Outsourcing Analysis in Closed-Loop Supply Chains for Hazardous Materials Víctor Manuel Rayas Carbajal Tecnológico de Monterrey, campus Toluca victor.rayas@invitados.itesm.mx Marco Antonio Serrato García Tecnológico de Monterrey, campus Toluca mserrato@itesm.mx Abstract In recent years, environmental issues have become a main topic worldwide. Governments around the world have established laws and policies to reduce the impact of industrial activity, forcing companies - especially those who produce or manage hazardous materials- to satisfy specific requirements on their supply chain systems. This is why many companies consider outsourcing as an option for these functions. Through this research, a Markov decision models are developed to support outsourcing decisions in a closed-loop supply chain system for hazardous materials. The models are based on the risk levels and sales behavior of the product considered. An optimal monotone nondecreasing policy is identified, which provides valuable insights for decision-makers involved in such systems. Keywords: Closed-loop supply chain; Markov Decision Model; Hazardous materials; Outsourcing. 1 Introduction Due to laws, international agreements, pressure from society, among other factors, human safety and health, environmental protection and security concerning hazardous materials supply chain are main topics for many countries, industries and organizations around the world (Mullai and Larsson, 2008). Hazardous materials are defined and regulated by a number of agencies around the world, whom establishes the regulations that concern the handling, storage and distribution of hazardous materials (Murray, 2013). For this reason, the shipping of hazardous materials can only be performed by carriers that are registered and only when the material is properly classed, described, packaged, marked, labeled, and in condition for shipment. Integrating environmental concerns into supply chain management has become increasingly important for manufacturers to gain and maintain competitive advantage (Zhu et al., 2008). As more executives adopt environmental practices, supply chain strategies will only increase in importance. As companies focus more tightly on their core competencies, they will rely more heavily on their suppliers for non-core activities such as the transportation, recovery and disposal of their products (Handfield et al., 2005). The characteristics of each product and activity suggest specific strategies. Low-value activities require little attention and might even be completely outsourced (Handfield et al., 2005). With an outsource strategy, companies can improve benefits while they are focusing on their core activity (Boyson, et al., 1999).
2 Environmental Risk The use of hazardous materials can cause unintentional accidents. Incidents have occurred in every system of the hazardous materials supply chain, including platforms, all modes of transport, chemical plants, terminals and storages (Mullai and Larsson, 2008). Managers have come to realize that a large and increasing amount of environmental risk can be found in nearly every company s supply chain, increasing the importance of the decisions in this area (Hanfield et al., 2008). This risk implies that the companies must be more specialized on each one of these activities or outsource some of them in order to focus on their core activity (Zhu et al., 2008). A risk/cost framework for the hazardous materials management system must include an assessment of the risk due to storage, transportation, treatment and disposal. The risk cost calculation may vary by the type of activity involved, but it must be according to the accident rate and possible affected population (Killmer et al., 2002). Only for the case of petroleum products, from 1990 to 2000, 36 accidents were reported in the management of these materials, which resulted in more than 2200 deaths and about 3,000 injured people (Alcantara and Gonzalez, 2001). 3 Closed-Loop Supply Chains and their Outsource The research of the supply chain management has passed through various stages, from the individual activities optimize to an entire analysis of the whole chain. This is the case of the closed-loop supply chain management, which is define as the design, control, and operation of a system to maximize value creation over the entire life cycle of a product with dynamic recovery of value from different types and volumes of returns over time (Guide and Van Wassenhove, 2009). The major difference between CLSC and traditional supply chains is for a forward supply chain, the costumer is at the end of the process, and for a CLSC, there is value to be recovered from the costumer or end-user. The value to be recovered is significant, only in the United States is over $50 billion in annual sales of remanufactured products (Guide and Van Wassenhove, 2003). Although, there are some complicating characteristics for planning and controlling a supply chain with remanufacturing of external returns. Some of them are the requirement for a reverse logistics network, the uncertain timing and quality of cores, the uncertainly in material recovered from cores, the problem of stochastic routings for materials and highly variable processing times and the need to balance returns of cores with demands for remanufactured products (Guide, 2000). Supply chain management is recognized as a strategy for improving competitiveness by improving customer value and reducing cost (Mentzer, 2004). Given the logistics costs that are implied in this activities and the customers demands