Transportation cost and CO2 emissions in location decisionmodelsCitation for published version (APA):Velazquez Martinez, J. C., Fransoo, J. C., Blanco, E. E., & Mora-Vargas, J. (2014). Transportation cost and CO2emissions in location decision models. (BETA publicatie : working papers; Vol. 451). Technische UniversiteitEindhoven.

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Transportation Cost and CO2 Emissions in Location Decision Models

Josue C. Vélazquez Martínez, Jan C. Fransoo,

Edgar E. Blanco, Jaime Mora-Vargas

Beta Working Paper series 451

BETA publicatie WP 451 (working paper)

ISBN ISSN NUR

804

Eindhoven March 2014

1

Transportation Cost and CO2 Emissions in Location Decision Models

Josue C. Vélazquez-Martínez1, Jan C. Fransoo1*, Edgar E. Blanco2, Jaime Mora-Vargas3

1 Technische Universiteit Eindhoven

School of Industrial Engineering

P.O. Box 513, Pav F4

NL-5600 MB Eindhoven

Netherlands

2 MIT Center for Transportation & Logistics

3 Instituto Tecnológico y de Estudios Superiores de Monterrey, Campus Estado de México

* Corresponding author: j.c.fransoo@tue.nl

2

Transportation Cost and CO2 Emissions in Location Decision Models

Josue C. Vélazquez-Martínez1, Jan C. Fransoo1, Edgar E. Blanco2, Jaime Mora-Vargas3

1 Technische Universiteit Eindhoven, School of Industrial Engineering

2 MIT Center for Transportation & Logistics

3 Instituto Tecnológico y de Estudios Superiores de Monterrey, Campus Estado de México

An increasing number of companies are making their supply chains more sustainable. Because

transportation accounts for a large share of global CO2 emissions, finding logistics alternatives that reduce

carbon emissions while keeping costs low is a priority. In this article, we study the trade-off between cost

and CO2 emissions by using a multiobjective approach for the facility location problem. We propose a

model with new cost and CO2 structures for the p-Median problem to determine a sustainable location. To

solve this problem, we develop the multiobjective combinatorial optimization cross-entropy method, to

address the difficulties of combinatorial models. We test the algorithm against two p-Median problems

from prior literature and show that it can approximate the Pareto frontier efficiently. We also conduct an

experimental study for a consumer packaged goods company in Mexico City to provide insights on the

structure of the Pareto frontier for a practical sustainable facility location case. The study shows that by

selectively changing a subset of locations, companies may achieve a substantial reduction in carbon

emissions under similar costs.

Key words: Sustainable facility location, Multiobjective combinatorial optimization.

1. Introduction Regardless of whether companies’ decision makers believe in green and sustainable practices, a market

shift is occurring, driving firms to measure and disclose their carbon emissions and implement solutions

to reduce those emissions (Hoffman and Woody, 2008). For example, the number of companies around

the world reporting their emissions to the Carbon Disclosure Project (2011), a not-for-profit foundation,

has doubled from 2007 to 2010, and approximately 1,000 of these companies have publicly committed to

a carbon reduction target. Transportation is one of the main contributors of carbon dioxide (CO2)

3

(Intergovernmental Panel on Climate Change, 2007), and predictions indicate increases in the next 20

years (European Commission, 2011); thus, more efficient transport operations would substantially reduce

carbon emissions.

A relevant logistics problem that determines the configuration of a company’s delivery of goods is the

facility location problem. The location of distribution centers is critical to the efficient and effective

operation of a supply chain; poorly placed plants can result in excessive costs and low service level no

matter how well tactical decisions (e.g., vehicle routing, inventory management) are optimized (Daskin et

al., 2005). In addition, this configuration can increase CO2 emissions, in that the main drivers of

transportation carbon emissions are distance, truck load (Greenhouse Gas Protocol Standard, 2011) and

the number of trips required to deliver demand to each customer.

A common facility location model that has multiple real-world applications is the p-Median problem

(ReVelle et al., 2008). The p-Median problem considers p facilities that must be located in a network,

such that the demand in each node must be satisfied while the total weighted demand-distance is

minimized (Hakimi, 1964). Because of the strategic nature of facility location problems, the cost structure

of the p-Median does not take into account capacity or cost of the truck fleet, and it assumes a constant

cost per distance per unit (ReVelle et al, 2008), linear to the distance and demand. However, in reality

these two factors are not linearly related; for example, the amount of items affects the transport cost (and

carbon emissions) when it implies an increase in the number of trucks or trips.

Previous operations research has addressed aggregations. Jalil et al. (2011) study cost aggregation for

real-life spare parts planning, and they find that errors can be significant. Velázquez-Martínez et al.’s

(2013) study addresses the effects of using different aggregation levels to measure transport carbon

emissions in the dynamic lot-sizing model, and they show that errors associated with aggregation tend to

be substantial and systematic. These findings suggest that increasing the level of detail in the p-Median

problem is necessary.

Because decision makers are likely interested in evaluating alternatives to increase carbon efficiency

while keeping low transport costs, we propose a multiobjective approach to analyze the trade-off between

cost and carbon emissions expressions for the p-Median problem. Although literature on multiobjective

facility location problems with environmental concerns has increased in the first decade of the twenty-

first century (e.g., Blanquero and Carrizosa [2002] study a semi-obnoxious location problem with cost

and negative effect; Medaglia et al. [2009] investigate a hospital waste management system; Fonseca et

al. [2009] address stochastic reverse logistics; Du and Evans [2008] study reverse logistics network), to

our knowledge, no studies include sustainability in their location models, because it is difficult to define a

4

structure that measures this attribute (Farahani et al., 2010). In this study, we propose an expression that

takes into consideration CO2 emissions in the p-Median problem.

The p-Median problem with a single objective is classified as NP-hard (Kariv and Hakimi, 1979);

therefore, defining the Pareto frontier for its multiobjective version is not an easy task. Traditional

optimization methods such as gradient- and simplex-based methods are difficult to extend to

multiobjective optimization (Fonseca and Fleming, 1995); however, the use of metaheuristics allows

researchers to manage these problems effectively. These techniques enable researchers to find several

solutions of the set in a single run instead of performing a series of separate runs (Ajith et al., 2005).

Bekker and Aldrich (2011) apply a new metaheuristic to solve multiobjective optimization problems

based on the cross-entropy (CE) method (De Boer et al., 2005), a simulation-based metaheuristic used to

solve single-objective optimization problems. Bekker and Aldrich (2011) adapt the CE method to solve

multiobjective optimization problems and test it against benchmark problems from the literature. They

show that the CE method applied to multiobjective optimization obtains satisfactory results. Although

their test results seem promising for applying the CE method in multiobjective problems, their study does

not address the use of the algorithm on multiobjective combinatorial optimization (MOCO) problems,

which corresponds to the structure of the p-Median model.

In the current research, we study the trade-off between cost and CO2 by using a multiobjective approach

to the p-Median problem. We name this new model the sustainable facility location (SFL) problem. Our

model captures a higher level of detail in the cost and CO2 formulations by taking into account truck

accessibility constraints per demand node and finer-grained expressions for both objective functions. To

approximate the Pareto frontier of the SFL, we develop an adaptation of the CE method applied to

multiobjective optimization problems, called the MOCO CE method (hereinafter, MOCO CEM). We test

our algorithm against problems from prior literature and demonstrate that the MOCO CEM is capable of

approximating the Pareto frontier for the SFL problem efficiently. Furthermore, we conduct an

experimental study of the MOCO CEM by solving the SFL for a consumer packaged goods (CPG)

company that operates in the Mexico City metropolitan area. The experiments provide managerial

insights on the structure of the Pareto frontier for an actual company in a large urban area and show that it

is possible to find location alternatives, such that for small increases in cost, firms can obtain large CO2

emission reductions.

The remainder of this article is organized as follows: Section 2 presents the mathematical formulation of

the sustainable facility location model. Section 3 describes the MOCO CEM. Section 4 presents a case

5

study in which we apply the MOCO CEM to an actual CPG company. In Section 5, we present our

conclusions.

2. The Sustainable Facility Location Problem Our model corresponds to the p-Median problem with cost and CO2 objective functions. The general

assumptions of the p-Median problem are applicable to our model; that is, deterministic demand and the

candidate locations are known in advance. We also assume that the company manages multiple trucks

with different capacities and the trucks are assigned according to demand node constraints. These

assumptions allow the model to include the possibility that certain customers are reachable only by

certain types of trucks, with distinct cost structures.

To formulate the carbon emissions objective function in our model, we use Network for Transport and

Environment’s methodology. For the estimation of carbon emissions, this methodology requires a high

level of detailed parameters: fuel consumption, distance traveled and weight per shipment (Network for

Transport and Environment Road, 2008). Fuel consumption is a function of the type of vehicle, the load

factor and the type of road. The methodology uses the European Assessment and Reliability of Transport

Emission Models and Inventory Systems database, which includes a detailed emissions model for all

transport modes to provide consistent emission estimates at the national, international and regional levels

(Transport Research Laboratory, 2010).

We therefore formulate our model as follows. Let 𝐼 be a set of demand nodes and 𝐽 be a set of candidate

locations. We define the following parameters:

ℎ𝑖 = Demand at node 𝑖 ∈ 𝐼

𝑑𝑖𝑗 = Distance between candidate facility site 𝑗 ∈ 𝐽 and

customer location 𝑖 ∈ 𝐼

𝐴𝑖𝑗 = Fixed cost per trip between candidate facility site

𝑗∈𝐽 and customer location 𝑖∈𝐼

𝑣𝑖𝑗 = Cost per distance traveled between candidate

facility site 𝑗∈𝐽 and customer location 𝑖∈𝐼

𝑊𝑖 = Truck capacity per trip restricted to customer

location 𝑖∈𝐼

𝑛𝑖𝑗 =ℎ𝑖𝑌𝑖𝑗𝑊𝑖

= Number of trips per period required to serve the

customer location 𝑖∈𝐼 from facility site 𝑗∈𝐽

𝑘 = Constant emission factor (2,621 grams of CO2/liter

6

of fuel)

𝑓𝑖𝑒 = Fuel consumption of the empty vehicle used to

serve at customer location 𝑖∈𝐼 (liters/km), and

𝑓𝑖𝑓 = Fuel consumption of the fully loaded vehicle used

to serve at customer location 𝑖∈𝐼 (liters/km)

We use the following decision variables:

𝑋𝑗 = 1 if we locate at site 𝑗 ∈ 𝐽, 0 otherwise.

𝑌𝑖𝑗 = Fraction of demand at customer location 𝑖 ∈ 𝐼 that is

served by facility at site 𝑗 ∈ 𝐽.

