Management cience and Engineering Vol. 5, No. 3,, pp. -54 DOI:.36/j.me.335X53.z44 IN 3-34[Print] IN 3-35X[Online] www.ccanada.net www.ccanada.org Logitic ervice Level Improvement Reearch and Demontration Baed on Queuing Theor ONG Zhilan,* ; LIU Yuei ; LI Kexian chool of Buine, Yunnan Univerit of Finance and Economic, Kunming, 5, China * Correponding author. Aociate profeor, mainl engaged logitic management and engineering. Addre: chool of Buine, Yunnan Univerit of Finance and Economic, Kunming, 5, China Email: keczhl@vip.ina.com Received June ; accepted 7 Jul Abtract The paper analze the problem of reducing Logitic ervice level caued b long waiting time in warehoue baed on queuing theor and combined with cae. Then propoe three olution: changing wa of queuing, M/ M/ model to optimize ervice peed, M/M/n model to optimize torage channel. The paper alo put forward ome meaure and uggetion to make up the hortage of lacking experience. Ke word: Warehouing operation; Queuing theor; ervice level ONG Zhilan, LIU Yuei, & LI Kexian (). Logitic ervice Level Improvement Reearch and Demontration Baed on Queuing Theor. Management cience and Engineering, 5(3), -54. Available from: URL: http://www.ccanada.net/index.php/me/article/view/j. me.335x53.z44 DOI: http://dx.doi.org/.36/ j.me.335x53.z44 INTRODUCTION It i common to queue in production operation, uch a in warehoue, ditribution center and other logitic area. Epeciall, with the development of logitic outourcing and building of logitic center, cargoe catter into logitic warehoue rapidl. And with expanding buine volume, the phenomenon of queuing too long in entering and out of warehoue, of long time to wait and of cutomer loing ha been appeared. No matter which phenomenon happen, it will damage the image of logitic ervice provider and lead to a decline in compan benefit ultimatel. o, whether or not providing fat ervice ha become one of important competitive advantage of logitic ervice provider. In thi paper, the meaning of tuding the problem of queuing in logitic center baed on the theor of queuing are following: () It help to coordinate contradiction between logitic ervice cot and cutomer waiting cot o that it can improve the level of deigning of ervice tem and achieve a reaonable allocation. It i related to: The allocation of equipment and peronnel. Conidering the factor of wa to reach cutomer, ervice, equipment and peronnel ervice, it i wie to increae the number of equipment and peron to improve ervice level, reduce queuing time and attract more cutomer; Principle of priorit of queuing. Arrange proper wa for cutomer to queue in variou ituation. And adopt principle of jutice to improve cutomer atifaction. () From the point of view of cutomer, olving the problem of queuing i effective for bettering cutomer ervice and aving cot. It can both uppl better ervice in a low cot and increae cutomer loalt to enhance competitivene in the market.. THEORY ANALYI Queuing theor i alo called theor of tochatic ervice tem, which i etablihed b Danih Engineer Erlang (A.K.Erlang) in when he wa tuding telephone tem. Nowada, the theor ha been uing in varietie area, uch a production indutr and o on.. The Problem Queuing Theor Reearch () Performance problem. It tudie probabilit law of variou queuing tem. The main problem to tud are Copright Canadian Reearch & Development Center of cience and Culture
