessary to develop mathematical models to predict the quality deterioration of fresh produce. Most approaches used in quality prediction models are based on the fact that there is usually the most rapidly changing criterion for a given product (Achour, 2006).
Traditionally, the most common method for food quality prediction during their thermal processing and storage is the kinetic model which has been described in terms of zero; first; or higher order kinetics (Labuza, 1985). However, the theory has been frequently challenged in the last years. The most studied alternative model is the Weill-Log logistic (Well) model, which is built on the notion that degradation or inactivation curve is the cumulative form of the temporal distribution of events that resulted in destruction of the affected molecules, requiring no specific mechanism (Corrdini and Peleg, 2004a). The Weill-Log logistic model has been demonstrated to be applicable of describing microbial growth, microbial inactivation, nutrients, pigments and enzymes degradation under nonisothermal conditions (Corradini and Peleg, 2006, Yu et al., 2011 and Derossi et al., 2010; etc). The Weill-logistic model assumes that the instantaneous deterioration rate function is a two-parameter Weibull distribution.
χ(t)=αβtβ−1χ(t)=αβtβ−1
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where α and β are temperature-dependent coefficients. α>0α>0, β>0β>0, t is the time of deterioration.
Recent developments of tracking and monitoring technologies such as Radio Frequency Identification Devices (FRID) and Time Temperature Indicator (TTI) provide great opportunities for effective management of fresh produce. While these technologies are more widely adopted, it enables to automatically capture product information regarding product identity and related data (e.g. temperature, humidity, and the time period during which products have been exposed to the temperature in the supply chain process) in real time. Such transparency generates the possibility that, as products pass through a supply chain, the shelf life can be dynamically predicted based on the environmental conditions during storage and transportation as well as the varied time required for these operations. In this paper, we formulate a fresh produce and foods inventory model to decide the pricing and lot-sizing policy assuming that the quality and physical quantity deteriorate simultaneously over time.
A model for optimal pricing and lot-sizing for fresh produce and foods is developed in this study. We assume that the quality and physical quantity of fresh produce and foods deteriorate simultaneously, and the demand is a function of the quality, the selling price and the stock on display. An algorithm to finding the optimal solution to the problem is developed. It shows that when the price sensitivity of demand is lower, the seller can increase selling price and replenishment order and reduce replenishment period to increase his profit and when the deterioration rates of quality are small, the seller can extend his replenishment time and order quantity to increase his profit.
The proposed model is appropriate for items that its quality and physical quantity deteriorate simultaneously, such as vegetables, strawberries, and litchi. From above numerical analysis, it shows that the replenishment period, order quantity, and the profit per unit time are not sensitive to the parameters of quality and physical quantity deterioration rate. Therefore, even the accurate values of the parameters of the quality and physical quantity deterioration rate cannot be acquired, the model still can be used to control the inventory. On the other hand, temperature has the most profound effect on the deterioration rate of fresh produce and foods. For example, when temperature changes from View the MathML source26°C to View the MathML source8°C, the deterioration rate parameter of the ascorbic acid in strawberries changes from 0.23 to 0.04 (Derossi et al., 2010), which has considerable impact on the replenishment period, order quantity and the profit per unit time. Thus, it is necessary to reduce temperature fluctuation as much as possible during logistics process (package, handling and transportation).
There are some limitations in the present study. One limitation is that shortages are not allowed, which would not be true in fact. In addition, we also assume that the lead time is zero. In reality, the lead time is not zero and fresh produce and foods deteriorate in the lead time. More research is need to be carried out in the future.