We then formulate the multiobjective SFL model as follows:

𝑀𝑖𝑛 → 𝑂𝐹1 = ��𝐴𝑖𝑗𝑛𝑖𝑗𝑖∈𝐼𝑗∈𝐽

+��𝑣𝑖𝑗𝑑𝑖𝑗�𝑛𝑖𝑗�𝑖∈𝐼𝑗∈𝐽

𝑀𝑖𝑛 → 𝑂𝐹2 = 𝑘 ���𝑑𝑖𝑗𝑓𝑖𝑒�𝑛𝑖𝑗�𝑖∈𝐼𝑗∈𝐽

+��𝑑𝑖𝑗𝑛𝑖𝑗�𝑓𝑖𝑓 − 𝑓𝑖𝑒��𝑛𝑖𝑗�

𝑖∈𝐼𝑗∈𝐽

�

subject to

∑ 𝑌𝑖𝑗𝑗∈𝐽 = 1 ∀𝑖 ∈ 𝐼 (1)

∑ 𝑋𝑗𝑗∈𝐽 = 𝑝 (2)

𝑌𝑖𝑗 − 𝑋𝑗 ≤ 0 ∀𝑖 ∈ 𝐼 ∀𝑗 ∈ 𝐽 (3)

𝑋𝑗 ∈ {0,1} ∀𝑗 ∈ 𝐽 (4)

𝑌𝑖𝑗 ≥ 0 ∀𝑖 ∈ 𝐼,∀𝑗 ∈ 𝐽 (5)

The first part of OF1 corresponds to the fixed cost per trip. It includes labor and costs related to the use of

the truck (e.g., depreciation, insurance). In turn, 𝑛𝑖𝑗 is the total number of trips required to deliver the

total demand from location j to demand node i taking into account the truck capacity Wi. Note that we do

not restrict 𝑛𝑖𝑗 to be an integer because of the strategic nature of the model, fixed costs tend to be

allocated across multiple demand nodes and trips. The second part of OF1 corresponds to the variable

cost per distance traveled from candidate facility site 𝑗 ∈ 𝐽 to customer location 𝑖 ∈ 𝐼. We apply a ceiling

7

function to estimate the number of times distance 𝑑𝑖𝑗 is traveled. The first part of OF2 corresponds to the

carbon emissions due to the number of trips required, and the second part corresponds to the carbon

emissions due to the units to be transported. Constraint 1 states that each demand node is covered.

Constraint 2 establishes that p facilities are located. Constraint 3 designates that the facility is opened

when a demand node is assigned. Constraint 4 encompasses the integrality constraints, and constraint 5

encompasses the non-negative constraints.

By reducing the expressions, and because the single sourcing condition holds for both OF1 and OF2, we

formulate the multiobjective SFL problem as follows:

𝑀𝑖𝑛 → 𝑂𝐹1 = ��� 𝐴𝑖𝑗ℎ𝑖𝑊𝑖

+ 𝑣𝑖𝑗𝑑𝑖𝑗 �ℎ𝑖𝑊𝑖��𝑌𝑖𝑗

𝑖∈𝐼𝑗∈𝐽

𝑀𝑖𝑛 → 𝑂𝐹2 = ��𝑑𝑖𝑗 �ℎ𝑖𝑊𝑖� �𝑓𝑖𝑒 + �𝑓𝑖

𝑓 − 𝑓𝑖𝑒�ℎ𝑖𝑊𝑖�𝑌𝑖𝑗

𝑖∈𝐼𝑗∈𝐽

subject to Constraints 1-5.

Note that the objective functions differ from each other: OF1 has fixed and variable costs, but only the

variable part depends on the distance traveled, whereas the entire OF2 expression depends on the distance

traveled. This relationship suggests that for a specific instance, if the highest fixed costs are assigned to

edges with the shortest distance (or the lowest fixed costs are assigned to edges with the largest distance),

SFL may provide multiple solutions, and thus, the Pareto frontier would contain a larger number of

points.

3. The Multiobjective Combinatorial Optimization Cross-Entropy Method 3.1. Multiobjective definitions

In general, the multiobjective optimization (MOO) problem involves having more than one objective

function to be minimized or maximized. Commonly, these objective functions are continuous. As in the

single-objective optimization problem, in the MOO problem, several constraints are clearly defined, and

any feasible solution must satisfy them. However, the main difference compared with single-objective

problems is that with MOO, it is commonly not possible to define an optimal solution for the problem (if

there were an optimal solution, the problem would not require a multiobjective setting, and a single

objective might suffice); instead, the result is a set of “efficient” solutions that are not superior to one

another in all the objective functions. In this sense, single-objective optimization problems are a

degenerate case of the MOO problem, not just an extension of it (Deb, 2001).

8

When a MOO problem involves discrete space, it is considered a MOCO problem. Similar to MOO,

MOCO has several objective functions, but the variables are integers or binary numbers. As in

combinatorial optimization with a single objective, MOCO has a finite and discrete set of feasible

solutions. A general formulation of the MOCO problem is as follows (Ehrgott, 2005):

𝑚𝑖𝑛�𝑓𝑗(𝒙):𝒙 ∈ 𝑋; 𝑗 = 1, … ,𝑚�

𝑋 = {𝒙:𝐴𝒙 = 𝒃,𝒙 ≥ 0 𝑖𝑛𝑡𝑒𝑔𝑒𝑟; 𝑖 = 1, … ,𝑛}

where 𝑓𝑗 is the 𝑗𝑡ℎ objective function and x is the vector of decision variables. The matrix A and vector b

define the set of linear constraints.

In the following subsections, we elaborate on concepts from Deb (2001), Ehrgott (2005) and Coello

(2009) to define relevant terms.

Definition 1. Dominance

A solution x is said to dominate solution y if both the following conditions hold for a minimization

problem:

1. The solution x is not worse than y in all objectives; that is, 𝑓𝑗(𝒙) ≤ 𝑓𝑗(𝒚) for all 𝑗 = 1, … , 𝐽

2. The solution x is strictly better than y in at least one objective; that is, 𝑓𝑗′(𝒙) < 𝑓𝑗′(𝒚) for at least

one 𝑗′ ∈ {1, … ,𝑀}

Definition 2. Efficient or Pareto-optimal solution

A feasible solution is called efficient or Pareto optimal if there is no other feasible solution that

dominates it. If the solution vector x is efficient, the vector 𝑓(𝒙) whose M components are the values of

the objective functions at the point x is called a non-dominated point.

Definition 3. Nondominated set

The nondominated set of solutions P’ is the set of all solutions that are not dominated by any member of

the feasible solution set P.

Definition 4. Pareto-optimal set

The nondominated set of the entire feasible space is the globally Pareto-optimal set. This set is also

called the efficient frontier or Pareto frontier.

9

Thus, the goal in MOO and MOCO is to find members of the Pareto-optimal set. Some solution

approaches obtain all elements of the Pareto set, while other techniques aid in the approximation of this

set. Such an approximation could result in a subset of the exact Pareto set or a set of points within a

specified distance of the Pareto set.

For MOO in continuous problems, a classic approach to obtain the Pareto set involves using the weighted

sum scalarization method, which corresponds to the set of solutions that can be obtained by solving

𝑚𝑖𝑛�∑ 𝜆𝑗𝑓𝑗(𝒙)𝑚𝑗=1 :𝒙 ∈ 𝑋�, where 0 ≤ 𝜆𝑗 ≤ 1 and ∑ 𝜆𝑗𝑚

𝑗=1 = 1. However, this approach does not work

for MOCO problems because of their discrete structure (Ehrgott and Gandibleux, 2000). The solutions for

the MOCO problems that can be obtained by this approach are called supported solutions. Typically,

MOCO problems have more efficient solutions that are not optimal for any weighted sum of the

objectives. These solutions are called nonsupported solutions, and their numbers increase exponentially

with the problem size (for the assignment problem, see Hansen 1980; for the traveling salesperson

problem, see Sergienko and Perepilitsa 1991). Ehrgott (2000) shows that the general MOCO problem is

NP-complete, and thus, it may be computationally prohibitive to use an exact method to determine all

efficient solutions. Therefore, we conclude that approximate methods are appropriate.

In the next section we review the main approximate algorithms for combinatorial multiobjective

problems.

3.2. Approximate algorithms for MOCO problems

Because most MOCO problems are NP-complete, literature mostly focuses on approximate (heuristic)

algorithms that address reasonably sized problems. These algorithms generate an approximated Pareto set

(or a subset of it) with solutions that either belong to the optimal Pareto set or are close to it.

Evolutionary algorithms are metaheuristic procedures that have become increasingly popular in recent

decades (Coello, 2009). Their ability to handle complex problems, involving features such as

discontinuities, multimodality and disjoint feasible spaces, have made them effective techniques to seek

approximately Pareto-optimal solutions for MOO problems (Fonseca and Fleming, 1995; Jaszkiewicz,

2002; Köksalan, 2008; Zitzler et al., 2000). Schaffer (1985) presents the vector evaluated genetic

algorithm (VEGA). Horn et al. (1994) propose the niched Pareto genetic algorithm (NPGA). Zitzler and

Thiele (1998) propose the strength Pareto evolutionary algorithm (SPEA). Deb et al. (2000) suggest an

elitist nondominated sorting genetic algorithm (NSGA-II) that uses an elite preservation strategy together

with an explicit diversity-preserving mechanism.

10

In the current study, we propose using the CE method (Rubinstein & Kroese, 2004) for MOCO problems

by adapting the MOO CE method (hereinafter, MOO CEM) that Bekker and Aldrich (2011) present. The

MOO CEM was tested against benchmarking problems from Coello et al. (2007) and the results were

promising by approximating all the problems to the true Pareto optimal set (Bekker and Aldrich, 2011),

with fewer objective function evaluations than in other experiments reported for the algorithms VEGA,

NPGA and SPEA (Zitzler et al., 2000).

The MOO CEM is a metaheuristic to solve MOO problems using the CE method (De Boer et al., 2005;

Rubinstein and Kroese, 2004). The CE method was motivated by an adaptive algorithm for estimating

probabilities of rare events in complex stochastic networks (Rubinstein, 1997). This algorithm can solve

difficult single-objective combinatorial optimization problems. It works by translating the deterministic

optimization problem into a related stochastic optimization problem and then using rare event simulation

techniques similar to Rubinstein (1997). Several recent applications demonstrate the power of the CE

method as a practical tool for solving NP-hard problems: buffer allocation (Alon et al., 2005), control and

navigation (Helvik and Wittner, 2001), DNA sequence alignment (Keith and Kroese, 2002), vehicle

routing (Chepuri and Homem-de-Mello, 2005), project management (Cohen et al., 2005), heavy-tail

distributions (Rubinstein and Kroese, 2004), network reliability (Hui et al., 2005), maximal cut and

bipartition problems (Rubinstein, 2002) and facility location problems (Caserta and Quiñonez Rico,

2009). De Boer et al. (2005) provide a tutorial on the CE method.

3.3. The MOCO CEM algorithm

3.3.1. The CE Method

The foundation of CE method for optimization is in Importance Sampling and the Kullback–Leibler

distance (Rubinstein and Kroese, 2004). In the following paragraphs, we present a brief description of the

CE method based on some definitions from Rubinstein and Kroese (2004) and include the algorithm to

solve single-objective combinatorial optimization problems (for a more complete review, see De Boer et

al. 2005).

Let 𝚾 = (𝑋1, … ,𝑋𝑛) be a random vector assuming values from some space x, and let f be some real

function on x. To determine the probability that 𝑓(𝚾) is greater than or equal to a real number 𝛾 under a

family of probability density functions ℎ(∙;𝑢) on x, we use 𝑙 = ℙ𝑢(𝑓(𝚾) ≥ 𝛾) = 𝔼𝑢𝐼(𝑓(𝚾)≥𝛾). Then

𝑓(𝚾 ≥ γ) is called a rare event if l is very small, and it can be efficiently estimated using importance

sampling. We thus generate a random sample 𝚾1, … ,𝚾𝑁 from a different density g on x and estimate l

using the following likelihood estimator (Rubinstein and Kroese, 2004): 𝑙 = 1𝑁∑ 𝐼{𝑓(𝚾𝑖)≥𝛾}𝑁𝑖=1

ℎ(𝚾𝑖;𝐮)𝑔(𝚾𝑖)

.

11

Thus, 𝑙 =𝐼�𝑓�𝚾𝑖�≥𝛾�ℎ(𝚾𝑖;𝐮)

𝑔∗(𝚾𝑖). In turn, 𝑔∗ can be approximated within the family of densities {ℎ(∙; 𝐯)} with

reference parameter v such that the distance between 𝑔∗ and ℎ(∙; 𝐯) is minimal. A measure of this

magnitude is called the Kullback–Leibler distance, or the CE between g and h.