Logitic ervice Level Improvement Reearch and Demontration Baed on Queuing Theor the ditribution of cutomer, cutomer waiting time and arrival ditribution method, which include two cae, random and fixed. () Improvement problem. Ue queuing theor to deign logitic ervice tem and better operation efficienc. (3) Model of queuing tem. It i a tem to determine whether the model meet tem or not.. The Compoition of Queuing tem A general queuing tem i compoed of cutomer ource, waiting before ervice, accepting ervice and leaving after ervice, et..3 The Contraint of Queuing Theor and Aumption () Contraint Logitic ervice provider mut undertand the contraint of queuing theor to anali ervice demand and manage queuing problem. The contraint are: In normal circumtance, cutomer ditribution of arrival method and arrival time are uneven. In order to reearch convenientl, the paper aume that the arrival rate of cutomer i balance. Each channel ervice rate in per hour i not the ame, which i a the reult of different equipment performance and peronnel operation. But the paper argue that the ervice level of each channel i the ame. 3Different patient level and opinion make different reult. omeone ma leave at once when he know it take a long time to wait, and the other ma wait. In thi paper, it aume that all cutomer would like to wait for a long time. () Hpothei Through author' urve in a compan, put forward hpothei of torage operation. Following are hpothei: Cutomer reource in torage operation i unlimited, and each cutomer arrive independent, which obe to Poion ditribution. Cutomer ha no pecial preference to torage channel. Each channel provide ame ervice. 3The operation complie with the principle of firt come firt erve, while no cutomer leave. It i conidered that the wa of queuing i a ingle tem. 4The ervice efficienc of each channel i random which obe Exponential ditribution and there i no difference between each channel ervice. 5Take torage proce a a whole, then the efficienc of it can be bettered b deigning more channel..4 Model of Queuing Etablih queuing model baed on characteritic of queuing tem compoition. Generall peaking, there have five model, M/M/, M/M/n, M/D/, M/M//m/ and M/M/n/m/. In practice, model, M/M/ and M/M/n are commonl ued. In thi paper, mainl appl thee two model..4. Character of Model Character of model M/M/: It i a ingle-channel but ingle phae. The manner cutomer reach obe to Poion ditribution while ervice time obe to negative exponential ditribution. Character of model M/M/n: It i a multi-channel but ingle-tage. The manner cutomer reach obe to Poion ditribution while ervice time obe to negative exponential ditribution. There i no limitation to the number of cutomer. If all channel are bu, cutomer will wait in a queue. Meanwhile, cutomer have no pecial preference to each ervice channel..4. Formula of M/M/ and M/M/n to olve () Formula of M/M/ The model can be ued to earch olution to a inglechannel but ingle-tage ervice tem. The indexe include ervice intenit, idle probabilit of ervice tem, average number of cutomer waiting time for ervice, average number of cutomer, average waiting time per cutomer took and average time of ta. Follow are pecific formula. ervice intenit p u P - ervice intenit; - The peed of arrival in per unit time; u - The average ervice rate of each dek. Idle probabilit of ervice tem P P () P - Probabilit of no cutomer in line. 3Average number of cutomer waiting for ervice Lq u u ( ) L q - Average number of cutomer waiting for ervice. 4Average number of cutomer L ( u ) L - The average number of waiting cutomer ervice in tem, which not onl include the cutomer waiting in line, but alo include erving cutomer. 5Average waiting time per cutomer took Wq W u W q - The average waiting time for per cutomer. 6Average time of ta W u W - The average time of ta of client. () (3) (4) (5) (6) Copright Canadian Reearch & Development Center of cience and Culture 5
