A Simulation-Based Robust Biofuel Facility Location Model for an Integrated Bio-Energy Logistics Network

Purpose: The purpose of this paper is to propose a simulation-based robust biofuel facility location model for solving an integrated bio-energy logistics network (IBLN) problem, where biomass yield is often uncertain or difficult to determine. Design/methodology/approach: The IBLN considered in this paper consists of four different facilities: farm or harvest site (HS), collection facility (CF), biorefinery (BR), and blending station (BS). Authors propose a mixed integer quadratic modeling approach to simultaneously determine the optimal CF and BR locations and corresponding biomass and bio-energy transportation plans. The authors randomly generate biomass yield of each HS and find the optimal locations of CFs and BRs for each generated biomass yield, and select the robust locations of CFs and BRs to show the effects of biomass yield uncertainty on the optimality of CF and BR locations. Case studies using data from the State of South Carolina in the United State are conducted to demonstrate the developed model’s capability to better handle the impact of uncertainty of biomass yield. Findings: The results illustrate that the robust location model for BRs and CFs works very well in terms of the total logistics costs. The proposed model would help decision-makers find the most robust locations for biorefineries and collection facilities, which usually require huge


Introduction
Diverse and affordable energy is critical for the future of every country in the world. To reduce the dependence on foreign oil and also mitigate the environmental impacts (e.g., climate change, pollution) of using fossil fuel, a significant amount of research in the United States has recently been devoted to methods of producing biofuel. Less attention has been given to the cost of transporting bulky biomass feedstock to biorefinery plants. The biomass transportation cost is, however, significant compared to the biofuel production cost. For this reason, a majority of existing biorefinery plants in the United States are located in the Midwest where biomass, such as corn and soybean, is abundant.
With the soaring and unstable gasoline price and the increasing environmental concern, many other states in the U.S. are now seeking the opportunity to use biomass feedstocks, such as switchgrass, for producing biofuel. Also, under the Energy Independence and Security Act  Management -http://dx.doi.org/10.3926/jiem.1196 scale BRs working on novel refining processes, and more than $400 million for bio-energy centers (2011).
The vast expansion in biofuels production and use mandated by EISA will require the development of new methods and equipment to collect, store, and pre-process biomass in a manner acceptable to biorefineries. These activities, which constitute as much as 20% of the current cost of finished cellulosic ethanol, are comprised of four main elements: • Harvesters & collectors that remove feedstocks from cropland and out of forests.
• Storage facilities that provide a steady supply of biomass to the biorefinery, in a manner that prevents material spoilage.
• Preprocessing/grinding equipment that transforms feedstocks to the proper moisture content, bulk density, viscosity, and quality.

• Transportation of feedstocks and biofuels
In this study, we consider an integrated biomass and bio-energy logistics network consisting of four different types of facilities: a supply point -farm or harvest site (HS), a storage point -collection facility (CF), a production point -biorefinery (BR), and a demand point -blending station (BS). We assume that the locations of HS and BS are fixed and the demand of each BS is constant throughout the planning period. The logistics network structure is depicted in Figure 1. The inbound flows (solid arrows) in Figure 1 represent the collection, storage, and transportation of biomass, which can be of many types. The biomass collected at each HS is brought by trucks into a local CF. Smaller loads of biomass collected from the HS are temporarily stocked at the CF before they are consolidated and transported to a BR by large-capacity trucks for processing into biofuel. A CF is a potential site to store and preprocess (e.g., compress) biomass to a more valuable density and/or to pre-treat biomass to make a better quality biomass feedstock so that they can be transported in a more costeffective way. In addition, a direct transportation of biomass from a HS to a BR is allowed and the resulting transportation cost is usually higher than going through the CF, since the direct shipping of biomass from a HS to the BR requires more space (due to the low biomass density) and more operations and preparation to be processed into biofuel. The outbound flows (dashed arrows) in Figure 1 show that biofuels are transported from BRs to BSs to be blended with fossil fuels before being distributed to gas stations. Given the locations of BSs and their demands, the transportation costs mainly depend on the proximity of BRs to BSs. In this logistics network, determining the locations of BRs and CFs will be the most important decision. This is because a BR usually requires several million dollars as the annualized construction and operation cost. Also, the use of CFs would affect the quality of biofuel that primarily depends upon the moisture content in the biomass (Dyken, Bakken & Skjelbred, 2010), letting alone the total transportation cost between HSs and BSs. What complicates the decision of CF and BR locations is the uncertainty in biomass yield.
Intuitively, different biomass yield scenarios will affect the optimality of a biofuel facility location plan. To develop a robust model, we first present a mixed integer quadratic program (MIQP) modeling approach to simultaneously determine the optimal locations of BRs and CFs and the transportation scheme for a given biomass yield scenario. We then investigate the effects of biomass yield on the optimality of the selected location by simulating the biomass yield of each HS, i.e., generating biomass yield for each HS using three probability distributions and finding the optimal locations of BRs and CFs for each yield scenario. Based on the simulation results, we identify the most frequently selected locations of BRs and CFs (referred to as 'robust locations',) for various biomass yields scenarios. By comparing the optimal solutions for the different biomass yield scenarios, a robust location is then identified.

