TWI769928B - System reliability evaluation method for food online delivery system - Google Patents
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Abstract
Description
本發明涉及運算科技之領域,特別是一種針對餐飲線上配送系統之系統可靠度評估方法。 The invention relates to the field of computing technology, in particular to a system reliability evaluation method for an online catering distribution system.
隨著網際網路技術的發展、智慧型手機電話的普及、人們的忙碌、以及生活方式的變化,使得線上餐飲配送(online food delivery,OFD)的市場蓬勃發展。在食品和飲料(Food & Beverage)行業中服務質量是獲得競爭優勢的重要因素。線上食物配送(OFD)是一個致力於協助客戶提供送餐服務的行業,並且近年來隨著行業的持續蓬勃發展行業,其服務品質也吸引了眾多消費者的關注。 With the development of Internet technology, popularization of smart phones, busy people, and changes in lifestyle, the online food delivery (OFD) market is booming. Service quality is an important factor in gaining a competitive advantage in the Food & Beverage industry. Online Food Delivery (OFD) is an industry dedicated to assisting customers in providing food delivery services. In recent years, as the industry continues to flourish, its service quality has also attracted the attention of many consumers.
線上食品配送系統與一般物流(logistics)的不同之處在於其即時性(instant)和多樣性(diversity)。即時性意味著線上餐飲配送系統的商品是實時(real-time)生成的。送貨服務必須在客戶製作商品後立即開始。多樣性的特點來自於物品的多樣性。亦即,它通常運輸不同種類的物品,而不是像一般物流那樣運輸相似的物品。 The difference between online food delivery system and general logistics is its instant and diversity. Immediacy means that the items of the online food delivery system are generated in real-time. The delivery service must start as soon as the customer makes the item. The characteristic of diversity comes from the diversity of objects. That is, it typically transports different kinds of items, rather than similar items as in general logistics.
由於送餐人員可以透過線上送餐系統選擇工作地點,因此每個送餐區域的可用送餐人員數量是隨機的。為了在涉及隨機性時評估系統的效能,許多研究人員使用網路分析方法將不同的系統轉化為網路拓撲,包括電力網路、製造網路、運輸網路以及電腦網路。文獻將傳輸邊(arcs)或節點(nodes)上的容量定義為隨機的,並將這種具有隨機容量的網路稱為多階狀態網路(multi-state network)。 Since food delivery personnel can choose their work location through the online food delivery system, the number of available food delivery personnel in each food delivery area is random. To evaluate the performance of systems when randomness is involved, many researchers use network analysis methods to transform different systems into network topologies, including power networks, manufacturing networks, transportation networks, and computer networks. The literature defines the capacity on transmission edges (arcs) or nodes (nodes) as random, and calls such a network with random capacity a multi-state network.
針對上述多階狀態網路(multi-state network)的系統效能評估,現有文獻方面著重於建構最佳化數學模型,於配送時間限制下以最小化成本為目標式,找出針對不同需求之最佳配送方案,或是分析服務指標與顧客接受服務之滿意度的關係,從而確定各因素影響顧客認知之服務品質程度,或利用量化方法建構配送服務質量表作為評估服務水準之依據,將其納入管理考量以控制影響較大之因子。抑或是針對綜合運輸物流系統達成配送需求之機率,探討時間閾值限制下運輸物流系統之系統效能指標。 For the system performance evaluation of the above-mentioned multi-state network, the existing literature focuses on the construction of an optimized mathematical model, which aims to minimize the cost under the constraints of the delivery time, and find the best solution for different needs. The best distribution plan, or analyze the relationship between service indicators and customer satisfaction with the service received, so as to determine the degree of service quality that each factor affects customer perception, or use quantitative methods to construct a distribution service quality table as a basis for evaluating service levels, and include it in Management considerations to control for the more influential factors. Or for the probability of fulfilling the distribution demand of the integrated transportation and logistics system, the system performance index of the transportation and logistics system under the time threshold limit is discussed.
然而,上述文獻僅考量事後顧客對配送系統的服務評估,並將其作為管理者管理之量化指標,並未有機率變動的因素考量其中。 However, the above literature only considers the customer's service evaluation of the distribution system after the fact, and regards it as a quantitative index of management management, and does not consider the factors that may change.
