Poceedings of the 10th WSEAS Intenational Confenence on APPLIED MATHEMATICS, Dallas, Texas, USA, Novembe 1-3, 2006 262 An Impoved Implementation of Activity Based Costing Using Wieless Mesh Netwoks with MIMO Channels LYONEL LAULIÉ (1), ISMAEL SOTO (1) and ROLANDO CARRASCO (2) (1) Industial Engineeing Depatment Engineeing Faculty Univesity of Santiago of Chile Av. Ecuado 3769, Santiago CHILE (2) School of Electical, Electonic and Compute Engineeing. Univesity of Newcastle upon Tyne Mez Cout Newcastle upon Tyne (NE1 7RU) UNITED KINGDOM Abstact: - The next pape bings the development of an impove implementation of Activity-based costing using Wieless Mesh Netwoks with MIMO channels. The study of the efficiency of this implementation in MIMO channels, is simulated with Space-Time Block Coding with convolutional codification and BPSK modulation, to show that this way of manages costing and the coect exploitation of wieless technologies in communications, geneate new value to entepises. Also the monetay diffeences of the costs, the impact of the use of bette channels ae pesented. Key-wods: - Activity Based Costing (ABC), Wieless Mesh Netwoks (WMNs), MIMO Channels, STBC. 1 Intoduction The detemination of the costs fo any company that poduces goods o sevices could esult a life o death opeation. A good cost calculation, give to the company a poweful tool that help, in evey ode of issues, to take bette decisions. That is to say, to fix pices, establish an optimal mix of poducts, detemine entability, offe special pomotions to pincipal customes, etc. In this context, emege the Activity Based Costing (ABC) as a paticula cost system that solves the faults of the taditional systems in the coect distibution of poducts, expenses and indiect costs. Actually, the implemented systems used fo some companies that have been designed, pincipally, in ode to valoize inventoies with the pupose of pepae the financial statements and to pay taxes, ae not poviding to the manages, oppotune and petinent infomation to intoduce impovements in the opeational efficiency and to measue the costs of poducts. In addition, while it moe inceases the vaiety of poducts with substantial diffeences, the infomation that this systems give, becomes less eliable. What this model does is to identify and classify the diffeent activities that ae made inside an oganization to poduce, develop, distibute o to give suppot to the poducts that ae commecialized. In that way, the model is based in two basic ideas: The fist is that the poducts demand activities and not esouces, that is to say, that the poducts do not consume costs but necessay activities to its fabication. The second idea is that the activities ae those that consume esouces o value of the poductive factos, and the costs ae, nothing else that the quantified expession of the esouces consumed by the activities. Thus, with the objective of make a bette contol of the costs, the companies that implements this system, must act on the activities that cay out, and have a meticulous monitoing of them. We could enumeate a lot of advantages of this cost system that ae elated with economics, finance, stategic and management factos that the lecto can consult in the liteatue. But like in evey ode of things in life, thee ae some disadvantages o limitations that this wok wants to impove. 2 Poblem Fomulation As we said befoe, to use this cost system, the company must act on the activities, but sometimes, they ae vey difficult to measue, especially in entepises with moved away locations and extensive sizes like constuction, ion and steel, and mining entepises. Fo this types of companies, thee is also impotant, the question of how to implement infomation systems that be effective and eliable at the same time. And in the case of use wieless technologies, how to make that the communications tun quicke, flexible and moe obust. How to have eal time infomation and thus, have the possibility of impove the total oganization?.