for shorter order cycles, some companies consider outsourcing these activities to third party logistics (3PL) providers. Warehouse, distribution and reverse logistics are the most common activities to outsource (Arroyo et al., 2006). Also, it is common to outsource multiple logistics services, but just a few companies outsource the manufacture or production activity (Lieb and Bents, 2005). Boyson et al. (1999) find that firms can improve customer service and reduce costs by outsourcing packages of functions and suggest as the main benefits of 3PL: cost savings, operational efficiency, flexibility and improved customer service. Generally, outsourcing logistics functions is a long term decision (Serrato, et. al. 2007). This is consistent with the survey by Boyson et al. (1999), where the respondents who have outsourced an activity in their company, only 4% reported that they stopped outsource this activity. 4 Problem Description
Because some activities of the closed-loop supply chain for hazardous materials do not represent the core business of the company, one of the most important decisions for any organization is which activities should be outsourced to a 3PL. Such decision considers not only whether or not outsource, but also when they should be outsourced, in order to minimize the total expected cost for the whole cycle and reduce the risk cost associated, this by a Markov Decision Model (MDM) which is ideal for stochastic problems. The models are based on the Risk Levels, Sales and Returns behavior of the hazardous material considered. For this model it is assumed that the CLSC consists of six main activities (figure 1). Lieb and Bentz (2005) indicate that in their surveys conducted in 2004, 67% of companies outsource distribution activities, warehousing activities 46% and 33% reverse logistics (RL) activities. According to this, it is assumed that these activities can be outsourced, while the production is a core activity and never will be outsourced and the market and re-use/disposal activity are probabilistic (with a known probability distribution) and the company does not directly control. 5 Markov Decision Model Developed Figure 1. Closed-loop supply chain activities. We define the follow notation for the MDMs developed: Sets Subactivities or expenses, { Parameters Cost of subactivity or expense j Unit shortage cost Environmental risk cost, L Length of the product life cycle W Time length defined by the firm to continue managing the returns for the product analyzed T Length of the study horizon, T = L + W t Decision epoch,, t={1,, T-1}, where decision epoch t represents the end of period t. Time T corresponds to the end of the problem horizon, where no decision is taken. Expected sales for period t Rate for sales increase,
Rate for devolutions, Random variables Amount of units sold by the firm during period t Cumulative sales experienced by the firm from period 1 through the end of period t, Number of units returned in period t Cumulative number of units returned from period 1 to the end of period t, State variables Amount of units sold by the firm during period t Number of units sold and not returned at the end of period t, Capacity at period t Model assumptions Returns are a function of the number of units previously sold but not yet returned. Each unit has a binomial distribution probability of being returned (Serrato, et al., 2007). Sales are assumed to be distributed Poisson with mean λ. Average sales change at a known rate in each period (Chen, 2014). There is a cost per unit for the collection and handling of a returned unit, which is considered less than the savings generated by remanufacturing one unit (Savaskan et al., 2004). Given that warehouse, distribution and RL does not represent a core activity, it is also assumed that once the outsourcing decision is taken, it remains in place for the rest of the problem horizon as an absorbing state (Serrato, et al., 2007). If any activity is still done internally and it incurs in a shortage, then there would exist a cost associated to meet this demand. If the activity is outsourced, the 3PL would always have enough capacity to satisfy such a demand (Serrato, et al., 2007). Because of the last assumption, each activity can be considered independent such that the decision will be made with a different and independent model, being analyzed together as a final stage in this research. 5.1 Markov Decision Model for Warehouse and Distribution Due to the similarities of the operations and parameters in the warehouse and distribution activities, both models shares the states, action, transition probabilities and rewards definitions, but there is a difference on the calculation of the environmental risk cost associated. The models are defined by: States. The system state at each decision epoch t is defined as { }, for t=1,, T. At decision epoch 0, the system state is { }, where. Also,. Actions. Given the purpose of the MDM, we assume that two actions are available: Continue performing the activity internally, by updating the firm s capacity to the expected amount of sales in the next period, i.e., [ ] [ ]. Adopt an outsourcing strategy for the activity by having a 3PL perform such activity and taking the firm s activity capacity to zero; i.e.,. Transition probabilities. As the sales at each period follow a Poisson distribution, the transition probabilities among states are defined as [( ) ]; i.e., [( ) ] { [( ) ] { [ ]
