کنترل موجودی کربن محدود یکپارچه و توقیف کامیونی حمل باری با کامیون حمل و نقل ناهمگن

This paper analyzes an integrated inventory control and transportation problem with environmental considerations. Particularly, explicit transportation modeling is included with inventory control decisions to capture per truck costs and per truck capacities. Furthermore, a carbon cap constraint on the total emissions is formulated by considering emission characteristics of various trucks that can be used for inbound transportation. Due to complexity of the resulting optimization problem, a heuristic search method is proposed based on the properties of the problem. Numerical studies illustrate the efficiency of the proposed method. Furthermore, numerical examples are presented to show that both costs and emissions can be reduced by considering heterogeneous trucks for inbound transportation.

Environmental awareness throughout supply chains is growing due to the regulatory policies legislated by governments (such as Kyoto Protocol, UNFCCC, 1997), voluntary organizations established to curb emissions (such as Regional Greenhouse Gas Initiative and the Western Climate Initiative) and the concerns of environmentally sensitive customers (see, e.g., Liu et al., 2012 and Zavanella et al., 2013). As a result, supply chain agents review their carbon footprints, and they replan their operations or invest in carbon emissions abatement projects to fulfill their environmental responsibilities (Bouchery et al., 2011). Supply chain operations such as inventory holding, freight transportation, logistics, and warehousing activities are the main contributors to emissions generated in many manufacturing, retailing, transportation, health, and service industries. In particular, transportation is one of the major contributors to greenhouse gas (GHG) emissions: approximately 13% of global GHG emissions in 2004 was due to transportation sector (Rogner et al., 2007). Contribution of transportation to 2010 GHG emissions of Europe Union was almost 20%: 25% of France GHG emissions, 17% of Germany GHG emissions, and 20% of the U.K. GHG emissions were due to transportation in 2010 (EEA, 2013). Furthermore, emissions from road transportation constitutes the majority of transportation emissions. Leonardi and Baumgartner (2004), for instance, note that 6% of total emissions and 29% of transportation emissions in Germany in 2001 were due to road freight transportation. In the U.S., transportation sector generated almost 27% of the national GHG emissions in 2010 (EPA, 2013). Furthermore, while passenger cars are the biggest GHG emitters in the transportation sector, freight trucks generate the majority of the U.S. GHG emissions due to freight transportation. In particular, light-duty trucks (18.9% of 2010 U.S. GHG emissions generated by transportation sector) and medium- and heavy-duty trucks (21.9% of 2010 U.S. GHG emissions generated by transportation sector) are the largest GHG emissions generators from freight transportation in the U.S. in 2010 (EPA, 2013). A 50% increase in freight transportation from 2000 to 2020 is estimated for European countries (see, e.g. Toptal and Bingol, 2011). In the U.S., over 68% of freight is transported with trucks and a dramatic increase in the U.S. freight truck traffic is expected by 2040 (FHWA, 2008). Given that the freight trucks is the most common mode for freight transportation, the above statistics are not surprising. It is, therefore, crucial to explicitly consider transportation in replanning supply chain operations for achieving environmental goals. We refer the reader to review papers by Corbett and Kleindorfer, 2001a and Corbett and Kleindorfer, 2001b, Kleindorfer et al. (2005), Linton et al. (2007), Srivastava (2007), Sbihi and Eglese (2010), Sarkis et al. (2011), and Dekker et al. (2012) for the class of supply chain and operations management and logistics problems studied with environmental considerations. This study analyzes an integrated inventory control and inbound transportation problem with carbon emissions constraint. Particularly, this paper focuses on the economic order quantity (EOQ) model with truckload transportation and carbon emissions constraint. Inventory control models have been recently studied with carbon emissions regulation policies. Most of these studies focus on the variants of the EOQ model as the EOQ model is a commonly used inventory control policy in practice in case of deterministic demand. Specifically, Chen et al. (2013) models the EOQ model with carbon emissions constraint, i.e., the carbon cap policy. They provide solutions for the carbon-constrained EOQ model and discuss the conditions under which carbon emissions reduction is relatively more than the increases in costs due to carbon cap. Hua et al. (2011a) also studies the EOQ model. They formulate and solve the EOQ model