Poceedings of the 10th WSEAS Intenational Confenence on APPLIED MATHEMATICS, Dallas, Texas, USA, Novembe 1-3, 2006 263 Anothe big poblem is the high costs that poduce the obtaining of the infomation of pocess, activities, times to develop these activities, and the amount of the factos that epesent the activities. If we will ty to fomulate this poblem like an opeation eseach optimization, we will find that the complexity inheent in this situation and the amount of the needed vaiables ae enomous. We only could find a bette solution, but not the best eve. In this questionings bon the idea of implement Wieless Mesh Netwoks like an efficient and appopiate instument to get infomation though mobile devices at the physical location of the diffeent activities of the cost system. In addition, we popose a multiple-antenna system in ode to incease the capacity of the channel, debilitated and affected by fading, delayspead and noise intefeence. And with mathematical techniques, we will codify data to achieve divesity and thus, make eliable communications. In that way we will have cost systems that pemit to obtain continuous infomation, in eal time, with a view of a constant activity contol. On anothe hand, we ae going to evaluate the convenience of this new implementation though atios that could say that, definitely, this method is convenient to get a bette appeciation of the eal costs of an entepise. 3 Development of the poposed solution The wieless mesh netwoks (WMNs) has been developed ecently to povide bette sevices in communications. In WMNs, nodes ae compised of mesh outes and mesh clients. Each node opeates not only as a host but also as a oute, fowading packets on behalf of othe nodes that may not be within diect wieless tansmission ange of thei destinations. Thee ae a lot of advantages of this paticula netwok: Incease the possible distance between oigin and destiny, educe the netwok costs and the need of have moe access points to Intenet. The development of WMNs with antenna divesity and smat antenna techniques ae still in pogess. And the pefomance in any ad-hoc netwoks needs moe evaluation. In that way, this aticle bings a new step in this field of knowledge. 3.1 System Desciption The poposed physical model of the implementation of this type of communication in ABC systems is epesented at Fig.1. This figue show how the diffeent activities in a company, distibuted in also diffeent aeas could be. We wish that all the opeations of this activities be contolled and ecoded by an online data base that also must be possible of change in any minute, fom anywhee inside the oganization (obviously with a coespondent authoization). A WMN help in the each of the infomation fom distant activities. Fo example, constuction companies ae always in movement. In time, paticula activities ae finished and begins othes, and in eal big buildings constuctions, the necessity of have diect access to the cental of infomation becomes a pimodial facto. Fig.1: Physic achitectue design of the Wieless Mesh Netwok with MIMO Channels fo a company that uses ABC. In such cases, the distance between an activity and the close ae too fa that the fading inheent in the wieless communication and the obvious noise in the ai of a poductive pocess, difficult the fidelity of the eceived infomation. If an opeato sends to the data base a code of some specific mateial that was moved, and the infomation that eceives the cental is wong in a pai of bits, the code could be eceived with othe symbols and, to the manages, the activities that wee ealized would have been diffeent. In fact, ecuent faults could be fatal in the making decision pocess and in costs calculation. To solve this, the MIMO channels bing bette esults and make moe eliable infomation tansfes (in Fig.1 is epesented by the two antennas daw in evey node). In addition, with MIMO channels we can send infomation not only as codes o chaactes but also like photogaphy, videos o sounds. In the next subsections, we ae going to simulate this netwok with MIMO channels and study the