To solve single-objective combinatorial optimization problems, the CE method associates an estimation

problem with the original combinatorial optimization problem, characterized by a density function q. The

stochastic problem is then solved by identifying the optimal importance sampling density q*, which is the

sampling density that minimizes the CE with respect to the original density q. The minimization of the

CE leads to the generation of improved feasible vectors, and it terminates when convergence to a point in

the feasible region is achieved. The four steps for the CE method are as follows (De Boer et al., 2005):

1. Start with some 𝒑�0, say 𝒑�0 = (0.5, … ,0.5). Let 𝑡 ∶= 1.

2. Draw a sample 𝚾1 , … ,𝚾𝑁 of Bernoulli vectors with success probability vector 𝒑�𝑡−1. Calculate the

performances of 𝑆(𝚾𝑖) for all i and order them from smallest to largest, 𝑆(1) ≤ ⋯ ≤ 𝑆(𝑁). Let 𝛾�𝑡

be (1− 𝜌) quantile of the performances: 𝛾�𝑡 = 𝑆(⌈1−𝜌⌉𝑁).

3. Use the same sample to calculate 𝒑�𝑡 = ��̂�𝑡,1, … , �̂�𝑡,𝑛� with the following:

𝒑�𝑡,𝑗 =∑ 𝑰�𝑆�𝚾𝑖�≥𝛾�𝑡� 𝑰�𝑋𝑖,𝑗=1�𝑁𝑖=1

∑ 𝑰�𝑆�𝚾𝑖�≥𝛾�𝑡� 𝑁𝑖=1

4. If the stopping criterion (e.g., stop when 𝛾�𝑡 does not change for several subsequent iterations, stop

when vector 𝒑�𝑡 has converged to a binary vector) is met, stop; otherwise set 𝑡 ∶= 𝑡 + 1 and

reiterate from Step 2.

3.3.2. The CE Method for Solving MOCO Problems

The MOO CEM is similar to the CE method for a single objective in terms of deriving the best solution

through the generation of random samples based on a mechanism and then updating the parameters of the

mechanism to obtain better solutions (Bekker and Aldrich, 2011). The algorithm works as follows: We

generate the random sample using the probability density of the truncated normal distribution, based on

the lower and upper bounds of each decision variable. Using these random values, we evaluate all the

solutions in the objective functions and rank them using Goldberg’s (1989) Pareto ranking algorithm. The

best solutions are located in a vector called Elite. We then update this vector by building histograms for

each decision variable, such that the best solutions are more likely to influence the next random sample.

Finally, we use a stopping criterion such as a low standard deviation or a defined number of runs to

determine the Pareto frontier approximation.

12

Although Bekker and Aldrich (2011) demonstrate that the MOO CEM is suitable for solving MOO

problems from the literature, their study does not address issues in solving combinatorial optimization

problems. First, the solution representation is different in terms of the decision variables domain. The

MOO CEM involves continuous variables, which make the application of the truncated normal

distribution effective in terms of updating the parameters to generate new, “better” samples. However, the

decision variables in MOCO problems are either integer or binary; therefore, this approach is not useful.

In addition, the solutions that the MOO CEM obtains are not limited to constraints (just the boundaries of

the decision variables); therefore, an extension to include them in the procedure is not trivial and would

require changing the histogram concept, which is the basis of the MOO CEM.

To address these two issues, we define a new updating rule to provide feasible and better solutions in each

iteration. We propose a new metaheuristic algorithm based on the MOO CEM to solve the SFL problem:

the MOCO CEM.

The first step to define the MOCO CEM is how to represent a solution. Caserta and Quiñonez Rico

(2009) present a CE-based algorithm for solving facility location problems for a single objective function.

In their study, a binary representation was used to model the number of located facilities among the

candidates. Using this approach we propose the following vector representation for a solution: Consider

SFL problem. Let n and m be the number of demand nodes and candidate locations respectively. Table 1

shows the solution representation.

Table 1. Solution representation

Facility location Cost assignment CO2 assignment

𝑋1, … ,𝑋𝑚 𝑌𝑎11, … ,𝑌𝑎𝑛𝑚 𝑌𝑏11, … ,𝑌𝑏𝑛𝑚

Thus, we define a solution k as �𝐗𝑘 ,𝐘𝑎𝑘 ,𝐘𝑏𝑘�, where

𝐗𝑘 = (𝑋1, … ,𝑋𝑚)

= the binary vector of candidate locations for solution k, where

𝑋𝑗 takes value of 1 if a facility is located at site j and 0

otherwise.

𝐘𝑎𝑘 = (𝑌𝑎11, …𝑌𝑎𝑛𝑚) = the binary vector for the optimal cost assignment of solution

𝐗𝑘.

𝐘𝑏𝑘 = �𝑌𝑏11, …𝑌𝑏𝑛𝑚� = the binary vector for the optimal CO2 assignment of solution

𝐗𝑘.

13

Because the assignment subproblem is solvable in polynomial time, it can be solved optimally during the

algorithm procedure. In other words, for a feasible solution 𝐗𝑘, we can calculate the optimal value

𝑆(𝚾𝑘) = �𝑆(𝐘𝑎𝑘), 𝑆�𝐘𝑏𝑘��, based on the optimal assignment subproblem 𝐘𝑎𝑘 and 𝐘𝑏𝑘 of SFL. This

representation allows the algorithm to deal only with 𝐗𝑘 vectors. The MOCO CEM differs from previous

applications of the CE method in several ways:

1. To generate random samples, we propose the Bernoulli distribution as in Caserta and Quiñonez

Rico (2009). Because the decision variables 𝑋𝑗 for all 1 ≤ 𝑗 ≤ 𝑚 are binary, the truncated normal

distribution that Bekker and Aldrich (2011) suggest is no longer adequate for the problem.

2. To generate more feasible solutions 𝐗𝑘, we propose using the success probability vector with

𝐏�0 = �𝑝𝑚

, … , 𝑝𝑚�, such that p is the number of facilities to be located and m is the number of

candidate locations, which enables us to obtain more feasible solutions using smaller population

sizes. Then, to test feasibility, we evaluate each solution for the decision variables with the

expression ∑ 𝑋𝑖𝑚𝑖=1 = 𝑚.

Previous applications in single combinatorial optimization problems suggest initializing the CE

method with 𝐏�0 = (0.5, … ,0.5) (Caserta and Quiñonez Rico, 2009; De Boer et al., 2005), which

implies assuming equal probability for locating a facility in all candidate locations. This approach

might be appropriate when the number of facilities to be located is approximately half the

candidate locations, in which case we could obtain several feasible solutions rapidly in the

random sample. However, if the number of facilities is substantially more or less than half,

obtaining feasible solutions may require a very large random sample.

3. To avoid premature convergence, the MOO CEM adjusts the histogram frequencies during each

iteration t with a preset probability between .1 to .3, by inverting all the histograms for all

decision variables. Because our calculations involve the Bernoulli distribution and the histogram

class vector is reduced to two options, {0,1}, we adapted the histogram inversion operation by

changing the probability of the original vector 𝐏�𝑗 = �𝑃�𝑡1, …𝑃�𝑡𝑚� by 𝐏�𝑗 = ��1− 𝑃�𝑡1�, … �1−

𝑃�𝑡𝑚�� with the same probability range of .1 to .3.

Next we present a narrative description of the MOCO CEM. We create a vector E that will contain the

efficient solutions, and initialize the iteration counter 𝑡 = 1 and the population size N. To generate sample

vectors 𝐗𝑗 for 𝑗 = 1, … ,𝑁, we use 𝐏�𝑡−1 = �𝑝𝑚

, … , 𝑝𝑚� with m elements, as success probability values for

the Bernoulli distribution. Each 𝐗𝑗 represents a feasible location of SFL. Then we calculate 𝐘𝑎𝑗 and 𝐘𝑏𝑗

14

and the values of the fitness functions 𝑆�𝐘𝑎𝑗� and 𝑆�𝐘𝑏𝑗� for the cost and CO2 emissions functions,

respectively (see Table 2).

Table 2. Representation of the random sample 𝚾1, … ,𝚾𝑁

Facility location Cost assignment CO2 assignment 𝑆�𝚾𝑗�

𝐗1 𝐘𝑎1 𝐘𝑏1 𝑆(𝐘𝑎1) 𝑆�𝐘𝑏1�

⋮ ⋮ ⋮ ⋮ ⋮

𝐗𝑁 𝐘𝑎𝑁 𝐘𝑏𝑁 𝑆(𝐘𝑎𝑁) 𝑆�𝐘𝑏𝑁�

We rank the solution using the Pareto-ranking algorithm (Goldberg, 1989), with a threshold (th) value of

2, as in Bekker and Aldrich (2011) (i.e., we keep all solutions dominated by no more than two solutions in

E and delete the rest). Next, we update vector 𝐩�𝑡 = ��̂�𝑡,1, … , �̂�𝑡,𝑚� by using �̂�𝑡,𝑗 =∑ 𝑰�𝑆�𝚾𝑗� ∈ 𝐸� 𝑰�𝑋𝑗=1�𝑟𝑗=1

|𝐸| ,

where 𝐩�𝑡 contains the new success probability values for the Bernoulli distribution. We smooth 𝐩�𝑡 using

�̂�𝑡,𝑗 = 𝛼𝑝�𝑡,𝑗 + (1− 𝛼)�̂�𝑡−1,𝑗, and we generate another random sample of vectors 𝐗𝑗 . After a given

number of iterations, we rank E again with 𝑡ℎ = 1. Finally, using the most updated version of E, we rank

the vector with 𝑡ℎ = 0 to obtain the final version of E, which contains the efficient solutions.

The pseudo-code for the MOCO CEM algorithm to solve the SFL problem is as follows:

1. Set vector 𝐄 = ∅. Set 𝑡 = 1, 𝑘 = 1.

2. Start with 𝐏�0 = �𝑝𝑚

, … , 𝑝𝑚� with m elements.

3. Draw a sample 𝚾1, … ,𝚾𝑁 of Bernoulli vectors with success probability vector 𝐩�𝑡−1.

4. Calculate the performances 𝑆�𝚾𝑗�, 1 ≤ 𝑗 ≤ 𝑁 by solving the assignment problem of SFL.

5. Rank the performance values using the Pareto-ranking algorithm (Goldberg, 1989), with a relaxed

𝑡ℎ = 2 to obtain an updated elite vector E.

6. Use the same sample to calculate 𝐩�𝑡 = ��̂�𝑡,1, … , �̂�𝑡,𝑚� with the following equation:

�̂�𝑡,𝑗 =∑ 𝑰�𝑆�𝚾𝑗� ∈ 𝐸� 𝑰�𝑋𝑗=1�𝑟𝑗=1

|𝐸|

7. Smooth the vectors 𝐩�𝑡 using �̂�𝑡,𝑗 = 𝛼𝑝�𝑡,𝑗 + (1 − 𝛼)�̂�𝑡−1,𝑗 .

8. If all 𝜎𝑡,𝑗 > 𝜖 or less than the allowable number of evaluations has been done, increment t and

reiterate from Step 3.

9. Rank E using the Pareto-ranking algorithm (Goldberg, 1989) with 𝑡ℎ = 1.

15

10. Increment k.

11. If k is less than the allowable number of loops, return to Step 2.

12. Rank E using the Pareto-ranking algorithm (Goldberg, 1989) with 𝑡ℎ = 0 to obtain the final

vector of efficient solutions.

3.4. Validation

This section presents an analysis of the application of the MOCO CEM in solving p-Median problems

from the literature. Our purpose is to show that the algorithm can solve the problems efficiently by

approximating to the Pareto frontier; thus, we do not provide a full experimental analysis of its

performance against other algorithms.