[ ] Rewards. The following reward structure is defined for actions a=0 or 1. [ ] ( ) ( ) [ ] [ ] Where denotes. Environmental Risk Cost for Warehouse. This cost is defined as (Killmer et al., 2002). Where: Probability of an accident occurs Cost per person affected Affected area in case of accident Population density of the area affected Environmental Risk Cost for Distribution. This cost is defined as (Killmer et al., 2002). Where: Probability of an accident occurs Cost per person affected Population of the destiny Travel distance Distance between the route and the destiny 5.3 Markov Decision Model for RL The MDM is defined by: States. The system state at each decision epoch t is defined as { }, for t=1,, T. At decision epoch 0, the system state is { }, where. Actions. Given the purpose of the MDM, we assume that two actions are available: Continue performing the activity internally, by updating the firm s capacity to the expected amount of returns in the next period, i.e., [ ] [ ]. Adopt an outsourcing strategy for the activity by having a 3PL perform such activity and taking the firm s activity capacity to zero; i.e.,. Transition probabilities. As the returns in each period follow a binomial distribution,, the transition probabilities among states are defined as [(( ) ) ]; i.e.: [(( ) ) ] { ( ) [( ) ] { ( ) Rewards. The following reward structure is defined for actions a=0 or 1. [ ] ( ) ( ) [ ] [ ] [ ] Where denotes. Environmental Risk Cost. This cost is defined as (Killmer et al., 2002). Where: Probability of an accident occurs Cost per person affected Affected area in case of accident
Population density of the area affected 5.4 System Dynamic For all the models, the system follows the dynamic presented at figure 2 for each period t. At the end of the last period of production and returns, all the capacity remaining in the system is sold. Figure 2. System dynamic. The action decided for each period is defined by the maximum reward earned by continuing optimally from state onwards for each independent activity at each period t. The optimal policy for each activity can be obtained by solving recursively: { [ ] [ ] [ ] [ ] }. The optimal policy will be the result of the decisions taken for each activity for each period. 6 Conditions for a Monotone Optimal Policy In principle, this problem can be solved recursively backwards from period T to identify an optimal action for each possible state. However, depending on the conditions of the problem, the number of states to evaluate could grow very large (Serrato, et al. 2007). For this reason, it is desirable to identify a simple form for an optimal policy. This policy corresponds to a threshold (in terms of the sales and cumulative returns given a particular capacity level), beyond which the outsourcing action a=1 is optimal. Sets of conditions exist that ensure that optimal policies are monotone in the system state (Puterman, 1994). One set of conditions stated for the existence of a monotone optimal policy is: 1. [ ] is nondecreasing in for { }. 2. [( ) ] is nondecreasing in for all and { }. 3. [ ] is a superadditive function on. 4. [( ) ] is a superadditive function on. 5. [ ] is nondecreasing in Where ( ) When all of these conditions are satisfied, there exists a monotone non-decreasing policy that is optimal. 7 Numerical Ilustration To demonstrate the behavior of the decisions for the MDMs for warehouse and distribution, consider a particular scenario defined by the parameters:
L = 5 W = 1 By solving recursively this model, we have the results shown at table 1. For this case, the optimal policy is to perform the activity internally until period t=5. This example confirms that under certain condition, there exists a monotone optimal policy. Table 1. Optimal policy for the MDMs for warehouse and distribution ( ) ( ) 1-581.2-586.6-581.2 0 2-497.1-502.8-497.1 0 3-396.5-401.4-396.5 0 4-280.4-283.4-280.4 0 5-151.3-149.5-149.5 1 6 0 0 0 1 For the MDM for RL, consider this scenario: L = 5 W = 1 By solving recursively this model, we have the results shown at table 2. For this case, the optimal policy is to outsource the activity internally since period t=1. This scenario also shows that the outsource decision results in an absorbing state. Table 2. Optimal policy for the MDM for RL ( ) ( ) 1-474.8-461.2-461.2 1 2-452.5-436.0-436.0 1 3-400.4-381.4-381.4 1 4-314.0-293.2 293.2 1 5-178.5-167.2-167.2 1 6 0 0 0 1 8 Conclusions and Future Work The importance of the CLSC for hazardous materials and the outsourcing as a strategy in order to minimize costs and focus on the core business has been stated in this study. Also, a MDMs to support the outsource decision in a CLSC for hazardous materials was developed. The models considers several elements that are critical in defining the characteristics of an CLSC for hazardous materials, such as expected sales, uncertainty in the return volume, capacity, operating, shortage and environmental risk costs. Some sufficient conditions for the existence of an optimal monotone nondecreasing policy have been generally described. The existence of an optimal monotone non-decreasing policy implies the presence of a threshold above which it is optimal to follow an outsourcing strategy for the RL system; otherwise, to continue performing the RL activities internally. This threshold is defined in terms of a partial ordering for the system states, where given a fixed capacity at a decision epoch, the states are ordered according to the sales and cumulative returned units, such that if that volume goes above a particular level, then it is optimal to follow an outsourcing strategy and take advantage of the economies of scale implied by involving a 3PL.