in the presence of an emissions trading system such as the European Union Emissions Trading System and the New Zealand Emissions Trading Scheme. That is, their focus is on the EOQ model under the carbon cap and trade policy, which allows trading carbon emissions at a specified carbon trading price. This study is then extended to include pricing decisions within the EOQ model by Hua et al. (2011b). Arslan and Turkay (2013) revisit the EOQ model with carbon cap, carbon cap and trade, carbon taxing (where emissions are taxed), and carbon offsetting (where carbon abatement projects can be used to curb emissions in case emissions exceed the carbon cap) policies. In a recent study, Toptal et al. (2014) jointly analyze inventory control and carbon emissions reduction investment decisions in an EOQ model under carbon cap, cap-and-trade, and tax policies. Similar to the above studies, we analyze the EOQ model but further include joint transportation decisions. Specifically, we study this model under a carbon cap policy. In a carbon cap policy, the emissions of a company is restricted by a mandatory emissions limit, which is referred to as the carbon cap (see, e.g., Chen et al., 2013). While the carbon cap can be imposed by governmental agencies, the companies can also define their carbon cap in the view of their green goals (Benjaafar et al., 2012 and Toptal et al., 2014). For instance, a survey conducted among 582 European companies by Loebich et al. (2011) documents that company management decisions are the main motivation for greening operations in 2011 while the main motivation for greening operations in 2008 was environmental regulations. Therefore, we analyze the model of interest with carbon cap policy. Furthermore, it should be noted that, instead of studying EOQ model with carbon emissions regulation policies, Bouchery et al., 2011 and Bouchery et al., 2012 analyze multi-objective EOQ model with cost and environmental impacts minimization (multi-objective optimization models with cost and environmental objectives have also been studied for different supply chain management problems). They focus on generating Pareto efficient inventory decisions. A very commonly used method to generate Pareto efficient solutions is the constrained method, which is introduced by Lin (1976). The constrained method is guaranteed to generate Pareto efficient solutions independent of the problem properties (such as convexity requirements). The EOQ model with joint transportation decisions under carbon cap policy is the subproblem required by the constrained method if one wishes to solve bi-objective EOQ model with joint transportation decisions, where both costs and carbon emissions are minimized. Therefore, the analysis presented in this study can be utilized in multi-objective models for similar settings. It should be noted that inventory control systems other than the classical EOQ model have also been analyzed with environmental considerations. Letmathe and Balakrishnan (2005) study a product mix problem with carbon cap, carbon trading, and carbon taxing policies. Benjaafar et al. (2012) and Absi et al. (2013) focus on lot-sizing problems with carbon emissions regulations. Song and Leng (2012) analyze the single period stochastic demand model (i.e., the newsvendor model) and Hoen et al. (2012) study transportation mode selection problem in the setting of newsvendor model with carbon emissions regulations. Jiang and Klabjan (2012) characterize the optimal emissions reduction investment and capacity planning in case of stochastic demand. Liu et al. (2012) and Zavanella et al. (2013) investigate two echelon supply chains with environmentally sensitive customers and Jaber et al. (2013) model the vendor-buyer coordination problem with carbon trading and emissions reduction investment. As noted previously, freight transportation, especially, freight trucks are major contributors to carbon emissions. Nevertheless, the studies focusing on the EOQ models with carbon emissions considerations fail to model not only explicit transportation costs but also explicit transportation emissions. Particularly, these studies assume less-than-truckload (LTL) transportation, that is, a single truck is considered to have sufficiently large capacity to carry any shipment. On the other hand, truckload (TL) transportation is common in practice and supply chain agents should consider TL transportation costs and emissions in controlling their inventory and transportation operations. The studies that account for basic truck characteristics such as truck capacity and truck emissions in the context of environmentally sensitive logistics operations focus on vehicle routing problems (see, e.g., Bektas and Laporte, 2011, Suzuki, 2011, Jabali et al., 2012 and Erdogan and Miller-Hooks, 2012, and Demir et al., 2012). In the supply chain literature, TL transportation