To validate the MOCO CEM applied in p-Median problems, we solve two test instances from Beasley

(1985) (see Table 3). Because there are no extant test instances for multiobjective p-Median problems

with known Pareto frontiers, we selected the first two instances simply to exemplify the application of the

algorithm. The instances were designed to test heuristics for single objective problems; therefore, they

include only the transport cost 𝑐𝑖𝑗 and not the carbon emissions 𝑐′𝑖𝑗. We calculate the carbon emissions as

follows: 𝑐′𝑖𝑗 = �𝑐𝑖𝑗 − 𝑚𝑎𝑥�𝑐𝑖𝑗|𝑗 ∈ 𝐽, 𝑖 ∈ 𝐼��. This operation does not change the complexity of the

problem; we calculate it with the purpose of defining a different carbon emissions objective function so

that the Pareto frontier can contain more points.

Table 3. Instances from Beasley (1985)

Instances nodes edges P possible solutions

pmed1 100 200 5 7.53 x 107

pmed2 100 200 10 1.73 x 1013

To measure the performance of our algorithm, we calculate the supported solutions by using the weighted

sum scalarization method (see Section 3.1) to identify some points of the real Pareto frontier. Note that

this method can be used for pmed1 and pmed2 because neither instance is as complex as the rest of the

instances Beasley (1985) provides. Therefore, we can compare solutions in terms of their quality. We use

∆𝜆 = 0.01 such that 𝜆𝑗 = 𝜆𝑗−1 + ∆𝜆 for 𝑗 = 1, … ,100 and 𝜆0 = 0. We obtain three supported solutions in

each instance. Using the efficient solutions the MOCO CEM obtains, we select the following metrics

from Knowles and Corne (2002) to assess the efficient solutions against the supported solutions: error

ratio (ER), general distance (GD), the maximum Pareto front error (MPFE), the overall nondominated

vector generation (ONVG) and the overall nondominated vector generation ratio (ONVGR). We

16

programmed the MOCO CEM in Mathematica 9 and performed the tests on an EliteBook laptop with two

Intel Core i7 CPUs and 8 GB memory. We used 𝛼 = 0.7 and a preset probability of .1 as Bekker and

Aldrich (2011) suggest. Table 4 presents the results.

Table 4. Test results for the MOCO CEM in solving pmed1 and pmed2

Instance N ER GD MFE ONVG ONVGR

pmed1 100 0% 0% 0% 11 3.67

pmed2 200 0% 0% 0% 24 8

Because the MOCO CEM generates all the supported solutions, the metrics ER, GD and MFE are equal

to zero. Furthermore, the ONVG indicates the cardinality of the nondominated set, which is equivalent to

the number of efficient solutions. The ONVGR shows the ratio between the nondominated solutions and

the real Pareto points—in this case, estimated as efficient solutions divided by supported solutions. It

indicates that the MOCO CEM reveals 3.67 and 8 times more efficient solutions than supported solutions

for pmed1 and pmed2, respectively. Figures 1 and 2 show the efficient and supported solutions (ES and

SS) for both instances. Note that none of the efficient solutions is dominated by any supported solutions.

Figure 1- Pareto approximation for pmed1.

13800

13900

14000

14100

14200

14300

14400

14500

14600

14700

13950 14000 14050 14100 14150 14200 14250 14300

Cost

Kg of CO2

ES

SS

17

Figure 2- Pareto approximation for pmed2.

The MOCO CEM thus is capable of solving the SFL problem. In the following section, we apply the

MOCO CEM to solve the SFL for a CPG company in the Mexico City metropolitan area. We aim to

provide managerial insights regarding the structure of efficient solutions for a practical case.

4. Case Study: CPG Company in the Mexico City Metropolitan Area

The Mexico City metropolitan area is among the largest regions in any developing country; it includes

more than 18 million inhabitants, more than 2.5 million vehicles and 35,000 industries that consume more

than 44 million liters of fuel per day (Molina and Molina, 2000). Therefore, a reduction proposal

conducted in this region could significantly affect global carbon emissions. To study the type of solutions

for the SFL, we ran experiments using data from a CPG company operating in this area. This company

has operations throughout Mexico. It manages approximately 80,000 delivery points in the Mexico City

metropolitan area, with an average demand per year of approximately 2.3 million tons. The company

assigns each truck to a specific zone of approximately 100 square kilometers.

The company decision makers want to evaluate the location of 10 distribution centers and have previously

defined 18 candidate locations. Figure 3 shows a map of the area divided by square zones. Dark colors

indicate high concentration of demand. We estimated the distance between points using the great circle

distance approximation (for the distance matrix, see the Appendix).

10000

10100

10200

10300

10400

10500

10600

10700

10800

10900

9300 9500 9700 9900 10100 10300 10500

Cost

Kg of CO2

ES

SS

18

Figure 3- Map of the Mexico City metropolitan area divided by squared clusters of 100 square

kilometers. Darker areas represent higher demand. Black points represent the candidate locations.

The goal of the experiment is to indicate which efficient solutions of the SFL problem are most beneficial

to the company. Because decision makers likely seek alternatives that reduce emissions but keep costs

low, we analyze the conditions in which the efficient frontier contains solutions, such that marginal

increases in cost imply significant reductions in carbon emissions. We also investigate the possible causes

of the problem that drive the number of efficient solutions.

We define the following factors with their respective levels:

1. Truck assignment:

a) Trucks are assigned based on the area’s conditions (e.g., only small trucks can access

downtown).

b) Trucks are assigned without considering the area’s conditions (e.g., large trucks are assigned

to regions with high demand).

19

2. Fixed cost assignment:

a) We identify high fixed costs for short distance trajectories and vice versa (High 𝐴𝑖𝑗 – Short

𝑑𝑖𝑗).

b) We identify high fixed costs for large distance trajectories and vice versa (High 𝐴𝑖𝑗 – Large

𝑑𝑖𝑗).

Our response variables are the number of nondominated solutions (NDS) and the ratio between the

reductions in carbon emissions divided by the increase in costs (RCC). For this last indicator, we consider

only the largest value. We replicate each setting 10 times. Table 6 shows the results for the NDS response

variable. The numbers suggest that when high fixed costs are present in short distance trajectories, the

number of nondominated solutions is larger than when high fixed costs exist in large distance trajectories.

Table 6. Results for NDS response variable

MCMA conditions Large trucks to high demand nodes Replicates High Aij - Large dij High Aij - Short dij High Aij - Large dij High Aij - Short dij

1 2 16 2 15 2 3 18 3 21 3 3 21 3 22 4 3 21 3 22 5 3 21 3 22 6 3 21 3 22 7 3 21 3 22 8 3 21 3 22 9 3 21 3 22 10 3 21 3 22

Table 7 shows the results for the RCC response variable. We notice similar behavior with the NDS

response variable, such that when high fixed costs are present for short distance trajectories, the

percentage of CO2 reduction divided by the cost increase percentage is larger than when high fixed costs

are present for large distance trajectories. We obtain large numbers (e.g., replicate 3 reports 1.9 million)

because the increase in cost is close to 0% (2 E^10-7%).

20

Table 7. Results for RCC response variable (CO2 reduction divided by the increase in cost)

MCMA conditions Large trucks to high demand nodes Replicates High Aij - Large dij High Aij - Short dij High Aij - Large dij High Aij - Short dij

1 1.09 47,442,889.08 0.12 384,331.72

2 0.05 1,946,988.58 0.12 384,721.67

3 0.05 1,946,988.58 0.12 384,721.67

4 0.05 1,946,988.58 0.12 384,721.67

5 0.05 1,946,988.58 0.12 384,721.67

6 0.05 1,946,988.58 0.12 384,721.67

7 0.05 1,946,988.58 0.12 384,721.67

8 0.05 1,946,988.58 0.12 384,721.67

9 0.05 1,946,988.58 0.12 384,721.67

10 0.05 1,946,988.58 0.12 384,721.67

To determine which factors affect the response variables, we conducted two analyses of variance. Table 8

shows the analysis of variance for the NDS response variable. We conclude that the assignment of fixed

costs to distances explains the number of nondominated solutions for the problem, independent of the

area’s conditions.

Table 8. Analysis of variance for the NDS response variable

Source DF SS MS F P

Truck assignment 1 .1 .1 .6 .444

Fixed cost & distance 1 220.9 220.9 1325.4 .000

Interaction 1 .1 .1 .6 .444

Error 36 6 .167

Table 9 shows the analysis of variance for the RCC response variable. We conclude that the truck

assignment, the assignment of fixed costs to distances and their interaction explain the percentage of CO2

reduction divided by the percentage of increase in cost for the problem.

21

Table 9. Analysis of variance for the RCC response variable (CO2 reduction divided by the increase

in cost)

Source DF SS MS F P

Truck assignment 1 2.82909E+18 2.82909E+18 19561.8 .000

Fixed cost & distance 1 6.14065E+18 6.14065E+18 42459.6 .000

Interaction 1 2.82909E+18 2.82909E+18 19561.8 .000

Error 36 5.20644E+15 1.44623E+14

To demonstrate the structure of Pareto approximation for the case study, we present some examples of the

results from the experiment. Figure 4, Panel A, shows an example of the Pareto approximation for the

area’s conditions with high fixed costs in short distance trajectories. Figure 4, Panel B, shows only the

nondominated solutions with an increase in cost close to zero (less than 1.4 E^10-6%). Note that it is

possible to achieve a significant reduction in carbon emissions (~40%) with almost no cost increase,

which may make the solutions equivalent for practical purposes.

Figure 4 (A): Pareto approximation for the area’s conditions with high fixed costs found in short

distance trajectories; and (B): Sample of points with less than 1% of increase in cost.

Figure 5 shows the locations in the map for three Pareto approximation points from Figure 4. Panel A

shows the cost optimal location, Panel B shows a location with 36% of carbon reduction with an increase

in cost of 3 E^10-5% and Panel C shows the carbon emissions optimal location with 12.5% of increase in

cost.

0.0E+00

2.0E-07

4.0E-07

6.0E-07

8.0E-07

1.0E-06

1.2E-06

1.4E-06

1.6E-06

0% 10% 20% 30% 40% 50%

% o

f Cos

t inc

reas

e

% of CO2 reduction

0%

2%

4%

6%

8%

10%

12%

0% 10% 20% 30% 40% 50%

% o

f Cos

t inc

reas

e

% of CO2 reduction

22

A: Cost optimal location B: Location with 36% of carbon reduction and

cost increase of 3 E^10-5%

C: CO2 optimal location

Figure 5- Examples of three Pareto points for the area’s conditions with high fixed costs in short

distance trajectories.

Note that the solutions shown in Panels A and B of Figure 5 are similar in terms of changing only two

locations (X8 and X14 by X15 and X10). Furthermore, the CO2 optimal location (Panel C) is different than

the other solutions in terms of locating facilities closer to regions with high concentration of demand (and

also in terms of truck constraints).

23

Figure 6 shows an example of the Pareto approximation with high fixed costs in large distance

trajectories. Note that for these conditions, the three solutions result in similar costs and carbon emissions

(the largest difference is .025% of CO2 reduction with a cost increase of .55%).

Figure 6- Pareto approximation with high fixed costs in large distance trajectories

Figure 7, Panel A, shows an example of the Pareto approximation when the company does not need to

accommodate Mexico City metropolitan area conditions (e.g., large trucks may be assigned to regions

with high demand) and when high fixed costs exist in short distance trajectories. Figure 7, Panel B, shows

only the nondominated solutions with an increase in cost close to zero (less than 5 E^10-6%). Note that it

is possible to achieve high reductions in carbon emissions (~25%) with almost no cost increase, similar to

the solutions shown in Figure 4, which may also make the solutions equivalent for practical purposes.

Figure 7 (A): Pareto approximation when the company does not accommodate Mexico City and

metropolitan area conditions and with high fixed costs in short distance trajectories; (B): Sample of

points with less than 1% of increase in cost.