ONG Zhilan; LIU Yuei; LI Kexian (). Management cience and Engineering, 5(3), -54 () Formula of M/M/n The model can be ued to earch olution to a ingletage but multi-channel ervice tem. The indexe include ervice trength, idle probabilit of ervice tem, average number of cutomer waiting for ervice, average number of cutomer, average waiting time per cutomer took and average time of ta. Follow are pecific formula. ervice intenit p un P - tem ervice intenit; - The peed of arrival in per unit time; u - The average ervice rate of each dek. n - Quantit of channel. Idle probabilit of ervice tem k n n po + k u k! u n!( ) un P - The probabilit of no cutomer in a ingle-tage but multi-channel ervice tem. 3Average number of cutomer waiting for ervice n po Lq u u ( n )!( nu ) L q - Average number of cutomer for ervice; 4Average number of cutomer L () Lq + u L - The average number of waiting cutomer ervice in tem not onl include the cutomer waiting in line, but alo include erving cutomer. 5Average waiting time per cutomer took Lq W () q W q - The average waiting time per cutomer. 6Average time of ta L W () W -The average time of ta of client..4.3 Optimization of Model It i impoible to eliminate queue in realit, becaue the ervice level and ervice cot are between the game. If we want to eliminate queue, we need to ue a large number of ervice peronnel and equipment that would increae the cot of ervice. However, if the efficienc of ervice equipment and ervice taff cannot meet requirement of cutomer, it will produce queue, too. Therefore, it i wie to ue queuing theor to determine (7) () () a reaonable level of ervice to minimize the total cot. ervice cot i an increaing function of level of ervice, while the function of waiting for ervice level cot i decreaing. The pecific function are hown in Figure. Figure The Relationhip Between Cot and ervice Level Time become more important for cutomer. Figure how that the cutomer waiting cot increae from to in realit. If improve ervice level or redeign the tem, the waiting time will horten and ervice cot will decreae from to. In order to reach the bet level of ervice, it i available to optimize the ervice tem from the following two apect. () Optimization of ervice peed for M/M/ model M/M/ model can improve the peed of equipment and peronnel to olve the problem of waiting too long in queuing. When we ue M/M/ model to optimize the peed of ervice, we need to know ervice cot for per unit time of each channel and each waiting cot when i one. It i mart to ue total cot to optimize ervice tem. The formula of total cot i: ( ) + ( ) f u C u L u (3) f(u) - Total cot in per unit time; C -ervice cot of each ervice channel in per unit of time when u i equal to one; - Each cutomer waiting cot in the per unit time; L (u) - The average number of cutomer in ervice tem. The formula (4) i: L u ( ) o the function of total cot in per unit time f(u) i: ( ) f u C u + u ( ) To find the minimum, uppoe that derivation ma: df ( u) du (). The 5 Copright Canadian Reearch & Development Center of cience and Culture
Logitic ervice Level Improvement Reearch and Demontration Baed on Queuing Theor df ( u) C du ( u ) u * After implified, it become: + C d f u ( ) (5) A 3, and when u >, it i poible to du ( u ) optimize the formula, > 3. ( u ) According to anali, when the level of ervice i proper, the total tem cot i lowet. () Optimization of ervice channel for M/M/n model It i poible to change the quantit of channel to better the ervice level and decreae waiting time. When ue M/M/n model to optimize the ervice channel, it need to know the ervice cot of each tem in per unit time, waiting cot of each cutomer and average number of cutomer. Then appl M/M/n model to calculate the total cot. The formula i: F(n) Cn + L (n) (6) F(n) - Total cot in per unit time; C - ervice cot in per unit time of each ervice tem; - Each cutomer waiting cot in the per unit time; L (n) - The average number of cutomer. Then ue the marginal anali method to minimize the total cot of ervice tem. F(n) F(n ) F(n) F(n +) (7) Union formula (6) and (7) Cn + L (n) C(n ) + L (n ) Cn + L (n) C(n +) + L (n +) () Be implified: Table tatitical of the Number of Cutomer to Reach in March and April L n L C n L n L n ( ) ( + ) ( ) ( ) () Finall, it i ea to get the number of channel, n(n,, 3 ) baed on knowing the difference between L (n) and C L (n +) a well a the arrangement. On theor, it can horten cutomer waiting time b determining the bet ervice level and the quantit of channel. However, the method of