Discussion of Optimize Method of Fire Alarm Dispatching Based on Operation Research Principle

Size: px

Start display at page:

Download "Discussion of Optimize Method of Fire Alarm Dispatching Based on Operation Research Principle"

Louisa Marsh
6 years ago
Views:

1 Available olie at Procedia Egieerig (20) The 5 th Coferece o Performace-based Fire ad Fire Protectio Egieerig Discussio of Optimize Method of Fire Alarm Dispatchig Based o Operatio Research Priciple ZHANG Miao * Chiese People s Armed Police Force Academy, Lagfag , Chia Abstract I recet years, fires i Chia are gradually developig to large, complex, cross-regioal ad other directios. The probability of multiple simultaeous major fire accidets is risig. How to optimize fire vehicles becomes the key poit of fire prevetio at the preset stage. This paper discusses a optimize method of Fire alarm vehicles dispatchig based o the trasportatio model ad assigmet problem, sets a mathematical model of this problem, which solutio is give by LINDO/LINGO software. It verifies the feasibility ad efficiecy of this optimal method through a real example. 20 Published by Elsevier Ltd. Ope access uder CC BY-NC-ND licese. Keywords: trasportatio model, assigmet problem, fire alarm dispatchig, liear program;. Itroductio I recet years, fires i Chia are gradually developig to large, complex, cross-regioal ad other directios. Due to the large scale, the harmfuless of fire, the persoel eeds, it is difficult to cotrol fire timely ad effectively by relyig o limited fire fightig forces. Istead, it ofte affects fire fightig ad rescue work ad cause s great damage. So, i the cases of may places occur great fire accidet simultaeously, it is a problem badly i eed of solutio that how should fire commad ceter set up a optimal distributio of equipmet for each fire statio to muster eough forces at first time ad douse the fire. As a importat brach of operatios research, trasport problem combies with the actual eeds. Trasport model is used to solve the delivery pla of a sigle origi of goods from several producig areas to several destiatios. Trasportatio problem is a typical liear programmig problem. As a specific form of the 0- iteger programmig, Assigmet problem is very importat. The commo applicatio of Assigmet problem is to distribute road for vehicle whose goal is cosume the miimum total resources. At the same time, may trasportatio problems ca evolve ito the assigmet problem to solve. * Correspodig author. Tel.: address: zhagmiao_86073@63.com Published by Elsevier Ltd. doi:0.06/j.proeg Ope access uder CC BY-NC-ND licese.

690 ZHANG Miao / Procedia Egieerig (20) 689 694 This paper discusses a optimize method of Fire alarm vehicles dispatchig based o the trasportatio model ad assigmet problem, sets a mathematical model

2 690 ZHANG Miao / Procedia Egieerig (20) This paper discusses a optimize method of Fire alarm vehicles dispatchig based o the trasportatio model ad assigmet problem, sets a mathematical model of this problem, which solutio is give by LINDO/LINGO software. It verifies the feasibility ad efficiecy of this optimal method through a real example. 2. The aalyses of trasport model ad assigmet model 2.. The mathematical model of the trasportatio problem Trasportatio problem is a special kid of liear programmig problem. It is used to solve the delivery pla of a sigle origi of goods from several producig areas to several destiatios []. Put the trasport costs of goods is proportioal to the trasportatio quatity. Ad x express the trasportatio quatity from origis to place of sales. O the premise of balace of productio, we eed solve the liear programmig problem below to get the miimum total freight. m. cx i= j= () (2) I the formula, the a i, b j, c express supply, quatity demaded ad uit price separately. O the problem of dispatchig fire service vehicles, supposig the amout of available forces are equal to the amout of vehicles for fire eed, the optimal method of Fire alarm vehicles dispatchig ca be built i the basis of mathematical model of trasportatio problem The mathematical model of assigmet problem The assigmet problem is uits to udertake m tasks. Due to the differet specialty, each uit accomplish differet missio, its efficiecy is differet. Therefore, it is ecessary to assig the task scietifically, esurig cosume the least resources to complete m tasks [2]. The assigmet problem is also a 0- iteger programmig model, the variable x oly values 0 or. The x called the 0- variables, or biary variable. Ad x geerally ca be expressed as:

ZHANG Miao / Procedia Egieerig (20) 689 694 69 The mathematical model of the assigmet problem ca be writte for:.