Poceedings of the 10th WSEAS Intenational Confenence on APPLIED MATHEMATICS, Dallas, Texas, USA, Novembe 1-3, 2006 264 implications in calculate best cost with best bit eo ates (BER). 3.2 Simulation To simulate the communication pocess between any two paticula nodes of the netwok that confom the defined activities of the cost system, and in paticula to simulate MIMO channels, necessaily, we have to use advanced mathematics techniques. The tansmission of the data in this kind of channels must have some basic steps showed in Figue 2, and explained afte. c) To MIMO channels is necessay to tansfom the binay message to anothe alphabet in a new constellation of points diffeent than 0`s and 1`s to do obligatoy opeations with complex numbes. This change of notation is called modulation and thee exists many methods to do this convesion. We ae going to use BPSK modulation. Then, the constellation of points is situated on the eal numbes axe of the constellation of possible points. To each divesity in MIMO technology we could use some techniques that help in the eduction of the effects of fading in the channel. In ou case, we used Space-Time Block Coding (STBC). In a 2-antenna system, the sending matix S is defined as: s1 S = (1) s1*,whee the columns epesent the antennas and the ows, the times of sending. As we ae using BPSK modulation that use only eal numbes, the paamete s1* that is the conjugate of the complex s1, is just itself. The eceived signal is a matix called R, and is epesented by: R = H*S + N (2) Fig.2: Schema of the simulated pocess of communication in MIMO channels with STBC. a) Afte taking the eal data (it could be by a cell phone, laptop/desktop PC, pocket PC, RFID, etc.), we have to do a binaization, that is to say, convet symbols like numbes o chaactes to bytes. In this pape we use eight bits pe byte. b) A codification method is necessay to divesify the tansmission and educe the pobability of damage bits. Actually, thee exist a lot of codification algoithms to codify data, like LDPC o all the diffeent types of convolutionals. In ou simulation, we use a vey simple convolutional algoithm that etuns the double of bits of the oiginal wod and that have 3 spaces in the memoy of the code. Figue 3 indicates how the convolutional algoithm is used and developed. Fig.3: achitectue of the convolutional method used.,whee H is the matix of fading coefficients and N is the noise matix. This noise was simulated dynamic, with an Additive White Gaussian Noise (AWGN), and fading was supposed constant in time and space, assuming a pefect estimation of the channel. d) Then, a sepaato phase is absolutely necessay. In this sub-pocess the two antennas eceive the two signals fom the diffeent antennas of the sende, and the systems must to identify which is fom what antenna. Afte the sepaato, fo a 2-antenna system, the signals eceived ae detemined by the following fomulas: xˆ 1 xˆ 2 = h = h 11 11 12 11 h 12 12 11 12 h (3) (4),whee h ij ae coefficients of the matix H and ij ae coefficients of the matix R. e) The eal numbes that came to the eceive antennas (message modulated but affected by fading and noise) must be ecognized again like binay factos. Thus, is necessay to implement a pocess
Poceedings of the 10th WSEAS Intenational Confenence on APPLIED MATHEMATICS, Dallas, Texas, USA, Novembe 1-3, 2006 265 called Detecto that said to which point epesent the eal numbe eceived. The logic of this pocedue is to obtain the Euclidean distance between the eceived numbe and the codes of the alphabet that we ae using (in this case BPSK). Then, we could ecognize the symbol though an aithmetical distance calculation. The Euclidean distance ae given by, ~ 2 2 2 2 2 x = xˆ s 1 (5 ( ) [( ) ] ) 1 1 1 11 12 s1 is compaed with s 1 =-1.0 and ~ 2 2 2 x = xˆ s 2 2 ( ) [( ) 1] (6) 1 1 2 11 12 is compaed with s 2 =1.0. The close point, ecognize the symbol as s i. Exactly the same poceeding is doing with ˆx 2. f) Fom this phase until the end, to ecupeate the oiginal message is necessay to do the complementay opeation of modulation, codification and debinaization. The Decodification was woked with the Vitebi algoithm with fou outputs pe iteation. This simulation was modelled in Java Language with a maximum of 100.000 tansmitted bits which is a sufficient numbe, consideing that we want to tansmit chaactes and not videos o photos. Next, we will show some esults elated with the efficiency of the communication and eo ates. 3.1 Results Discussion As we can see on Gaphic 1, fo this paticula simulation using STBC and a BPSK modulation, the bit eo ate (BER) is quite good, eaching levels of 10-5 with elative small signal-to-noise atios (SNR). Compaing this simulation with the tansmission of the same data by a 1-antenna system, we note that fo have 0 eos in the tansmission of data, we need appoximately 4 db less with this new implementation than the taditional communications systems. This is taduced in less need of potency and theefoe less use of esouces. The question now is how to use this ate to the calculation of the convenience of this supposed impovement of Activity-based Costing. O this question maybe might be how this ate is taduced in a bette calculation of costs. The BER is a measue of eo, and if we multiply this ate with a theoy eal cost calculated by delay infomation of the taditional computational