queuing mut be change in practice.. EXAMPLE OF WAREHOUE TORAGE Thi tud et a coffee compan a an example. torage ha a greater impact on the compan.. The tatu of Warehoue torage Operation () Proce of torage The proce include carring, inpection, procedure for torage and inventor. ()ituation of cutomer or good arrival Time to harvet coffee i generall form December to June, but the heav time of entering torage i in March and April. The compan ha three accee and operation of inventor are provided from a.m to a.m o that cutomer alwa arrive at the ame time. Table how collected data. Data Quantit Data Quantit Data Quantit Data Quantit Data Quantit Week 3-3- 3-3 3-4 3-5 3-6 3-7 3-3- 3-3- 3-3-3 3- ubtotal Total 6 4 5 3 3-5 3-6 3-7 3-3- 3-3- 3-3-3 3-4 3-5 3-6 3-7 3-4 3 3-3-3 3-3 4-4- 4-3 4-4 4-5 4-6 4-7 4-4- 4-4- 5 5 4 4-4-3 4-4-5 4-6 4-7 4-4- 4-4- 4-4-3 4-4 4-5 43 3 5 3 5 4-6 4-7 4-4- 4-3 7 6 43 Mon. Tue. Wed. Thur. Fri. at. un. Mon. Tue. Wed. Thur. Fri. at. un. It i ea to oberve that the number of cutomer i oppoite completel in aturda and unda. In order to tud the quetion eail, we do not conider the above ituation. Uing formula () can calculate the average number of cutomer arrival. a A / B () a - The average number of cutomer arrival in one hour; Copright Canadian Reearch & Development Center of cience and Culture 5
ONG Zhilan; LIU Yuei; LI Kexian (). Management cience and Engineering, 5(3), -54 A - The number of all cutomer (not including weekend); B - The total time of ervice. a (43-)/(45 3)3 (3)ervice rate of entering torage channel Mot of operation of entering torage are manual, whoe operation efficienc i low. Table tatitic of ervice Time of Entering torage in March and April No. Time No. Time No. Time No. Time (min.) (min.) (min.) (min.) 5 3 3 35 3 3 44 3 5 3 4 3 4 3 4 33 46 4 55 36 4 5 34 4 5 35 5 5 5 3 35 4 6 46 6 6 36 5 7 6 7 4 7 54 37 3 45 35 5 3 4 4 5 6 3 4 54 5 3 6 4 3 ubtotal 463 ubtotal 47 ubtotal 474 ubtotal 43 Total 45 Baed on the data, ue formula () can calculate the average number of client of each channel. b A / B () b - The number of erviced cutomer in per hour; A - One hour; B - The average time of each cutomer to be provided. b6/ (45/4).3. The olution to horten Entering torage Waiting Time For thee problem, take ue of queuing theor to improve torage ervice. According to the actual anali of collected data, cutomer reache in ever 3 hour but there are onl three channel in warehoue. If aume that cutomer ta in three channel and do not be allowed to change queue, the arrival peed of cutomer for each channel i one in per hour, and the average rate of channel ervice i.3 in per hour. o we can get following concluion: ervice cot of each channel i ; ervice cot of each cutomer in per hour i 53.5 and waiting cot in per hour i 4. To horten the queuing time of torage, following data are ued. C / h; 4 / h; C 53.5 /h; 3. In three M/M/ queuing model, and u.3. () Better wa of queuing The compan ha three M/M/ queuing model currentl which can be changed into one. M/M/3 queuing model i formed b 3 channel and do not be allowed to change team. If the rate of cutomer arrival i one in per hour, it need three M/M/ channel. But in M/ M/3 queuing model, there onl need one queue, which ha three ervice window. Calculate olution to the correponding index baed on model M/M/ and model M/ M / n. The reult are hown in Table 3. Table 3 Comparion Between M/M/3 Model and M/M/ in Queuing Wa Indexe M/M/3 model Three M/M/ model Rate of idle P.67.3(for one tem) Average number of cutomer waiting for ervice L q..56 3 The average number of waiting cutomer L 4. 