0.0%

0.1%

0.2%

0.3%

0.4%

0.5%

0.6%

0.000% 0.005% 0.010% 0.015% 0.020% 0.025% 0.030%

% o

f Cos

t inc

reas

e

% of CO2 reduction

0.0E+00

5.0E-07

1.0E-06

1.5E-06

2.0E-06

2.5E-06

3.0E-06

3.5E-06

4.0E-06

4.5E-06

5.0E-06

0% 5% 10% 15% 20% 25% 30%

% o

f Cos

t inc

reas

e

% of CO2 reduction

0%

1%

2%

3%

4%

5%

6%

7%

8%

9%

10%

0% 5% 10% 15% 20% 25% 30%

% o

f Cos

t inc

reas

e

% of CO2 reduction

24

Figure 8 shows the locations in the map for three Pareto approximation points from Figure 7. Panel A

indicates the cost optimal location, Panel B shows a location with 26% of carbon reduction with an

increase in cost of 4.7 E^10-4% and Panel C shows the carbon emissions optimal location with 9% of

increase in cost.

A: Cost optimal location B: Location with 26% of carbon reduction and

cost increase of 4.7 E^10-4%

C: CO2 optimal location

Figure 8- Examples of three Pareto points when the company does not accommodate Mexico City

and metropolitan area conditions and with high fixed costs in short distance trajectories.

Note that the CO2 optimal location (Panel C) is different than the other solutions in terms of locating

facilities closer to regions with high concentration of demand (and also in terms of truck constraints).

25

Figure 9 shows an example of the Pareto approximation when the company accounts for Mexico City

metropolitan area conditions and experiences high fixed costs with large distance trajectories. Similar to

Figure 6, under these conditions, the three solutions result in similar costs and carbon emissions (the

largest difference is .12% of CO2 reduction with an increase in cost of almost 1.2%).

Figure 9- Pareto approximation for nonconstrained delivery conditions with high fixed costs for

large distance trajectories

5. Conclusions

Transportation is a main contributing factor of carbon emissions, and studies indicate that these emissions

will increase in the future. This situation suggests that firms need more efficient transport logistics

operations to reduce CO2 emissions while keeping costs low. In the current study, we investigate the

trade-off between cost and CO2 using a multiobjective approach for the p-Median problem. We provide

three main contributions: First, we introduce the SFL problem, a multiobjective p-Median model with

new cost and CO2 objective functions that allow us to take into account vehicle access limitations in the

demand nodes. Second, to solve the SFL, we develop an adaptation of the MOO CEM: the MOCO CEM.

We test our algorithm against problems from prior literature and show that the MOCO CEM can solve the

multiobjective p-Median problem efficiently by finding efficient and supported solutions and by

performing better in the different metrics. Finally, we provide managerial insights on the structure of the

Pareto frontier using an application for an actual company: we conduct an experimental study of the

MOCO CEM by solving the SFL for a multinational CPG company that operates in Mexico City

metropolitan area. Our intention is to analyze two scenarios: when high fixed costs exist in short distance

trajectories and when high fixed costs exist in large distance trajectories. The results show that regardless

of Mexico City conditions, when high fixed costs are present in short distance trajectories, CO2 emission

0.0%

0.2%

0.4%

0.6%

0.8%

1.0%

1.2%

1.4%

0.00% 0.02% 0.04% 0.06% 0.08% 0.10% 0.12% 0.14%

% o

f Cos

t inc

reas

e

% of CO2 reduction

26

reductions are much larger (~40% considering area conditions and 25% not considering these conditions)

than the increase in cost (almost 0% in both cases). The results also show that these CO2 savings can be

achieved by only changing a small subset of locations. The study provides insights that can help

companies make better decisions by analyzing the cost and CO2 trade-offs for the facility location

problem.

We leave comparison of the MOCO CEM against other algorithms from the literature as a fruitful future

research avenue. Furthermore, including other type of pollutants—such as noise, particulate matter, CO

and NOx—as possible objective functions in the SFL model is a worthwhile research direction. For this

problem, researchers may need to develop new heuristics strategies to accommodate the complexities.

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30

APPENDIX: DISTANCE MATRIX (IN KILOMETERS) FOR THE CPG COMPANY

Node/Candidate Location 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 181 57.5 59.3 62.4 78.4 59.1 49.9 59.2 83.5 62.4 62.8 60.6 68.6 81.7 73.8 42.6 83.6 84.1 88.62 63.0 64.6 67.2 82.1 64.1 55.0 65.5 87.5 67.2 67.2 65.7 73.2 85.7 78.7 47.9 88.0 88.6 92.73 45.0 46.8 50.2 66.7 46.7 37.5 46.5 71.6 50.2 50.7 48.3 56.5 69.7 61.4 30.2 71.5 71.9 76.64 50.3 51.9 54.6 70.0 51.5 42.3 52.8 75.2 54.6 54.7 53.0 60.6 73.4 66.1 35.2 75.6 76.1 80.35 56.4 57.9 59.9 74.1 57.2 48.3 59.8 79.6 59.9 59.7 58.7 65.7 77.9 71.5 41.4 80.4 81.0 84.86 28.6 30.8 36.2 54.4 32.2 25.3 25.6 57.6 36.2 38.1 33.4 42.2 55.6 44.7 21.3 55.7 55.9 61.87 29.4 31.5 36.2 54.2 32.3 23.8 28.7 58.2 36.2 37.5 33.6 42.5 56.2 46.2 17.8 57.0 57.3 62.88 32.6 34.5 38.3 55.5 34.6 25.4 33.8 60.1 38.2 39.1 36.1 44.6 58.1 49.2 18.3 59.6 60.0 64.99 37.5 39.2 42.1 58.0 38.9 29.7 40.2 63.1 42.1 42.4 40.4 48.2 61.3 53.5 22.5 63.2 63.7 68.2