Literature Review
Many existing studies have focused on bio-processing technologies to improve the biofuel yield and quality (Antonpoulou, Gavala, Skiadas, Angelopoulos & Lyberatos, 2008;Lee, Chou, Ham, Lee & Keasling, 2008;Ranganathan, Narasimhanm & Muthukumar, 2008;van Dyken, Bakken & Skjelbred, 2010;Weyens, Lelie, Taghavi, Newman & Vangronsveld, 2009). Although the cost of transporting bulky and unrefined biomass feedstock is also significant as compared to the total cost for producing biofuel, much less attention has been given to the understanding of biomass and bio-energy logistics systems and the reduction of biomass and bio-energy logistics costs.
The remaining of the paper is organized as follows. Section 3 introduces an integrated facility location and transportation model in detail. Following the description of the model formulation, case studies are conducted and analysis for simulation results is presented in section 4.
Section 5 summarizes the developed models and research findings. It also provides recommendations for future research directions.

Development of Integrated Optimization Model
We propose the integrated optimization mathematical model by modifying the model (Eksioglu et al., 2009). In our proposed model, we assume that CFs can be located at any HS and a biorefinery (BR) can only be built at candidate BR location, since BR locations must satisfy some realistic requirements. This is a reasonable assumption at the planning stage for the bioenergy logistics model. It may be difficult to decide potential CF locations which are not HSs, since the assignment of HSs to a CF is not known.
Let F be the set of all harvesting sites (HSs) and potential collection facility (CF) locations, indexed by f. Now, let J, I, and K respectively be the set of CFs, BRs, and BSs, indexed by j, i, and k. Also, let L and G respectively be the set of capacities of BR and CF, indexed by l and g.
The parameters used in this formulation are the following: is amortized annual cost of constructing and operating a BRi with the l t h size; is amortized annual cost of constructing and operating a CFj with the g th size; and denote the actual capacity of l th and g th size of (1) (3) (8) -1420- Constraints (2) and (3) ensure that a BR and a CF of size l and g are located in sites i and j.
Constraints (4) and (5) require that at most Nb BRs and Nc CFs can be constructed. Constraints (6) ensure that each HS is assigned to a CF or a BR. Constraints (7) ensure that each selected CF should cover at least uj and at most uj HSs (set to 2 and 10 in this study). Constraints (8) are capacity constraint for CFs, that is, the amount of biomass a CF receives should not exceed its capacity. Constraints (9) are capacity constraint for BRs, that is, the amount of biofuel a BR can produce should not exceed its capacity. Constraints (10) ensure that a CF supplies biomass to the selected BR sites only. Constraints (11) ensure that at most δi HS is directly covered by BRi. Constraints (12) and (13) ensure that the total amount of biofuel converted from biomass by all BRs is enough to satisfy the total demand of biofuel for all BSs. If not, a dummy biorefinery, BRm, is added to satisfy the shortage.
To solve the above MIQP problem, letting to linearize the term in Equations (1), (9) and (11), we add the following: Hereafter, this newly introduced model given by Equations (1)-(14) is referred to as the Integrated Biofuel Facility Location (IBFL) model.