costs are modeled in various inventory control models (see, e.g., Aucamp, 1982, Lee, 1986, Toptal et al., 2003, Toptal and Çetinkaya, 2006, Toptal, 2009, Toptal and Bingol, 2011 and Konur and Toptal, 2012). These studies account for the per truck capacities and per truck costs in the context of inventory control. In this study, similar to these studies, we model transportation costs by explicitly accounting for per truck capacities and per truck costs. Furthermore, transportation emissions are formulated considering truck capacities and truck characteristics. In particular, a retailer who operates under the basic EOQ model settings is considered. Additional to the retailer's inventory holding and order setup costs, the retailer is subject to inbound transportation costs, which are determined by the numbers of specific trucks used for inbound transportation. It is also assumed that a fixed amount of carbon emissions is generated by each empty truck and emissions due to transportation increase with the loads of the trucks. We note that Hoen et al. (2012) and Pan et al. (2010) similarly define transportation emissions from freight trucks. In this study, we contribute to environmental inventory control studies by analyzing the deterministic inventory control models with carbon emissions considerations and explicit modeling of TL transportation costs as well as emissions. Furthermore, we consider availability of different truck types for inbound transportation. In practice, it can be the case that a retailer outsources its inbound transportation from a TL carrier, who offers a set of trucks with different characteristics. Moreover, it can be the case that the retailer has different TL carriers available in the market and each TL carrier offers trucks with different per truck costs and per truck capacities. In these cases, the retailer has to consider different truck types in modeling his/her transportation costs. Additionally, trucks types with distinct truck characteristics will have varying emissions generations (see, e.g., Demir et al., 2011). For instance, fuel type used, type of engine, year of built, vehicle mass, and driving characteristics (such as drag force, resistance) are all effective on the emissions generated by a freight truck (Ligterink et al., 2012). McKinnon (2005) and Mallidis et al. (2010), for instance, list sets of British and EURO truck types, respectively, and their emissions characteristics. Reed et al. (2010) also note that different truck types should be considered in calculating transportation emissions. In the analysis of a beverage industry in the U.S., Daccarett-Garcia (2009) notes that fleet management (truck configurations used) has significant effect on not only costs but also carbon emissions. According to the results of survey conducted by Leonardi and Baumgartner (2004) among 200 German companies, selecting the optimum vehicle categories is crucial for reducing fuel consumption (and; thus, emissions) from logistic activities. In a recent study, Bae et al. (2011) analyze competitive firms’ investment decisions for greening their transportation fleets. Based on these studies, it is an important decision to choose truck configurations (fleet management) for managing emissions as well as costs due to transportation. The current study, therefore, models emissions due to freight transportation considering different truck types. To the best of our knowledge, this study is first in explicitly considering different truck characteristics (cost and emission characteristics) in an integrated inventory control and transportation problem with carbon emissions constraint. We contribute to the current body of literature on carbon sensitive inventory models by modeling the EOQ model with TL transportation costs and emissions in the presence of heterogeneous trucks. The complexity of the problem is stated and an efficient heuristic solution method is developed. Furthermore, it is illustrated that considering different trucks in the inventory control and inbound transportation planning can reduce not only total costs but also emissions. The rest of the paper is organized as follows. Section 2 models the integrated inventory control and inbound transportation problem with carbon cap. Particularly, the retailer's cost and emissions functions are formulated with heterogeneous freight trucks. In Section 3, the properties of the problem of interest are discussed and a heuristic solution method is proposed. Results of a set of numerical studies are documented in Section 4 to illustrate the efficiency of the proposed heuristic method and analyze the effects of carbon cap. Furthermore, sample examples are solved to show the benefits of explicitly modeling different truck types. Section 5 summarizes the contributions and the findings of the paper and discusses possible future research directions.