systems of ABC (with independence of the value), it poduce cuves like in Gaphic 2 that show the monetay diffeence of the costs between the new system and the olde. Bit eo ate 1 0,1 0,01 0,001 0,0001 BPSK with STBC BPSK of 1-antenna 0,00001 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 SNR(dB) Gaphic 1: The BER pefomance of BPSK modulation and Space-Time Block Coding with a 2-antenna MIMO channel compaed with a 1-antenna system, and a data of 100.000 bits. Monetay Diffeence of Costs BPSK of 1-antenna BPSK with STBC -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 SNR Gaphic 2: Behaviou of the monetay diffeence between the calculated costs though taditional ABC methods and with these wieless new technologies. In this last gaphic we can see that fo smalle BER ates associated with bigge SNR, the diffeence becomes ceo in an asymptote. Thus, the system bings the same eliability of infomation but impove with eal time infomation. This excellent quality, as we said befoe, bings the oppotunity to have in anytime infomation of the activities and the development of thei nomal tasks, to take bette decisions and thus, impove the entie ole of the entepise in its envionment. Compaed with the taditional methods of send data, we also can see that the diffeences in cost calculating ae big too. The theoy cost calculation with wose ways of make communications is affected by this inefficiency of data tansmission and
Poceedings of the 10th WSEAS Intenational Confenence on APPLIED MATHEMATICS, Dallas, Texas, USA, Novembe 1-3, 2006 266 in long tem could be fatal fo a company. Fo the simulation of the multiple-antennas system, we see that with less db`s than the contende, the cost calculated with a theoetical one tuns moe eliable. With MIMO channels we need a smalle effot to obtain bette esults. 4 Conclusions In this aticle, we lean that the Activity-based costing using and implemented by wieless mesh netwoks with multiple-antennas channels could poduce bette management in companies of all kinds. We show the eliability that this system could bing and we saw it with a quantitative expeiment. This pape gives an expeimental eason to manages to implement this type of systems and to impove the entie behaviou of thei entepises. Fo one side we measued the gain in tems of the signal-to noise atio with this paticula channel, and we calculate than this impovement (compaed with 1-antenna channels) is in the ode of 4 db appoximately. Thus, we need less use of esouces. On the othe hand, we studied the behaviou of the monetay diffeences between eal costs and the costs affected by the bad tansmission of data, and we note that this diffeence could be fatal fo the taking decision pocess. Acknowledgements manufactuing, Jounal of Opeations Management, Vol. 10, No. 1, 1991, pp. 119-137. [6] Ian Akyildiz, Xudong Wang and Weiling Wang, Wieless mesh netwoks: a suvey, Elsevie Compute Netwoks, Vol. 47, 2005, pp. 445-487. [7] I. Chlamtac, M. Conti, J. Liu, Mobile ad hoc netwoking: impeatives and challenges, Ad Hoc Netwoks, Vol. 1, No. 1, 2003, pp. 13 64. [8] Mohinde Jankiaman, Space-Time codes and MIMO Systems, Atech House Inc., 2004. [9] V. Taokh, H. Jafakhani and A. Caldebank, Space-Time Block Coding fo Wieless: Pefomance Results, IEEE J. Select. Aeas Commun, Vol. 17, No. 3, 1999, pp. 451-460. [10]V. Taokh, H. Jafakhani and A. Caldebank, Space-Time Block Codes fom othogonal designs, IEEE Tans. Infom. Theoy, Vol. 45, No. 5, 1999, pp. 1456-1467. [11]A. Paulaj, R. Naba and D. Goe, Intoduction to Space-Time Wieless Communications, UK: Cambidge Univesity Pess, 2003. [12] S. Alamounti, A Simple Tansmit Divesity Technique fo Wieless Communications, IEEE Jounal Select. Aeas Commun, Vol. 16, No. 8, 1998, pp. 1451-1458. [13]E. Teleta, Capacity of Multi-Antenna Gaussian Channels, Euopean Tansactions on Telecommunications, Vol. 10, No. 6, 1999, pp. 585-595. The authos would like to thank PBCT/CONICYT ACT11/04 -Chile, fo thei financial suppot. Refeences: [1] Robet Kaplan and Robin Coope, Cost and Effect, Havad Business School Pess Boston, 1998. [2] Chales Hongen, Cost Accounting, Pentice Hall, 2005. [3] C. Ittne, D.F. Lacke and T. Randall, The activity-based cost hieachy, poduction policies and fim pofictability, Jounal of Management Accounting Reseach, Vol.9, 1997, pp. 143-162. [4] Mina Pizzini, The elation between cost-systems design, manages` evaluation of the elevance and usefulness of cost data, and financial pefomance: an empiical study of US hospitals, Elsevie Accounting, oganizations and society, Vol. 31, 2006, pp. 179-0. [5] Data, S. M., S. Keke, T. Mukhopadhyay & E. Svaan, Oveloaded ovehead: Activity-based cost analysis of mateial handling in cell