یک مدل موجودی جدید برای آیتم های سرد که هزینه ها و تولید گازهای گلخانه ای در نظر می گیرد

A new inventory model that considers both cost and emission functions is proposed for environments where temperature-controlled items need to be stored at a certain, non-ambient temperature and to do so modular temperature-control units are used. Transportation unit capacity and storage unit capacity are considered, which results in non-linear, non-continuous cost and emissions functions. A set of exact algorithms are developed to find the optimal order quantity based on cost and emission function minimization, and the mathematical proof of the optimality of the solutions are presented. Using a variety of parameter ratios, a set of experiments are run to show the effectiveness of the proposed model compared to the current models in the literature and to provide managerial insights into the cold item inventory problem. Optimum order quantity for cost function optimization and emission function optimization are compared against each other and the tradeoff between the functions is analyzed to provide insights.

According to a study by the University of Michigan1, the top two contributors to the Green House Gas (GHG) emissions are the electric and transportation sectors. In the electric sector, refrigerants are the second highest contributor. In the transportation sector, small and heavy duty trucks together form more than 50% of the GHG emissions. Thus, policies that attempt to reduce emissions from transportation or refrigerant utilization have the potential to make an impact in the reduction of GHG emissions. The handling, holding and transportation of temperature-sensitive products along a supply chain is known as the cold supply chain. Cold chain items are items that are required to be maintained in a specific temperature range. Examples of cold chain items are deep freeze items (−28 to −30 ºC) such as seafood, frozen items (−16 to −20 ºC) such as meat, chill items (2 to 4 ºC) such as fruit, vegetables and fresh meat, and pharmaceutical items (2 to 8 ºC), such as medications and vaccines (Routledge, n.d.). Numerous recent studies have focused on the emissions resulting from the cold supply chain (Calanche et al., 2013, Dekker et al., 2012, James and James, 2010 and Wang et al., 2013). These studies consider the emissions from refrigerated trucks and transporters, cold warehouses, packaging and other components in the supply chain.

In this work we have introduced a new inventory model entitled the Cold Items Cost and Emission Model (CICEM) to determine the optimal order quantity in an environment with capacitated refrigerated units for holding and transportation. The model considers the holding cost at the distribution center and the transportation costs from the warehouse to the distribution center of cold item inventory. Thus, the CICEM model is a variation of the EOQ model with holding and transportation unit capacities that considers objectives of minimizing both costs and emissions. The transportation cost, holding cost and total cost are modeled in 3.1.1, 3.1.2 and 3.1.3, while the transportation emission, holding emission, and the total emission functions are modeled in 3.2.1, 3.2.2 and 3.2.3. For the CICEM model, we consider the emission function and two cases for the holding cost function: (1) not considering the interest rate of the investment capital as a part of the holding cost (iC=0), and (2) considering the investment opportunity of the items (iC>0). To model the holding and transportation unit capacity, all of the mentioned functions are non-linear and non-continuous. We develop exact algorithms to find the optimum value for the cost function when iC=0 and iC>0, as well as for the emission function. The solution algorithm for the second cost case has a similar structure to the solution algorithm of the emission function (as both algorithms search among the end points up to a point and then search the beginning points for the intervals after). A set of numerical experiments were run comparing the cost objective of the CICEM model to the EOQ model and the emission objective of the CICEM to the SOQ model. The results confirmed the effectiveness of the CICEM model for different parameter settings, and provided the following managerial insights into the cold item inventory environment that has segmented holding and transportation units. • For the cost function when iC=0, the CICEM outperforms the EOQ model for different values of λ, which is the ratio of holding cost to transportation cost and δ, which is the demand to unit capacity ratio. • For the case of iC>0, we run experiments to analyze the effect of item cost (C) on the optimum order quantity and the performance of the CICEM and EOQ models. Our results ( Table 5 and Table 6) show that for small values of C, the two models produce largely different cost objectives. But as the item price increase, the differences between the two models' cost functions become smaller and for large values of item price, the CICEM model can be approximated using the EOQ model. • For the emission function, the CICEM outperforms the SOQ model (sustainable version of the EOQ) for different values of θ, which is the ration of holding emission to the transportation emission and δ, which is the demand to unit capacity ratio. Our results ( Table 8) show that as δ increases, the difference in the CICEM and SOQ model performance also increases. • Finally, to explore the tradeoff between the cost and emission function of the cold chain inventory problem, the optimum value for each function of the CICEM model is calculated. We then conduct a trade-off analysis to determine the impact that only considering the cost function has on the environmental function (and vice versa). Due to the structure of the two functions within each interval, the emission function is more sensitive to deviation from optimality than the cost function when iC>0. This is due to the fact that within each interval the transportation cost and emission functions are decreasing, yet the holding emission is a constant function and the holding cost is an increasing function (due to the presence of iC). The results illustrate that using the emission function to set the order quantity results in smaller deviations in the cost function than using the cost function and calculating the emission function based on that. As an example, according to Table 10, if the optimum order quantity of the emission function is used for the cost function (and λ=0.5), the cost function would increase only by 4% than its optimum value. However, if the optimum order quantity is determined by the cost function, the emission function (using the order quantity determined via the cost function) would increase 42% over the optimal order quantity found using the emission function. Due to the structure of the two functions within each interval, the emission function is more sensitive to deviation from optimality than the cost function.