10 43.7 45.2 47.2 61.7 44.4 35.6 47.3 67.2 47.2 47.1 46.0 53.1 65.4 58.8 28.8 67.8 68.4 72.311 50.7 51.9 53.3 66.4 50.9 42.5 55.0 72.1 53.3 52.8 52.4 58.8 70.4 64.9 36.1 73.2 73.8 77.312 22.1 24.0 29.7 47.0 26.1 22.6 16.3 49.2 29.8 32.1 26.8 34.8 47.4 35.8 22.5 46.7 46.7 52.913 19.5 21.6 27.0 45.2 23.1 16.9 16.7 48.3 27.1 29.0 24.2 33.0 46.4 35.5 14.7 46.5 46.7 52.614 20.5 22.6 27.1 45.0 23.2 14.6 21.1 49.1 27.1 28.3 24.6 33.4 47.1 37.4 8.9 48.1 48.4 53.715 24.8 26.6 29.8 46.5 26.4 17.1 27.6 51.3 29.7 30.3 27.9 36.0 49.4 41.1 9.8 51.1 51.5 56.316 31.1 32.5 34.5 49.5 31.7 22.9 35.2 54.8 34.5 34.5 33.2 40.4 53.0 46.1 16.4 55.3 55.8 60.017 38.3 39.5 40.7 53.8 38.3 30.2 43.1 59.5 40.6 40.1 39.8 46.1 57.8 52.2 24.3 60.5 61.1 64.618 46.1 47.1 47.6 59.1 45.7 38.1 51.4 64.9 47.6 46.7 47.1 52.6 63.4 58.9 32.7 66.4 67.1 70.119 21.9 23.0 28.0 42.3 25.5 26.6 14.1 43.0 28.0 30.7 25.5 31.1 41.4 29.7 29.7 39.6 39.4 45.720 14.7 16.3 21.8 38.3 18.6 18.1 7.6 40.2 21.9 24.4 19.0 26.3 38.4 26.7 20.9 37.5 37.5 43.721 10.3 12.4 18.0 36.1 14.1 10.1 8.4 39.1 18.0 20.1 15.1 23.8 37.2 26.3 12.2 37.4 37.6 43.422 12.2 14.0 18.0 35.8 14.3 5.4 15.4 40.0 18.0 19.2 15.7 24.4 38.1 28.8 3.5 39.2 39.6 44.823 18.6 19.8 21.9 37.7 19.0 10.4 23.6 42.7 21.8 22.0 20.5 27.9 40.8 33.4 5.4 42.8 43.4 47.824 26.4 27.3 28.0 41.3 25.9 18.5 32.0 46.9 28.0 27.4 27.3 33.4 45.2 39.5 14.1 47.8 48.4 52.125 34.6 35.3 35.3 46.4 33.7 27.0 40.7 52.2 35.2 34.2 35.0 40.0 50.6 46.4 22.9 53.7 54.4 57.426 51.6 52.1 51.2 59.1 50.2 44.3 58.0 65.2 51.2 49.8 51.4 55.1 63.8 61.7 40.4 67.5 68.2 70.127 19.5 19.7 23.4 34.9 22.0 26.3 12.7 34.8 23.4 26.0 21.5 24.8 33.3 22.0 31.4 31.1 30.8 37.128 10.7 11.1 15.5 29.9 13.6 17.7 4.5 31.3 15.5 18.2 13.2 18.4 29.5 17.7 23.3 28.4 28.3 34.629 2.1 3.6 9.3 27.0 5.9 9.4 5.7 29.9 9.4 11.8 6.4 14.7 28.0 17.2 15.9 28.2 28.4 34.230 6.9 7.5 9.3 26.7 6.3 3.9 14.1 31.0 9.3 10.1 7.8 15.6 29.1 20.8 10.7 30.6 31.1 35.931 15.6 15.9 15.5 29.1 14.0 9.8 22.7 34.4 15.5 14.7 15.3 20.7 32.7 26.9 11.5 35.1 35.7 39.632 24.3 24.5 23.4 33.7 22.5 18.1 31.4 39.5 23.4 22.0 23.7 27.6 37.9 34.1 17.4 41.0 41.7 44.733 33.1 33.2 31.7 39.7 31.2 26.7 40.2 45.7 31.7 30.1 32.2 35.4 44.3 41.9 25.0 47.8 48.6 50.834 50.6 50.7 48.9 54.1 48.6 44.1 57.7 60.1 48.8 47.0 49.6 51.8 58.9 58.4 41.6 62.8 63.6 64.835 29.4 28.8 30.6 35.9 30.8 37.2 24.2 33.7 30.7 32.8 29.7 29.4 32.8 24.1 43.0 29.2 28.6 34.236 21.1 20.4 21.9 28.6 22.2 29.2 17.1 27.3 21.9 24.1 21.1 20.9 26.1 16.1 35.5 23.2 22.8 28.937 13.5 12.3 13.1 22.2 13.8 21.7 12.3 22.6 13.2 15.3 12.6 12.6 21.0 9.4 28.5 19.4 19.3 25.638 8.5 6.5 4.5 18.0 6.5 15.6 12.8 20.7 4.5 6.6 4.9 5.9 18.7 8.4 22.9 19.1 19.4 25.039 10.7 9.2 4.5 17.5 6.8 13.1 18.2 22.3 4.5 2.3 6.6 8.0 20.4 14.3 19.7 22.5 23.1 27.340 17.6 16.8 13.2 21.1 14.3 15.9 25.5 26.8 13.1 11.0 14.7 15.7 25.2 22.2 20.1 28.4 29.1 32.041 25.7 25.1 21.9 27.1 22.7 22.0 33.5 33.1 21.9 19.7 23.3 24.1 31.7 30.6 24.0 35.4 36.2 38.142 34.1 33.7 30.7 34.3 31.3 29.5 41.8 40.3 30.6 28.4 32.0 32.7 39.1 39.1 30.0 43.1 43.9 45.143 42.6 42.3 39.4 42.1 39.9 37.6 50.2 48.0 39.4 37.2 40.7 41.4 47.0 47.7 37.1 51.1 51.9 52.644 33.2 32.1 32.3 32.5 33.5 41.3 29.8 29.0 32.3 33.9 32.2 29.2 28.5 22.9 47.9 24.3 23.6 28.245 26.2 24.8 24.1 24.2 25.9 34.3 24.4 21.2 24.2 25.5 24.4 20.6 20.5 14.2 41.2 16.6 16.0 21.546 20.5 18.7 16.6 16.2 19.2 28.2 21.3 14.6 16.6 17.6 17.6 12.1 13.4 5.6 35.5 10.7 10.4 16.747 17.6 15.5 11.1 9.6 14.8 23.9 21.6 11.5 11.1 10.8 13.3 4.9 9.5 3.7 31.1 10.2 10.7 15.848 18.8 16.9 11.1 8.7 14.9 22.3 25.1 14.2 11.1 8.9 14.1 7.3 12.5 12.2 28.8 15.7 16.5 19.349 23.4 21.9 16.6 14.6 19.5 24.0 30.8 20.6 16.6 13.9 19.2 15.3 19.4 20.9 29.1 23.3 24.1 25.550 30.0 28.8 24.1 22.4 26.3 28.5 37.7 28.3 24.1 21.5 26.4 23.9 27.3 29.6 31.9 31.5 32.3 32.851 37.4 36.5 32.3 30.7 34.0 34.6 45.2 36.4 32.2 29.7 34.3 32.5 35.6 38.4 36.6 39.9 40.8 40.752 45.3 44.6 40.7 39.2 42.1 41.7 53.1 44.8 40.6 38.2 42.5 41.2 44.1 47.1 42.7 48.5 49.3 48.953 38.9 37.4 36.2 31.6 38.3 47.0 36.9 26.7 36.3 37.3 36.9 31.8 26.9 25.3 53.9 22.4 21.6 24.454 33.1 31.4 29.2 22.8 31.9 40.9 32.7 18.0 29.3 29.9 30.3 24.2 18.1 17.8 48.1 13.7 12.8 16.155 28.8 26.8 23.4 14.1 26.7 36.0 30.4 9.4 23.5 23.5 25.2 17.5 9.4 12.0 43.3 4.9 4.1 8.856 26.8 24.7 19.9 5.5 23.8 32.7 30.6 2.3 19.9 19.0 22.4 13.5 0.7 11.3 39.8 3.8 4.7 6.957 27.6 25.6 19.9 3.6 23.9 31.5 33.2 8.6 19.9 18.0 22.8 14.6 8.1 16.2 38.0 12.6 13.4 13.158 31.0 29.1 23.5 12.2 27.0 32.8 37.7 17.2 23.4 20.9 26.3 19.8 16.9 23.5 38.2 21.3 22.1 21.159 36.2 34.6 29.3 20.9 32.2 36.2 43.5 25.9 29.2 26.6 31.9 27.0 25.6 31.5 40.4 30.0 30.9 29.660 42.5 41.2 36.3 29.7 38.7 41.2 50.2 34.6 36.2 33.6 38.7 34.9 34.3 39.8 44.2 38.8 39.6 38.261 49.6 48.5 43.9 38.4 46.0 47.3 57.4 43.4 43.9 41.2 46.1 43.1 43.1 48.3 49.3 47.5 48.4 46.862 40.9 39.0 36.0 25.1 39.1 48.4 41.4 19.2 36.0 36.2 37.6 30.2 20.2 24.5 55.6 16.3 15.6 15.163 37.5 35.5 31.5 17.5 35.1 44.3 39.6 11.5 31.5 31.1 33.6 25.2 12.9 20.7 51.5 10.2 9.8 6.764 36.0 33.9 29.0 11.7 32.9 41.7 39.8 7.0 29.0 27.9 31.5 22.6 9.0 20.3 48.6 9.7 10.0 3.965 36.6 34.5 29.0 11.0 33.0 40.8 41.8 10.9 29.0 27.2 31.9 23.3 12.1 23.4 47.2 15.4 16.1 11.866 39.2 37.3 31.5 16.0 35.3 41.7 45.4 18.5 31.5 29.2 34.5 26.9 19.1 28.9 47.4 23.1 23.8 20.367 43.4 41.7 36.0 23.4 39.4 44.4 50.4 26.8 36.0 33.5 38.9 32.5 27.1 35.7 49.2 31.3 32.1 29.068 48.9 47.3 41.9 31.4 44.9 48.6 56.2 35.3 41.9 39.3 44.6 39.3 35.5 43.2 52.3 39.8 40.6 37.769 55.1 53.8 48.7 39.8 51.3 53.9 62.7 43.9 48.6 46.0 51.2 46.8 44.0 51.1 56.7 48.3 49.1 46.470 46.5 44.4 40.1 24.2 43.8 52.9 48.8 18.6 40.1 39.4 42.3 33.7 20.4 29.7 60.1 18.8 18.5 13.571 45.3 43.1 38.1 20.4 42.1 50.7 48.9 16.2 38.1 36.9 40.7 31.8 18.2 29.4 57.6 18.6 18.7 12.472 45.7 43.6 38.1 20.0 42.1 50.0 50.6 18.3 38.1 36.4 41.0 32.3 19.9 31.6 56.4 22.1 22.5 16.673 47.8 45.8 40.1 23.1 44.0 50.8 53.6 23.6 40.1 37.9 43.0 35.0 24.8 35.9 56.6 28.0 28.6 23.574 51.3 49.5 43.7 28.7 47.3 53.0 57.9 30.5 43.7 41.3 46.7 39.5 31.4 41.6 58.1 35.1 35.8 31.375 56.0 54.3 48.7 35.6 52.0 56.6 63.0 38.2 48.7 46.1 51.5 45.2 38.8 48.2 60.8 42.8 43.5 39.576 61.6 60.0 54.6 43.1 57.6 61.1 68.9 46.2 54.6 52.0 57.3 51.8 46.7 55.4 64.6 50.8 51.6 47.977 67.8 66.4 61.2 51.1 63.9 66.5 75.4 54.5 61.2 58.5 63.8 59.0 54.9 63.0 69.3 59.1 59.9 56.478 54.5 52.3 47.3 29.4 51.3 59.8 58.1 25.5 47.3 46.0 49.9 41.0 27.4 38.6 66.7 27.7 27.7 21.579 54.9 52.7 47.3 29.1 51.3 59.2 59.5 26.8 47.3 45.6 50.1 41.4 28.6 40.3 65.6 30.1 30.4 24.280 56.6 54.6 48.9 31.4 52.8 59.9 62.1 30.7 48.9 46.8 51.8 43.5 32.1 43.7 65.8 34.7 35.1 29.381 59.6 57.7 51.9 35.7 55.7 61.8 65.8 36.2 51.9 49.6 54.9 47.2 37.5 48.5 67.0 40.6 41.2 35.982 63.7 61.9 56.2 41.4 59.7 64.8 70.4 42.9 56.1 53.7 59.1 52.1 43.9 54.3 69.4 47.5 48.1 43.283 68.6 66.9 61.4 48.0 64.6 68.9 75.7 50.2 61.3 58.8 64.2 57.9 51.0 60.8 72.8 54.8 55.5 51.084 63.7 61.6 56.5 38.5 60.5 69.0 67.3 34.7 56.5 55.2 59.1 50.2 36.6 47.8 75.7 36.8 36.8 30.685 64.0 61.9 56.5 38.3 60.5 68.4 68.5 35.7 56.5 54.8 59.3 50.5 37.5 49.2 74.8 38.7 38.9 32.686 65.5 63.5 57.8 40.0 61.8 69.0 70.8 38.7 57.8 55.8 60.7 52.3 40.3 52.0 75.0 42.4 42.7 36.6

Working Papers Beta 2009 - 2014 nr. Year Title Author(s) 451 450 449 448 447 446 445 444 443 442 441 440 439

2014 2014 2014 2014 2014 2014 2014 2014 2014 2014 2013 2013 2013

Transportation Cost and CO2 Emissions in Location Decision Models Tracebook: A Dynamic Checklist Support System Intermodal hinterland network design with multiple actors The Share-a-Ride Problem: People and Parcels Sharing Taxis Stochastic inventory models for a single item at a single location Optimal and heuristic repairable stocking and expediting in a fluctuating demand environment Connecting inventory control and repair shop control: a differentiated control structure for repairable spare parts A survey on design and usage of Software Reference Architectures Extending and Adapting the Architecture Tradeoff Analysis Method for the Evaluation of Software Reference Architectures A multimodal network flow problem with product Quality preservation, transshipment, and asset management Integrating passenger and freight transportation: Model formulation and insights The Price of Payment Delay On Characterization of the Core of Lane Covering Games via Dual Solutions

Josue C. Vélazquez-Martínez, Jan C. Fransoo, Edgar E. Blanco, Jaime Mora- Vargas Shan Nan, Pieter Van Gorp, Hendrikus H.M. Korsten, Richard Vdovjak, Uzay Kaymak Yann Bouchery, Jan Fransoo Baoxiang Li, Dmitry Krushinsky, Hajo A. Reijers, Tom Van Woensel K.H. van Donselaar, R.A.C.M. Broekmeulen Joachim Arts, Rob Basten, Geert-Jan van Houtum M.A. Driessen, W.D. Rustenburg, G.J. van Houtum, V.C.S. Wiers Samuil Angelov, Jos Trienekens, Rob Kusters Samuil Angelov, Jos J.M. Trienekens, Paul Grefen Maryam SteadieSeifi, Nico Dellaert, Tom Van Woensel Veaceslav Ghilas, Emrah Demir, Tom Van Woensel K. van der Vliet, M.J. Reindorp, J.C. Fransoo Behzad Hezarkhani, Marco Slikker, Tom van Woensel

438 437 436 435 434 433 432 431 430 429 428

2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013

Destocking, the Bullwhip Effect, and the Credit Crisis: Empirical Modeling of Supply Chain Dynamics Methodological support for business process Redesign in healthcare: a systematic literature review Dynamics and equilibria under incremental Horizontal differentiation on the Salop circle Analyzing Conformance to Clinical Protocols Involving Advanced Synchronizations Models for Ambulance Planning on the Strategic and the Tactical Level Mode Allocation and Scheduling of Inland Container Transportation: A Case-Study in the Netherlands Socially responsible transportation and lot sizing: Insights from multiobjective optimization Inventory routing for dynamic waste collection Simulation and Logistics Optimization of an Integrated Emergency Post Last Time Buy and Repair Decisions for Spare Parts A Review of Recent Research on Green Road Freight Transportation

Maximiliano Udenio, Jan C. Fransoo, Robert Peels Rob J.B. Vanwersch, Khurram Shahzad, Irene Vanderfeesten, Kris Vanhaecht, Paul Grefen, Liliane Pintelon, Jan Mendling, Geofridus G. Van Merode, Hajo A. Reijers B. Vermeulen, J.A. La Poutré, A.G. de Kok Hui Yan, Pieter Van Gorp, Uzay Kaymak, Xudong Lu, Richard Vdovjak, Hendriks H.M. Korsten, Huilong Duan J. Theresia van Essen, Johann L. Hurink, Stefan Nickel, Melanie Reuter Stefano Fazi, Tom Van Woensel, Jan C. Fransoo Yann Bouchery, Asma Ghaffari, Zied Jemai, Jan Fransoo Martijn Mes, Marco Schutten, Arturo Pérez Rivera N.J. Borgman, M.R.K. Mes, I.M.H. Vliegen, E.W. Hans S. Behfard, M.C. van der Heijden, A. Al Hanbali, W.H.M. Zijm Emrah Demir, Tolga Bektas, Gilbert Laporte