3.33 3 Average time to ta W 5.6 minute. minute Average time to wait W q 3.76 minute 53.6 minute According to Table 3, when three M/M/ queuing model are changed into M/M/3 queuing model, ever parameter reduce b everal time which introduce that model M/M/3 can horten the queuing time a well a improve ervice level. ()Improve peed of ervice Without enlarging the torage channel, it i poible to improve ervice peed b increaing the peed of equipment and taff. Through the optimization formula (5) we can calculate the optimal ervice rate u *. * 4 u + +.6 C 53.5 ervice peed before and after are compared in Table 4. Table 4 ervice peed Before and After Indexe u.3 u.6 Rate of idle P.3(for one tem).6(for on tem) Average number of cutomer waiting for ervice L q.56 3.4 3 The average number of waiting cutomer L 3.33 3.6 3 Average time to ta W. minute 37. minute Average time to wait W q 53.6 minute.4minute (3) Optimize torage channel On perpective of cot, it i bet deign to make the total of cutomer waiting cot and torage ervice minimum. Calculate olution to n b formula (6), (7), () of M / M / n model: L( n) L( n+ ) C L( n ) L( n) 3 p <, namel p <. o the olution i n >.3. nu.3n We can alo calculate the correponding value of n combining with M/M/n model relevant formula and the 53 Copright Canadian Reearch & Development Center of cience and Culture
Logitic ervice Level Improvement Reearch and Demontration Baed on Queuing Theor reult are hown in Table 5. Table 5 Value to n n L(n) L(n)-L(n+) L(n-)-L(n) F(n) 3 4..75. 4.53.64.75 5. 5.34.35.64 3. 6.3.35 5.6 C According to the formula, L ( 4) L (5) L (3) L (4), we can calculate the quantit of channel. The ervice indexe of 4 channel are indicated in table 6. Table 6 ervice Indexe of 4 Channel Indexe Four channel Rate of idle P.5 Average number of cutomer waiting for ervice L q.3 The average number of waiting cutomer L.53 Average time to ta W 5.4 minute Average time to wait W q 4. minute.3 Anali and Comparion of Three olution.3. Comparion of ervice Level The indexe of ervice level of three different optimization olution are indicated in Table 7. Table7 Indexe of ervice Level of Three Different Optimization olution Indexe Four channel peed better M/M/3 medol Rate of idle P.5.6(for one tem).67 Average number of cutomer waiting for ervice L q.3.4 3. The average number of waiting cutomer L.53.6 3 4. Average time to ta W 5.4 minute 37. minute 3 5.6minute Average time to wait W q 4. minute.4 minute 3 3.76minute After comparing three optimization olution in Table 7, it i bet olution to et 4 channel to improve ervice peed. 3.3. Comparion of Total Cot The total cot of torage of current ingle-channel in per unit time F(n) Cn + L (n) + 4 3.33 53 The total cot of three channel i 456. ()The total cot of improving ervice peed of a ingle M/M/ model in per unit time f(u) C u + L (u) 53.5.6 + 4.6 64.55 The total cot of three channel i.65. (3) The total cot of changed M/M/3 and M/M/4 model in per unit time F(n) Cn + L (n) F(3) 3 + 4 4.. F(4) 4 + 4.53 5. Through anali and comparion, it can be een that etting four torage channel i the bet olution. CONCLUION With the rapid increaing in logitic ervice, cutomer have higher demand of time. o whether can provide fat ervice or not become a competitive advantage. Waiting too long will make cutomer diatified. The paper ue queuing theor to tud the cheduling problem of warehoue to find the mot proper quantit of entering torage channel that can improve ervice efficienc. At the ame time, the paper introduce queuing model o addre the problem of torage operation b collected data in urve. The quantitative approach make up the weakne of judging b experience and put forward ome meaure and uggetion. REFERENCE [] JIN Fang, FANG Kai, & Wang Jinglin (4). AGV Dipatching Baed on Queuing Theor tudie. cience Intrument,. [] ZHAO Yuan, & DING Wening (). Determine a Reaonable Amount of Crane Baed on Queuing Theor. Logitic Technolog,. [3] HEN Jian, & WANG Dong (). Anale for RFID Garment Manufacturing on Queuing Theor. Computer Information, 5. [4] FENG Lingge, & WANG Hao (6). Operation Management. Pre of Capital Economic Univerit, 5. [5] HU Liege. (7). Operation Reearch of Logitic. Beijing: Pre of China Tranportation. Copright Canadian Reearch & Development Center of cience and Culture 54