outsourcing analysis in closed-loop supply chains for
TRANSCRIPT
Outsourcing Analysis in Closed-Loop Supply Chains for Hazardous
Materials
Víctor Manuel Rayas Carbajal
Tecnológico de Monterrey, campus Toluca
Marco Antonio Serrato García
Tecnológico de Monterrey, campus Toluca
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.
Figure 1. Closed-loop supply chain activities.
5 Markov Decision Model Developed
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.
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