Case Study
We conduct a case study using the scenario illustrated in Figure 2 (EPA Tracked Sites in South Carolina with Biorefinery Facility Siting Potential, 2013). Fifteen (15) counties, whose biomass resources are classified 'good' or better as shown in Figure 2, are selected as the harvesting sites (HSs). Then, one city is chosen from each county using a centroid approach and is considered a candidate location for collection facility (CF). Five (5) locations and ten locations (10) throughout South Carolina are considered as candidate sites for BRs and blending stations (BSs), respectively, as shown in Figure 3. The potential locations for BRs are selected based upon low population density, easy access to interstate highways, etc.
-1421- Although not shown in Figure 3, the actual distances among cities representing HSs, CFs, BRs, and BFs, are calculated. To simulate the uncertainty in biomass yields, we randomly generate biomass yield for each HS using three popular probability distributions. The minimum and maximum biomass yield values for each HS are obtained from the ranges shown in Figure 2. The probability distributions considered in this paper are normal distribution, uniform distribution, and triangular distribution.    where wf and Wf denote minimum and maximum amounts of biomass yield at HSf shown in Figure 2. To derive Equation (16), we assume that wf and Wf are located at three standard deviations on either side of its mean.
Case 2. Uniform Distribution: we use the minimum, wf, and maximum value, Wf for the parameters of the uniform distribution.
Case 3. Triangular Distribution: two skewed distributions are considered for biomass yield. The first one is a right-skewed distribution. Its mode, O(r)f, is located at The other one is a left-skewed distribution. Its mode, O(l)f, is located at For Equations (17) and (18), we assume that a mode is located at (Wf, -wf)/4 to the right side of the minimum amount (wf) for the right-skewed distribution and to the left side of the maximum amount (Wf) for the left-skewed distribution, respectively.

Numerical Results and Observations
We assume shortage costs to be equal to zero, since the occurrence of biofuel shortage would not affect the optimal locations of BRs and CFs. We solve the developed model for forty (40) different sets of simulated biomass yields for each probability distribution and present the frequencies of BR and CF to be included in the optimal solutions in Tables 2a through 2d. '1' for BR location columns in these tables denotes that this location is selected in the optimal solution and '0' otherwise. For the case of normal distribution (see Table 2a Table 2b). However, for the skewed triangle distribution case, one BR location set is dominant over the other. For the right-skewed triangle distribution, the simulated biomass yields are more likely to be less than the middle value of wf and Wf. Due to this, the BR location set 2 {Prosperity, Cayce} is selected more frequently (33 times out of 40) as shown in Table   2c, whereas the BR location set 1 {Branchville, Cayce} is selected more frequently (36 times out of 40) for the left-skewed distribution as shown in Table 2d.
The selected locations of CFs depend upon the locations of BRs. As the results in Tables 2a   through 2d and Table 3 suggest, when the BR location set 1 {Branchville, Cayce} is chosen, the CF location set {Colleton, Dorchester, Newberry, Orangeburg, Richland} is selected 83 times out of 86 (see Table 3). Given that the BR location set 2 {Prosperity, Cayce} is selected, the CF location set {Chester, Newberry, Orangeburg, Richland} is selected 39 times out of 73.
The total capacity of these four (4) CF locations is sometimes insufficient. Therefore, the second most frequent CF location set, {Chester, Newberry, Orangeburg, Richland, Darlington} selected 16 times out of 17, is considered. From     In Table 4, we compare the optimal solutions of each simulated biomass yield scenario with Robust Location 1 and Robust Location 2. We also report the percentage deviation (PD) of Robust 1 and Robust 2 from the optimal solution for each scenario. As expected from Tables 2   and 3 and seen in Table 4, for Scenario I, which is an extreme case of the right skewed distribution, Robust 2 performs better than Robust 1. For Scenario III, an extreme case of the left skewed distribution, Robust 1 outperforms Robust 2. For Scenario II, both Robust 1 and Robust 2 perform well compared to the optimal solution, since the PDs yielded by Robust 1 and Robust 2 are 0% and 0.04%. In terms of the maximum PD (MXPD) for all scenarios, Robust 1 with 11.4% performs better than Robust 2 with 18.3%. On the average of PD (AVPD), Robust 1 with 6.3% performs slightly better than Robust 2 with 7.3%, which is consistent with the results shown in Table 3.

Summary and Conclusions
In this paper, we develop an IBFL (Integrated Biofuel Facility Location) model to simultaneously find the optimal locations of collection facilities (CFs) and biorefineries (BRs) for a biomass and bio-energy logistics network. We formulate the proposed model as a mixed integer quadratic program (MIQP), construct an Excel spreadsheet model, and solve it using Excel Analytic -1428-Journal of Industrial Engineering and Management -http://dx.doi.org/10. 3926/jiem.1196 Solver Platform with VBA (Visual Basic for Applications). For the biomass and bio-energy logistics network, the uncertainty in biomass yield has been a critical factor for determining the optimal locations of BRs and CFs, since it significantly affects the logistics network operational costs. To demonstrate the developed model's capability and to evaluate the effects of the uncertainty in biomass yield, a case study is conducted using the data from United States EPA as shown in Figure 2. We simulate the biomass yield uncertainty by randomly generating biomass yield for each HS using normal, uniform, and triangular probability distributions. We then find the optimal locations of BRs and CFs for each generated set of biomass yield data.