3 ZHANG Miao / Procedia Egieerig (20) The mathematical model of the assigmet problem ca be writte for:. cx i= j= (3) (4) Accordig to the mathematical model of the assigmet problem, we ca easily fid that the assigmet problem is ot oly the exceptio of 0- iteger programmig, but also is the exceptio of trasportatio problem. Therefore, the optimal method of fire alarm vehicles dispatchig ca be built based o the modelig of the assigmet problem. 3. The mathematical model of the fire alarm dispatchig problem 3.. Loss fuctio Whe fire cotrol commad cetre dispatches vehicles to multiple locatios of the fire, it ca be regarded as a trasformatio of traffic assigmet problem ad trasportatio problem. Therefore, this paper sets a mathematical model of this problem based o the mathematical model of trasport problem ad itroduces the 0- iteger variable to improve the model. Ad the problem of optimized objectives is solved through the optimal vehicle schedulig to miimize the total loss of multiple fire sites. I the estimatio of fire damage, this is the key problem i the actual situatio, but also is difficult to estimate accurately. However, because of the statistical data of the travel time of fire egie betwee each fire statio ad fire site ca be obtaied easily i the peacetime fire fightig. Thus each loss of fire locatio ca be expressed as fuctio of time. That is D = f() t.time t is the travel time of fire egie betwee each fire statio ad fire site. The fire damage of each fire locatio makes up the loss matrix, specified by C. First, i order to solve this problem with trasport modelig, aturally put fire statio m as outlets. Sice the author cosiders the loss fuctio as liear fuctio of fire truck arrival time, if put fire sites p as demad poit, it is difficult to describe the sequece of fire truck arrival coveietly, so difficult to determie the size of the loss. Therefore, we ca cosider the amout of available fire truck of m fire sites as demad poit. Thus, the value of each demad poit is oly or 0. So the 0- iteger variable x is decisio variables, expressig whether the fire statio i sed fire truck to the demad poit j ( meas sed, 0 meas ot sed) Hece, the total loss miimum decisio goal is:. cx (5) i= j= Costrait coditios have two kids, oe kid is the fire statio with quatitative restrictio, ad aother kid is the demad restrictio of fire truck for fire. b i is the quatity of fire truck that fire statio possessed, as show by the followig formula: x = bi i, =,2,..., m (6) j=

4 692 ZHANG Miao / Procedia Egieerig (20) The demad restrictio of fire truck for each demad poit ca be expressed by the followig formula: m x =, j =,2,..., i= (7) x = 0 (8) The above four equatios are simultaeously solved, ad give the mathematical model of the fire alarm dispatchig problem. Due to the arrival time of fire egie to each fire sites is differet, so the selectio of optimal solutio should also cosidered the arrived sequece of fire egie to each fire. Ad specific costrait coditios should be based o the aalysis of cocrete examples. But must follow such a priciple: the fire statio which is recet distace from fire place priority to sed fire egie The solvig of model This study is a t trasformatio of the trasportatio problem ad the assigmet problem. Based o the mathematical model of the trasportatio problem, the author itroduced the 0- iteger variable x ad added specific costraits, establishig the mathematical model of the fire alarm dispatchig problem. So the Hugary method of the assigmet problem o loger applies to this problem. Because of this problem is still belogs to liear programmig problems, therefore, the geeral solvig method of liear programmig problem is also applied to this problem. I order to get a more rapid solutios, computer software ofte be used to solve the actual problem solutio. At preset, maily used for statistical data processig software has Matlab, LINDO/LINGO, Origi, ad Excel. LINDO/LINGO is a kid of software package used specifically to solve mathematical programmig problem. LINDO/LINGO ruig fast ad executio, easy to iput, aalyze ad solve the mathematical programmig problem. Therefore, it is widely used i mathematics, sciece ad idustry. LINDO/LINGO maily used for solvig liear programmig, oliear programmig, a quadratic programmig ad iteger programmig problems. It also ca be used i some oliear ad liear equatios for solvig algebraic equatio ad the root. LINDO/LINGO cotais a kid of modelig laguage ad may commo mathematical fuctios for users ivokig to establish programmig problem. The problem discussed i this paper ca solve by LINDO/LINGO software. 4. Example aalysis 4.. Case descriptio Some city fire commad ceter received three fire calls simultaeously. Accordig to the curret fire behavior, three fire sites separately eed 2, 2 ad 3 fire trucks to put out a fire. The loss of three fire sites will deped o the truck arrived i degree: t is the arrival time of fire egie j to fire site i, the loss fuctio of three fire site (millio) are: 4t +6t 2,3t 2 +7t 22,5t 3 +8t 32 +9t 33. Curretly, the quatity of available fire truck is seve belogs to three fire statios (respectively 3, 2, ad 2). The travel time of fire truck from three fire statios to three fire sites is show i the table. How to formulate ratioal schedulig solutio ad gettig the miimum total loss? Table. The travel time of fire truck from three fire statios to three fire sites

