Ashish Soni EMBA 1st Semester C-4/EMM/60 PRODUCTION AND OPERATIONS MANAGEMENT A Case Study on the Facility Location Problem for a Large-Scale Cosmetics Product CompanyAbstractFacility location models have been extensively studied and their practical use reported in supply chain related literature. However, few studies exist that relate these models to Disaster Operations Management, where abundant application may be found, for example the possibility of a large scale production that demands immediate action and requires service to a densely populated area. This work takes a facility location model proposed in literature and presents a case study for its application to DuPage County in Illinois. Prospective medical facilities are selected to service the needs of the various communities. Meaningful results are obtained and discussion of future research possibilities.

1. IntroductionLarge scale emergencies are an issue that all levels of the government are gravely concerned about. Since the 2001 terror attacks in New York City, it has become imperative to pursue research into Disaster Operations Management where facility location planning is crucial for the event of a large scale production. Large scale emergencies come in many forms such as man-made disasters, acts of nature, or even during times of combat. Models that suggest facility location plans in the event of emergencies must consider the facility location objective, facility quantity, and service quality. Facility location models have been largely studied and their practical use reported in supply chain related literature [3] [4] [12]. However, very few articles [11] are found reporting the application of these models to situations where medical services are required for emergencies that affect most of the population. Specifically, in this article a case study is presented where it is assumed a terrorist attack occurs over DuPage County in the State of Illinois. The P-center model is applied to determine how to allocate a given number of emergency facilities to satisfactorily meet the population demands. In this work, the distance from major population centers from various communities throughout DuPage County and the prospective production facility locations is calculated. Much of this information is obtained from city officials and using commercially available mapping software. The information collected is put into the facility location model and we then run our model using Lingo.

2. Large Scale Production ServicesFacility location problems that deal with large scale production services are a special case since they involve low frequency of attacks and substantial impact on the local communities. An appropriate model should be able to assign a limited number of facilities to service all required demand points. Moreover, the distance between the demand point and the prospective medical facility site should be kept to a minimum to ensure that the service is able to manage a large area. However, the choice of model and the location assignments will remain ambiguous since a large-scale attack is bound to affect the livelihood of thousands regardless of medical facilities available. Therefore, it is plausible to state that resources should be pooled and distributed to address the needs of many in a large area. Some of the techniques used in LEMS stems from Disaster Operations Management (DOM) and includes research on mathematical programming [1-2] [9] [13] [15] [17], probability theory and statistics [6], simulation [5] [10] [14] [16], decision theory and multi-attribute utility theory [7-8]. 2.1 Terrorist Attack

Unlike the anthrax scare of the early part of this decade, the smallpox virus is able to transmit from person to person rapidly. In the event of a smallpox terror attack, civil service personnel (policemen, paramedics, firemen, etc.) will need to be protected to ensure that they are able to assist civilians with greater ease and finesse. Medical equipment and supplies need to be available to emergency responders at facilities that can quickly distribute the necessary materials. Furthermore, treatment solutions need to be available on a mass scale to allow all affected persons to be treated and released in a timely manner. Eventually, the facility will not only have to take into consideration distribution at the local level, but also determine how to optimize logistics to receive assistance from the federal level. An excellent article that proposes facility location models for several potential terrorist attacks is that of Jia, Ordez, and Dessouky [11].

3. P-Center Model3.1 Model Introduction The P-center models goal is to minimize the worst performance of a system where the average system performance is not considered a primary goal. More commonly, the P-center model is referred to as the minmax model since it tries to minimize the maximum distance between a required demand point and a prospective site point [11]. One of the major assumptions of this model is that it is assumed that a demand point is fully serviced and a limited number of facilities are available. 3.2 Model Formulation The proposed P-center model is found in [11] and is represented as follows: Minimize L s.t. xJ PjJ

(1) (2) (3)

zij pjk = Qi i IjJ

zij xj i I,j J

L i I,k K

ikeikMidijzij jJ

(4) Qi (5)

xj ,zij = {0,1} i I,j J

The L represents the total weighted distance between the demand points and prospective facilities. This value is the model objective and it is the intent of the P-center model to ensure that it is the smallest maximum distance required. The table below outlines the respective values and their definitions: Table 1: Variable Definitions Value Meaning

Ii ?Demand Point (city)

Jj ?