427 426 425 424 423 422 421 420 419 418 417 416

2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013

Typology of Repair Shops for Maintenance Spare Parts A value network development model and Implications for innovation and production network management Single Vehicle Routing with Stochastic Demands: Approximate Dynamic Programming Influence of Spillback Effect on Dynamic Shortest Path Problems with Travel-Time-Dependent Network Disruptions Dynamic Shortest Path Problem with Travel-Time-Dependent Stochastic Disruptions: Hybrid Approximate Dynamic Programming Algorithms with a Clustering Approach System-oriented inventory models for spare parts Lost Sales Inventory Models with Batch Ordering And Handling Costs Response speed and the bullwhip Anticipatory Routing of Police Helicopters Supply Chain Finance: research challenges ahead Improving the Performance of Sorter Systems By Scheduling Inbound Containers Regional logistics land allocation policies: Stimulating spatial concentration of logistics firms

M.A. Driessen, V.C.S. Wiers, G.J. van Houtum, W.D. Rustenburg B. Vermeulen, A.G. de Kok C. Zhang, N.P. Dellaert, L. Zhao, T. Van Woensel, D. Sever Derya Sever, Nico Dellaert, Tom Van Woensel, Ton de Kok Derya Sever, Lei Zhao, Nico Dellaert, Tom Van Woensel, Ton de Kok R.J.I. Basten, G.J. van Houtum T. Van Woensel, N. Erkip, A. Curseu, J.C. Fransoo Maximiliano Udenio, Jan C. Fransoo, Eleni Vatamidou, Nico Dellaert Rick van Urk, Martijn R.K. Mes, Erwin W. Hans Kasper van der Vliet, Matthew J. Reindorp, Jan C. Fransoo S.W.A. Haneyah, J.M.J. Schutten, K. Fikse Frank P. van den Heuvel, Peter W. de Langen, Karel H. van Donselaar, Jan C. Fransoo

415 414 413 412 411 410 409 408 407 406 405 404 403

2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013

The development of measures of process harmonization BASE/X. Business Agility through Cross- Organizational Service Engineering The Time-Dependent Vehicle Routing Problem with Soft Time Windows and Stochastic Travel Times Clearing the Sky - Understanding SLA Elements in Cloud Computing Approximations for the waiting time distribution In an M/G/c priority queue To co-locate or not? Location decisions and logistics concentration areas The Time-Dependent Pollution-Routing Problem Scheduling the scheduling task: A time Management perspective on scheduling Clustering Clinical Departments for Wards to Achieve a Prespecified Blocking Probability MyPHRMachines: Personal Health Desktops in the Cloud Maximising the Value of Supply Chain Finance Reaching 50 million nanostores: retail distribution in emerging megacities A Vehicle Routing Problem with Flexible Time Windows

Heidi L. Romero, Remco M. Dijkman, Paul W.P.J. Grefen, Arjan van Weele Paul Grefen, Egon Lüftenegger, Eric van der Linden, Caren Weisleder Duygu Tas, Nico Dellaert, Tom van Woensel, Ton de Kok Marco Comuzzi, Guus Jacobs, Paul Grefen A. Al Hanbali, E.M. Alvarez, M.C. van der van der Heijden Frank P. van den Heuvel, Karel H. van Donselaar, Rob A.C.M. Broekmeulen, Jan C. Fransoo, Peter W. de Langen Anna Franceschetti, Dorothée Honhon,Tom van Woensel, Tolga Bektas, GilbertLaporte. J.A. Larco, V. Wiers, J. Fransoo J. Theresia van Essen, Mark van Houdenhoven, Johann L. Hurink Pieter Van Gorp, Marco Comuzzi Kasper van der Vliet, Matthew J. Reindorp, Jan C. Fransoo Edgar E. Blanco, Jan C. Fransoo Duygu Tas, Ola Jabali, Tom van Woensel

402 401 400 399 398 397 396 395 394 393

2012 2012 2012 2012 2012 2012 2012 2012 2012 2012

The Service Dominant Business Model: A Service Focused Conceptualization Relationship between freight accessibility and Logistics employment in US counties A Condition-Based Maintenance Policy for Multi-Component Systems with a High Maintenance Setup Cost A flexible iterative improvement heuristic to Support creation of feasible shift rosters in Self-rostering Scheduled Service Network Design with Synchronization and Transshipment Constraints For Intermodal Container Transportation Networks Destocking, the bullwhip effect, and the credit Crisis: empirical modeling of supply chain Dynamics Vehicle routing with restricted loading capacities Service differentiation through selective lateral transshipments A Generalized Simulation Model of an Integrated Emergency Post Business Process Technology and the Cloud: Defining a Business Process Cloud Platform

Egon Lüftenegger, Marco Comuzzi, Paul Grefen, Caren Weisleder Frank P. van den Heuvel, Liliana Rivera,Karel H. van Donselaar, Ad de Jong,Yossi Sheffi, Peter W. de Langen, Jan C.Fransoo Qiushi Zhu, Hao Peng, Geert-Jan van Houtum E. van der Veen, J.L. Hurink, J.M.J. Schutten, S.T. Uijland K. Sharypova, T.G. Crainic, T. van Woensel, J.C. Fransoo Maximiliano Udenio, Jan C. Fransoo, Robert Peels J. Gromicho, J.J. van Hoorn, A.L. Kok J.M.J. Schutten E.M. Alvarez, M.C. van der Heijden, I.M.H. Vliegen, W.H.M. Zijm Martijn Mes, Manon Bruens Vasil Stoitsev, Paul Grefen

392 391 390 389 388 387 386 385 384 383 382

2012 2012 2012 2012 2012 2012 2012 2012 2012 2012 2012

Vehicle Routing with Soft Time Windows and Stochastic Travel Times: A Column Generation And Branch-and-Price Solution Approach Improve OR-Schedule to Reduce Number of Required Beds How does development lead time affect performance over the ramp-up lifecycle? Evidence from the consumer electronics industry The Impact of Product Complexity on Ramp- Up Performance Co-location synergies: specialized versus diverse logistics concentration areas Proximity matters: Synergies through co-location of logistics establishments Spatial concentration and location dynamics in logistics:the case of a Dutch province FNet: An Index for Advanced Business Process Querying Defining Various Pathway Terms The Service Dominant Strategy Canvas: Defining and Visualizing a Service Dominant Strategy through the Traditional Strategic Lens

D. Tas, M. Gendreau, N. Dellaert, T. van Woensel, A.G. de Kok J.T. v. Essen, J.M. Bosch, E.W. Hans, M. v. Houdenhoven, J.L. Hurink Andres Pufall, Jan C. Fransoo, Ad de Jong Andreas Pufall, Jan C. Fransoo, Ad de Jong, Ton de Kok Frank P.v.d. Heuvel, Peter W.de Langen, Karel H. v. Donselaar, Jan C. Fransoo Frank P.v.d. Heuvel, Peter W.de Langen, Karel H. v.Donselaar, Jan C. Fransoo Frank P. v.d.Heuvel, Peter W.de Langen, Karel H.v. Donselaar, Jan C. Fransoo Zhiqiang Yan, Remco Dijkman, Paul Grefen W.R. Dalinghaus, P.M.E. Van Gorp Egon Lüftenegger, Paul Grefen, Caren Weisleder Stefano Fazi, Tom van Woensel, Jan C. Fransoo

381 380 379 378 377 375 374 373 372 371 370 369

2012 2012 2012 2012 2012 2012 2012 2012 2012 2012 2012 2011

A Stochastic Variable Size Bin Packing Problem With Time Constraints Coordination and Analysis of Barge Container Hinterland Networks Proximity matters: Synergies through co-location of logistics establishments A literature review in process harmonization: a conceptual framework A Generic Material Flow Control Model for Two Different Industries Improving the performance of sorter systems by scheduling inbound containers Strategies for dynamic appointment making by container terminals MyPHRMachines: Lifelong Personal Health Records in the Cloud Service differentiation in spare parts supply through dedicated stocks Spare parts inventory pooling: how to share the benefits Condition based spare parts supply Using Simulation to Assess the Opportunities of Dynamic Waste Collection Aggregate overhaul and supply chain planning for

K. Sharypova, T. van Woensel, J.C. Fransoo Frank P. van den Heuvel, Peter W. de Langen, Karel H. van Donselaar, Jan C. Fransoo Heidi Romero, Remco Dijkman, Paul Grefen, Arjan van Weele S.W.A. Haneya, J.M.J. Schutten, P.C. Schuur, W.H.M. Zijm H.G.H. Tiemessen, M. Fleischmann, G.J. van Houtum, J.A.E.E. van Nunen, E. Pratsini Albert Douma, Martijn Mes Pieter van Gorp, Marco Comuzzi E.M. Alvarez, M.C. van der Heijden, W.H.M. Zijm Frank Karsten, Rob Basten X.Lin, R.J.I. Basten, A.A. Kranenburg, G.J. van Houtum Martijn Mes J. Arts, S.D. Flapper, K. Vernooij J.T. van Essen, J.L. Hurink, W. Hartholt,

368 367 366 365 364 363 362 361 360 359 358 357 356 355

2011 2011 2011 2011 2011 2011 2011 2011 2011 2011 2011 2011 2011 2011

rotables Operating Room Rescheduling Switching Transport Modes to Meet Voluntary Carbon Emission Targets On two-echelon inventory systems with Poisson demand and lost sales Minimizing the Waiting Time for Emergency Surgery Vehicle Routing Problem with Stochastic Travel Times Including Soft Time Windows and Service Costs A New Approximate Evaluation Method for Two-Echelon Inventory Systems with Emergency Shipments Approximating Multi-Objective Time-Dependent Optimization Problems Branch and Cut and Price for the Time Dependent Vehicle Routing Problem with Time Window Analysis of an Assemble-to-Order System with Different Review Periods Interval Availability Analysis of a Two-Echelon, Multi-Item System Carbon-Optimal and Carbon-Neutral Supply Chains Generic Planning and Control of Automated Material Handling Systems: Practical Requirements Versus Existing Theory Last time buy decisions for products sold under warranty

B.J. van den Akker Kristel M.R. Hoen, Tarkan Tan, Jan C. Fransoo, Geert-Jan van Houtum Elisa Alvarez, Matthieu van der Heijden J.T. van Essen, E.W. Hans, J.L. Hurink, A. Oversberg Duygu Tas, Nico Dellaert, Tom van Woensel, Ton de Kok Erhun Özkan, Geert-Jan van Houtum, Yasemin Serin Said Dabia, El-Ghazali Talbi, Tom Van Woensel, Ton de Kok Said Dabia, Stefan Röpke, Tom Van Woensel, Ton de Kok A.G. Karaarslan, G.P. Kiesmüller, A.G. de Kok Ahmad Al Hanbali, Matthieu van der Heijden Felipe Caro, Charles J. Corbett, Tarkan Tan, Rob Zuidwijk Sameh Haneyah, Henk Zijm, Marco Schutten, Peter Schuur M. van der Heijden, B. Iskandar Frank P. van den Heuvel, Peter W. de Langen, Karel H. van Donselaar, Jan C. Fransoo

354 353 352 351 350 349 348 347 346 345 344 343 342 341 339

2011 2011 2011 2011 2011 2011 2011 2011 2011 2011 2011 2011 2010 2010 2010

Spatial concentration and location dynamics in logistics: the case of a Dutch provence Identification of Employment Concentration Areas BOMN 2.0 Execution Semantics Formalized as Graph Rewrite Rules: extended version Resource pooling and cost allocation among independent service providers A Framework for Business Innovation Directions The Road to a Business Process Architecture: An Overview of Approaches and their Use Effect of carbon emission regulations on transport mode selection under stochastic demand An improved MIP-based combinatorial approach for a multi-skill workforce scheduling problem An approximate approach for the joint problem of level of repair analysis and spare parts stocking Joint optimization of level of repair analysis and spare parts stocks Inventory control with manufacturing lead time flexibility Analysis of resource pooling games via a new extenstion of the Erlang loss function Vehicle refueling with limited resources Optimal Inventory Policies with Non-stationary Supply Disruptions and Advance Supply Information Redundancy Optimization for Critical Components in High-Availability Capital Goods