5 ZHANG Miao / Procedia Egieerig (20) Time(mi) Fire site Fire site 2 Fire site 3 Fire statio Fire statio Fire statio Model itroducig Regardig three fire statios as supply cetre, seve fire egies eeds respectively as seve demad poits (the arrival time are t, t 2, t 2, t 22, t 3, t 32 ad t 33 ). The value of each demad poit is 0 or, a total of 2 0- variables. The form is show below. Table 2. Form of the fire alarm dispatchig problem C Fire site Fire site 2 Fire site 3 j = j = 2 j =3 j =4 j =5 j =6 j =7 Fire statio i= C C 2 C 3 C 4 C 5 C 6 C 7 3 Fire statio i=2 C 2 C22 C23 C 24 C 25 C 26 C 27 2 Fire statio i=3 C 3 C32 C33 C 34 C35 C 36 C 37 2 Demad C is the loss of fire truck from fire statio i to fire site j. Due to the loss fuctio is liear fuctio of fire truck arrival time, through simple calculatio by give data, if the fire statio sed fire egie to fire site 6, the fire loss is 8 x 9 = 72 (millio). Similarly, the matrix loss ca be show by the followig table. Table 3. Loss matrix (millio) Supply C Fire site Fire site 2 Fire site 3 j = j = 2 j =3 j =4 j =5 j =6 j =7 Fire statio i= Fire statio i= Fire statio i= Hece, to get the miimum total loss, ca solve optimizatio solutio uder the mathematical model:. cx (9) 3 7 i= j= (0)

6 694 ZHANG Miao / Procedia Egieerig (20) At the same time to cosider the arrived sequece of fire egie to each fire. So, we should add the ew costrait coditio to this model as follow. The costrait coditio of fire site is: x22 x2 () The costrait coditio of fire site 2 is: The costrait coditio of fire site 3 is: (2) (3) 4.3. Solvig calculatio This paper use LINDO/LINGO software to solve. Iput the mathematical model of the fire alarm dispatchig problem which combies formula (9) ~ (3) to LINGO software. Through this software ca get the solutio x4=x5=x3=x2=x22=x36=x37=, other variables is 0, the miimum total loss is 335 millio. Namely, the fire statio sed two fire trucks to fire site 2, ad sed oe fire truck to fire site 3. The fire statio 2 should sed two fire trucks to fire site, ad the fire statio 3 sed two fire trucks to fire site 3. After testig ca be foud, this optimizatio scheme is reasoable. If do't adopt the optimizatio scheme, the rage of fire loss are about 37~354(millio). By cotrast, the fire loss reduces by 6.6% ~9.7%. 5. Coclusio This paper sets a mathematical model of the fire alarm dispatchig problem based o the theory of the trasport model ad the assigmet model, fially obtais the reasoable optimizatio scheme. Through a real example, this paper verifies the feasibility of the trasport model ad the assigmet problem to solve the fire alarm dispatchig problem. Usig this optimizatio scheme to reduce the fire loss by 6.6% ~9.7%, show the high efficiecy of the trasport model ad the assigmet problem i solvig the problem. Ackowledgemets The authors would like to thak Chia People s Armed Police Forces Academy for its great support, without which the coduct of this research would ot be possible. Refereces [] Li Rog-Ju, kuag Yig-Qag. Operatioal Research. South Chia sciece ad techology uiversity press, [2]He Jia-Yog. Optimizatio Method. Tsighua uiversity press, 2007.

Heating/Ventilation Control Systems

Heatig/Vetilatio Cotrol Systems ANALYSIS OF STABILITY OF LIVESTOCK BUILDING HEATING/VENTILATION CONTROL SYSTEMS Y. Zhag, E.M. Barber, H.C. Wood Executive Summary Mathematical models ca be used to predict