As a future research, the conditions for the existence of an optimal monotone nondecreasing policy must be verified and proven, as well as an extended numerical evaluation for a case of study. Also, many other important characteristics of the system could be analyzed in order to take a better decision, as the life cycle length. References 1. Alcantara, M., and Gonzalez, T. Modelacion de radios de afectacion por explosions en instalaciones de gas. CENAPRED. 2001. Mexico. 2. Arroyo, P. Gaytan, J. and Boer, L. A survey of third party logistics in Mexico and a comparison with reports on Europe and USA. International Journal of Operations and Production Management. 26(6): 639-667, 2006. 3. Boyson, S., Corse, T., Dresner, D. and Rabinovich, E. Managing effective third party logistics relationships: What does it take? Journal of Business Logistics, 20: 73 100, 1999. 4. Chen, Y. An Inventory Model with Poisson Demand and Linear Lost Sales, International Journal of Service Science, Management and Engineering. 1(1): 17-20, 2014. 5. Guide, V. D. and Van Wassenhove, L. Special section on closed-loop supply chains. Interfaces 33(6): 1 2, 2003. 6. Guide, V.D. and Van Wassenhove, L. The evolution of closed-loop supply chain research. Operations Research. 57(1): 10-18, 2009. 7. Handfield, R., Sroufe, R. and Walton, S. Integrating environmental management and supply chain strategies. Business Strategy and the Environment. 14: 1-19, 2005. 8. Killmer, K. A risk/cost framework for logistics policy evaluation: Hazardous waste management. The Journal of Business and Economics Studies. 8(1): 51-65, 2002. 9. Lieb, R. and Bentz, B. The use of Third-Party Logistics Services by Large American Manufacturers: The 2004 Survey. Transportation Journal. 44(2): 5-15, 2005. 10. Mentzer, J.T. Fundamentals of Supply Chain Management, Sage, United States. 2004. 11. Mullai, A. and Larsson, E. Hazardous material incidents: Some key results of a risk analysis. WMU Journal of Maritime Affairs, 7(1): 65-108, 2008. 12. Murray, M. Federal Hazardous Materials Transportation Regulations. About.com. Retrieved February, 2013, from http://logistics.about.com/od/legalandgovernment/a/federal-hazardous-materials-transportation- Regulations.htm 13. Puterman, M.L., Markov Decision Processes: Discrete Stochastic Dynamic Programming, John Wiley & Sons. New York, NY. 1994. 14. Savaskan, R., Bhattacharya, S. and Van Wassenhove, L. Closed-Loop Supply Chain Models. Management Science. 50(2): 239-252, 2004. 15. Serrato, M. A., Ryan, S. M. and Gaytán, J. A Markov decision model to evaluate outsourcing in reverse logistics. International Journal of Production Research, 45(18): 4289 4315, 2007. 16. Sherbrooke, C. C. Metric: A Multi-Echelon Technique for Recoverable Item Control. Operations Research, 16(1): 122-141, 1968. 17. Zhu, Q., Sarkis, J, and Lai, K. Confirmation of a measurement model for green supply chain management practices implementation. International Journal of Production Economics, 111: 261-273, 2008.