Prospective Site Point (facility)

Kk ?Scenario (Smallpox Attack) xj if a facility is placed at site j zij If a facility i services site j Qi Number of facilities required at demand point i pjk reduction in service capability of facility j under scenario k ?ik likelihood for demand point i to have a large-scale emergency situation k eik impact coefficient for demand point i under large-scale emergency situation k M Population of demand point dij Distance between demand point i and prospective facility site j

Site Addison Bloomingdale Downers Grove It is critical to note that x and z are both binary variables. Lisle Wheaton 4. Case Study Naperville Bartlett For this case study, it was considered the situation of a smallpox terrorist attack in DuPage County. The smallpox disease can West Chicago be transmitted through person-to-person contact, and thus it can spread really faster than other disease (anthrax). First Lombard responders (e.g. fire, police, medical personnel, etc.) are the people who need immediate vaccination once a smallpox 1 emergency is detected to remain effective during the emergency. Therefore medical supplies need to be stored at local 5.3 facilities for instantaneous use by the first responders. Furthermore, during smallpox emergency mass vaccination is often 3.2 necessary, which requires tremendous medical supplies; hence the strategic national stockpiles (SNS) would be requested to 11.5 meet this massive demand. Jia, Ordez, and Dessouky [11] establish an integer model based on the P-center model, well 12.6 known in facility location literature. They illustrate the use of this model with an example using information from California. 6.9 17.2 Figure 1: DuPage County Map 11.1 9.6 The following table represents the distance between village 6.2 of each community and the prospective site. The village hall hall was used as the center for each community since it allowed for 2 easily accessible information and serves as the center for any community. 12.1 Each prospective site is a major hospital facility that is equipped with an 17.7 Emergency Room capable of handling above normal number of cases. 6.1 The numbers below are in miles and are approximate. 9 16.3 Table 2: Distance Table from Demand Point to Site Point 13.5 24.9 25.2 9.3 3 12.9 13.1 1.9 6.3 9 11.2 21.1 17.9 3.6 4 12.8 9.5 14.5 10 3.3 7.7 10.1 2.7 10 5 21.8 18.5 25.2 21.3 14.6 19.4 City/Town Site14.3 Demand Point (I) Addison 9.3 Population (M) Bloomingdale 19.6 Downers Grove Smallpox Occurrence Likelihood (?) 6 Lisle Impact Coefficient (e) 19.9 Wheaton Weight (?eM) 20 Naperville Required Facility Quantity (Q) 9.8 Bartlett Addison 5.8 West Chicago 36378 8.7 Lombard 1 0.9 1 1 20.4

Bloomingdale 7 21675 5 1 11.6 1 12.5 21.675 14.9 Given that this is an integer problem with binary variables,13.1 are certain complexity issues associated with the model, there 1 which means that for large size problems the computer effort to solve the model by means of an exact algorithm to optimality Downers Grove 19.8 will increase exponentially with the problem size. Therefore, the recommendation would be to use heuristics based methods 49302 18.8 when facing large size problems. For the small case study constructed we used LINGO. The information of parameters for 2 1 15.8 our model is shown in the table 1 below. 1 8.8 49.302 8 Table 3: Model Input Data Values 2 28.5 Lisle 28.7 23376 The values of and e are arbitrary and assumed to be 19.6 simplicity. The Required Facility Quantity column also 1 for 1 15.7 once more reliable information is made available or has arbitrary values assigned. These values can easily be adjusted 1 16.5 and this value is represented by P. demanded. The total number of facilities available for use is four 23.376 13.7 1 22.9 5. Results Wheaton 13.8 55416 Results indicated that sites 3, 4, 5, and 6 should be used to 21.5 the needs of all the communities listed. More specifically, service 3 91 the table below gives a tabulation of what the results are to be like: 1 13.2 55.416 19.5 Point Facility Assignments Table 4: Demand Point and Site x 2 5.3 Naperville 9.5 Since the P-center model works as a minmax system, it is determined to find the minimum maximum distance that is to be 140106 x 15.5 traveled between all demand points and the service facility 14.7 (sites). In this case, it has determined that sites 3, 4, 5, and points x 1 6 should be utilized to satisfy the demand points. The weighted-distance is calculated as 924.7049 miles, which is an 1 26.7 approximate value since the exact total distance is notx 140.106 considered. 26.5 x 3 10.4 4 Bartlett 6. Conclusions x 37304 1 Since the catastrophic events of September 11, 2001, interest in large scale production scenarios has increased and given new 1 life to a topic that is not visited often. A P-center model proposed in literature [1] was easily applied to DuPage County and 37.304 its communities. The P-center model might not represent many other factors needed; however, it does suggest how county 2 officials could allocate their resources given a smallpox terror attack. The data used was selected in a manner that would West Chicago allow it to run on commercially available software such as LINGO without too much time consumption. As more x 26554 increase drastically and become computationally more communities are added to the P-center model; the elapsed timex could 1 expensive. DuPage County is adjacent to Cook County, the largest county in Illinois, and any terror attack on DuPage 1 County would also adversely affect the residents and communities close to the DuPage and Cook County border. 26.554 5 1 x Lombard 42975 1 x 1 42.975 2x x 6 x x x x

7

8

If DuPage County was divided into a 5 mile by 5 mile grid, and each grid required having at least one prospective site, the total number of prospective sites would easily exceed 100 sites. In this case, heuristics would be required to approach an optimal solution without navigating prohibitive computing time. Future research will endeavor into linking multiple counties suffering terror attacks and allocating resources between multiple counties.

9