5. Conclusions and future research This paper studies an integrated inventory control and truckload transportation with carbon emissions considerations. An EOQ model is formulated with explicit transportation costs. A carbon cap constraint is considered to limit the emissions from inventory holding, order placement, and truckload transportation. We consider different truck types in modeling truckload transportation costs and emissions. Specifically, to capture the fact that different truck types have distinct characteristics, each truck type is considered to have distinct per truck capacities and per truck costs as well as distinct emissions generations. In particular, each truck type is assumed to generate a specific amount of emissions due to its empty vehicle weight and the rates of emissions generated due to the loads of the trucks depend on the truck type. The resulting integrated inventory control and truckload transportation problem with heterogeneous truck types subject to carbon cap constraint is a mixed-integer-nonlinear programming model. The complexity of this problem is shown to be NP-hard; thus, heuristic methods are provided to solve this problem. Particularly, an heuristic local search algorithm is proposed based on the properties of the problem. For the special case with single truck type, an exact solution method is provided in the Appendix. The solution of the problem with single truck type has been utilized in the starting process of the local search heuristic. Through comparing the heuristic method to a commercial solver (BARON) over a set of numerical studies, it is observed that the heuristic method is efficient in terms of solution time and it finds good quality solutions. It should also be noted that the solutions found by the heuristic method result in less carbon emissions. Another set of numerical studies is conducted to analyze the effects of carbon cap on the retailer's integrated inventory control and transportation decisions. As expected, as carbon cap increases, the retailer's cost decrease while the emissions increase. It is observed that, as the carbon cap gets tighter, the retailer tends to increase the number of different truck types used for inbound transportation. On the other hand, the number of trucks used for shipment does not follow an increasing or decreasing pattern as carbon cap increases. Furthermore, through two sample scenarios, it is discussed that considering heterogeneous trucks for inbound transportation not only decreases costs but also reduces the emissions. This study contributes to the body of literature on environmentally sensitive inventory models by integrating practical aspects of truckload transportation with heterogeneous trucks. There is a growing awareness on emissions throughout supply chains and freight transportation, especially, is the major contributor to emissions throughout supply chains. It is also known that freight trucks are the most common transportation mode. It is, therefore, important to model freight truck costs as well as freight truck emissions in inventory control models as inventory control determines the freight amounts shipped throughout the supply chains. We believe that the modeling approach of this study and the analyses of the formulated model along with the insights gained will pioneer modeling integrated inventory control and transportation problems with environmental considerations. One of the possible future research directions is to study inventory control models with further generalized transportation models. For instance, different transportation modes, freight discounts, and nonlinear transportation costs can be analyzed in environmentally sensitive integrated inventory control and transportation models. One can also analyze multi-item or multi-echelon inventory systems with truckload transportation. For instance, it is important to analyze the effects of vendor-managed-delivery on carbon emissions. Another research direction is to study stochastic inventory control with environmental considerations and integrated transportation decisions. As discussed in Section 1, there are limited studies focusing on environmentally sensitive inventory models with stochastic demand and these studies focus on the single-period inventory decisions (see, e.g., Song and Leng, 2012 and Hoen et al., 2012). It is an important research area to study continuous or periodic inventory review systems (such as (Q,R) or (s,S) inventory models) with environmental considerations integrated with transportation. The modeling approach and findings of this study can be used in these aforementioned studies. Finally, the tools provided throughout this study can be used in policy development for truck weight limits. For instance, McKinnon (2005) study the effects of increasing freight vehicle loads in U.K. on environment. Through statistical analyses, it is noted that increasing freight loads has environmental benefits. The current study can be used in finding analytical results on the effects of truck characteristics on emissions.