Frank P. van den Heuvel, Peter W. de Langen, Karel H. van Donselaar, Jan C. Fransoo Pieter van Gorp, Remco Dijkman Frank Karsten, Marco Slikker, Geert-Jan van Houtum E. Lüftenegger, S. Angelov, P. Grefen Remco Dijkman, Irene Vanderfeesten, Hajo A. Reijers K.M.R. Hoen, T. Tan, J.C. Fransoo G.J. van Houtum Murat Firat, Cor Hurkens R.J.I. Basten, M.C. van der Heijden, J.M.J. Schutten R.J.I. Basten, M.C. van der Heijden, J.M.J. Schutten Ton G. de Kok Frank Karsten, Marco Slikker, Geert-Jan van Houtum Murat Firat, C.A.J. Hurkens, Gerhard J. Woeginger Bilge Atasoy, Refik Güllü, TarkanTan Kurtulus Baris Öner, Alan Scheller-Wolf Geert-Jan van Houtum Joachim Arts, Gudrun Kiesmüller

338 335 334 333 332 331 330 329 328 327 326 325 324

2010 2010 2010 2010 2010 2010 2010 2010 2010 2010 2010 2010 2010

Analysis of a two-echelon inventory system with two supply modes Analysis of the dial-a-ride problem of Hunsaker and Savelsbergh Attaining stability in multi-skill workforce scheduling Flexible Heuristics Miner (FHM) An exact approach for relating recovering surgical patient workload to the master surgical schedule Efficiency evaluation for pooling resources in health care The Effect of Workload Constraints in Mathematical Programming Models for Production Planning Using pipeline information in a multi-echelon spare parts inventory system Reducing costs of repairable spare parts supply systems via dynamic scheduling Identification of Employment Concentration and Specialization Areas: Theory and Application A combinatorial approach to multi-skill workforce scheduling Stability in multi-skill workforce scheduling Maintenance spare parts planning and control: A framework for control and agenda for future research

Murat Firat, Gerhard J. Woeginger Murat Firat, Cor Hurkens A.J.M.M. Weijters, J.T.S. Ribeiro P.T. Vanberkel, R.J. Boucherie, E.W. Hans, J.L. Hurink, W.A.M. van Lent, W.H. van Harten Peter T. Vanberkel, Richard J. Boucherie, Erwin W. Hans, Johann L. Hurink, Nelly Litvak M.M. Jansen, A.G. de Kok, I.J.B.F. Adan Christian Howard, Ingrid Reijnen, Johan Marklund, Tarkan Tan H.G.H. Tiemessen, G.J. van Houtum F.P. van den Heuvel, P.W. de Langen, K.H. van Donselaar, J.C. Fransoo Murat Firat, Cor Hurkens Murat Firat, Cor Hurkens, Alexandre Laugier M.A. Driessen, J.J. Arts, G.J. v. Houtum, W.D. Rustenburg, B. Huisman R.J.I. Basten, G.J. van Houtum

323 322 321 320 319 318 317 316 315 314 313

2010 2010 2010 2010 2010 2010 2010 2010 2010 2010

Near-optimal heuristics to set base stock levels in a two-echelon distribution network Inventory reduction in spare part networks by selective throughput time reduction The selective use of emergency shipments for service-contract differentiation Heuristics for Multi-Item Two-Echelon Spare Parts Inventory Control Problem with Batch Ordering in the Central Warehouse Preventing or escaping the suppression mechanism: intervention conditions Hospital admission planning to optimize major resources utilization under uncertainty Minimal Protocol Adaptors for Interacting Services Teaching Retail Operations in Business and Engineering Schools Design for Availability: Creating Value for Manufacturers and Customers Transforming Process Models: executable rewrite rules versus a formalized Java program Getting trapped in the suppression of exploration: A simulation model A Dynamic Programming Approach to Multi-Objective Time-Dependent Capacitated Single Vehicle Routing Problems with Time Windows

M.C. van der Heijden, E.M. Alvarez, J.M.J. Schutten E.M. Alvarez, M.C. van der Heijden, W.H. Zijm B. Walrave, K. v. Oorschot, A.G.L. Romme Nico Dellaert, Jully Jeunet. R. Seguel, R. Eshuis, P. Grefen. Tom Van Woensel, Marshall L. Fisher, Jan C. Fransoo. Lydie P.M. Smets, Geert-Jan van Houtum, Fred Langerak. Pieter van Gorp, Rik Eshuis. Bob Walrave, Kim E. van Oorschot, A. Georges L. Romme S. Dabia, T. van Woensel, A.G. de Kok

312 2010 Tales of a So(u)rcerer: Optimal Sourcing Decisions Under Alternative Capacitated Suppliers and General Cost Structures

Osman Alp, Tarkan Tan

311 2010 In-store replenishment procedures for perishable inventory in a retail environment with handling costs and storage constraints

R.A.C.M. Broekmeulen, C.H.M. Bakx

310 2010 The state of the art of innovation-driven business models in the financial services industry

E. Lüftenegger, S. Angelov, E. van der Linden, P. Grefen

309 2010 Design of Complex Architectures Using a Three Dimension Approach: the CrossWork Case R. Seguel, P. Grefen, R. Eshuis

308 2010 Effect of carbon emission regulations on transport mode selection in supply chains

K.M.R. Hoen, T. Tan, J.C. Fransoo, G.J. van Houtum

307 2010 Interaction between intelligent agent strategies for real-time transportation planning

Martijn Mes, Matthieu van der Heijden, Peter Schuur

306 2010 Internal Slackening Scoring Methods Marco Slikker, Peter Borm, René van den Brink

305 2010 Vehicle Routing with Traffic Congestion and Drivers' Driving and Working Rules

A.L. Kok, E.W. Hans, J.M.J. Schutten, W.H.M. Zijm

304 2010 Practical extensions to the level of repair analysis R.J.I. Basten, M.C. van der Heijden, J.M.J. Schutten

303 2010 Ocean Container Transport: An Underestimated and Critical Link in Global Supply Chain Performance

Jan C. Fransoo, Chung-Yee Lee

302 2010 Capacity reservation and utilization for a manufacturer with uncertain capacity and demand Y. Boulaksil; J.C. Fransoo; T. Tan

300 2009 Spare parts inventory pooling games F.J.P. Karsten; M. Slikker; G.J. van Houtum

299 2009 Capacity flexibility allocation in an outsourced supply chain with reservation Y. Boulaksil, M. Grunow, J.C. Fransoo

298

2010

An optimal approach for the joint problem of level of repair analysis and spare parts stocking

R.J.I. Basten, M.C. van der Heijden, J.M.J. Schutten

297 2009 Responding to the Lehman Wave: Sales Forecasting and Supply Management during the Credit Crisis

Robert Peels, Maximiliano Udenio, Jan C. Fransoo, Marcel Wolfs, Tom Hendrikx

296 2009 An exact approach for relating recovering surgical patient workload to the master surgical schedule

Peter T. Vanberkel, Richard J. Boucherie, Erwin W. Hans, Johann L. Hurink, Wineke A.M. van Lent, Wim H. van Harten

295

2009

An iterative method for the simultaneous optimization of repair decisions and spare parts stocks

R.J.I. Basten, M.C. van der Heijden, J.M.J. Schutten

294 2009 Fujaba hits the Wall(-e) Pieter van Gorp, Ruben Jubeh, Bernhard Grusie, Anne Keller

293 2009 Implementation of a Healthcare Process in Four Different Workflow Systems

R.S. Mans, W.M.P. van der Aalst, N.C. Russell, P.J.M. Bakker

292 2009 Business Process Model Repositories - Framework and Survey

Zhiqiang Yan, Remco Dijkman, Paul Grefen

291 2009 Efficient Optimization of the Dual-Index Policy Using Markov Chains

Joachim Arts, Marcel van Vuuren, Gudrun Kiesmuller

290 2009 Hierarchical Knowledge-Gradient for Sequential Sampling

Martijn R.K. Mes; Warren B. Powell; Peter I. Frazier

289 2009 Analyzing combined vehicle routing and break scheduling from a distributed decision making perspective

C.M. Meyer; A.L. Kok; H. Kopfer; J.M.J. Schutten

288 2009 Anticipation of lead time performance in Supply Chain Operations Planning

Michiel Jansen; Ton G. de Kok; Jan C. Fransoo

287 2009 Inventory Models with Lateral Transshipments: A Review

Colin Paterson; Gudrun Kiesmuller; Ruud Teunter; Kevin Glazebrook

286 2009 Efficiency evaluation for pooling resources in health care

P.T. Vanberkel; R.J. Boucherie; E.W. Hans; J.L. Hurink; N. Litvak

285 2009 A Survey of Health Care Models that Encompass Multiple Departments

P.T. Vanberkel; R.J. Boucherie; E.W. Hans; J.L. Hurink; N. Litvak

284 2009 Supporting Process Control in Business Collaborations

S. Angelov; K. Vidyasankar; J. Vonk; P. Grefen

283 2009 Inventory Control with Partial Batch Ordering O. Alp; W.T. Huh; T. Tan

282 2009 Translating Safe Petri Nets to Statecharts in a Structure-Preserving Way R. Eshuis

281 2009 The link between product data model and process model J.J.C.L. Vogelaar; H.A. Reijers

280 2009 Inventory planning for spare parts networks with delivery time requirements I.C. Reijnen; T. Tan; G.J. van Houtum

279 2009 Co-Evolution of Demand and Supply under Competition B. Vermeulen; A.G. de Kok

278 277

2010 2009

Toward Meso-level Product-Market Network Indices for Strategic Product Selection and (Re)Design Guidelines over the Product Life-Cycle An Efficient Method to Construct Minimal Protocol Adaptors

B. Vermeulen, A.G. de Kok R. Seguel, R. Eshuis, P. Grefen

276 2009 Coordinating Supply Chains: a Bilevel Programming Approach Ton G. de Kok, Gabriella Muratore

275 2009 Inventory redistribution for fashion products under demand parameter update G.P. Kiesmuller, S. Minner

274 2009 Comparing Markov chains: Combining aggregation and precedence relations applied to sets of states

A. Busic, I.M.H. Vliegen, A. Scheller-Wolf

273 2009 Separate tools or tool kits: an exploratory study of engineers' preferences

I.M.H. Vliegen, P.A.M. Kleingeld, G.J. van Houtum

272

2009

An Exact Solution Procedure for Multi-Item Two-Echelon Spare Parts Inventory Control Problem with Batch Ordering

Engin Topan, Z. Pelin Bayindir, Tarkan Tan

271 2009 Distributed Decision Making in Combined Vehicle Routing and Break Scheduling

C.M. Meyer, H. Kopfer, A.L. Kok, M. Schutten

270 2009 Dynamic Programming Algorithm for the Vehicle Routing Problem with Time Windows and EC Social Legislation

A.L. Kok, C.M. Meyer, H. Kopfer, J.M.J. Schutten

269 2009 Similarity of Business Process Models: Metics and Evaluation

Remco Dijkman, Marlon Dumas, Boudewijn van Dongen, Reina Kaarik, Jan Mendling

267 2009 Vehicle routing under time-dependent travel times: the impact of congestion avoidance A.L. Kok, E.W. Hans, J.M.J. Schutten

266 2009 Restricted dynamic programming: a flexible framework for solving realistic VRPs

J. Gromicho; J.J. van Hoorn; A.L. Kok; J.M.J. Schutten;

Working Papers published before 2009 see: http://beta.ieis.tue.nl