儘管線上餐飲配送系統是新興的運輸系統之一,並已被證明可以為人們的生活帶來便利,但與線上餐飲配送系統相關的文獻或是專利還是相當罕見的,特別是如何量化系統的負載相關的研究。 Although the online food delivery system is one of the emerging transportation systems and has been proven to bring convenience to people's lives, the literature or patents related to the online food delivery system are quite rare, especially how to quantify the load of the system related research.
綜上所述,有鑑於與線上餐飲配送系統相關的現有文獻以及相關專利並未考慮機率變動因素,本發明則將實務狀況中每個區域之每一單位時間不同配送人員數量的機率特性納入考量,根據歷史資料評估餐飲線上配送系統中各區域配送人員狀態的機率分佈,依此計算隨時間變化之系統可靠度,可提供管理者作為一管理系統之績效指標。 To sum up, in view of the fact that the existing literature and related patents related to the online catering distribution system do not consider the probabilistic factor, the present invention takes into account the probabilistic characteristics of the different number of delivery personnel per unit time in each area in practical situations. , according to the historical data to evaluate the probability distribution of the distribution personnel status in each region in the catering online distribution system, and then calculate the system reliability over time, which can provide managers as a performance indicator of the management system.
本發明定義系統可靠度為給定之空間和時間閾值下,該系統中配送人員分佈可成功配送所有訂單的機率。相對其他文獻或專利而言,本發明所提出之餐飲線上配送系統之系統可靠度評估方法可看出即時的餐飲線上配送系統狀態,該指標亦可提供給相關之配送企業以瞭解該系統配送人員分佈是否滿足訂單之依據,以進行配送人員的指派或管理。 The invention defines the system reliability as the probability that the distribution personnel in the system can successfully deliver all orders under a given space and time threshold. Compared with other documents or patents, the system reliability evaluation method of the online catering distribution system proposed by the present invention can see the real-time online catering distribution system status, and this indicator can also be provided to the relevant distribution companies to understand the system distribution personnel. Whether the distribution satisfies the order basis for the assignment or management of delivery personnel.
根據上述說明,本發明提出能夠解決現有技術存在的缺失,提出 一種餐飲線上配送系統之系統可靠度評估方法,該方法包含下列步驟:利用網路分析方法構建網路模型並輸入時間閥值、外送人員空間限制、餐廳等待時間、各路線配送時間等參數;計算滿足該空間限制之最低該外送人員的數量;利用分支界限法求出滿足該空間限制之訂單配送組合;計算各配送狀況的消耗時間,去除超過該時間閥值之訂單狀況;將該訂單狀況轉換為最小下界向量;以及計算該系統的可靠度。 According to the above description, the present invention proposes to solve the deficiencies existing in the prior art, and proposes A system reliability evaluation method for an online catering distribution system, the method comprising the following steps: constructing a network model by using a network analysis method and inputting parameters such as time threshold, space limitation of delivery personnel, restaurant waiting time, and delivery time of each route; Calculate the minimum number of the delivery personnel that meets the space limit; use the branch-and-bound method to find the order delivery combination that meets the space limit; The conditions are converted into a least lower bound vector; and the reliability of the system is calculated.
以一實施例而言,上述網路模型係考慮上述外送人員之隨機性將該餐飲線上配送系統轉換為一個網路拓樸。 In one embodiment, the above-mentioned network model converts the catering online distribution system into a network topology considering the randomness of the above-mentioned delivery personnel.
以一實施例而言,上述網路拓樸包含複數個節點、連結該複數個節點的複數個傳輸邊、商品、該商品的空間權重、該商品的等待時間、以及傳輸該商品的行駛時間。 In one embodiment, the network topology includes a plurality of nodes, a plurality of transmission edges connecting the plurality of nodes, a commodity, a spatial weight of the commodity, a waiting time of the commodity, and a travel time to transmit the commodity.
以一實施例而言,上述複數個節點中每個節點的容量為一個隨機變量,其機率是基於一給定的機率分布。 In one embodiment, the capacity of each node in the plurality of nodes is a random variable, and the probability thereof is based on a given probability distribution.
以一實施例而言,上述利用分支界限法求出滿足該空間限制之訂單配送組合係根據該訂單中商品的權重由大到小將商品排列然後以該分支界限法分配該訂單中商品的配送,利用上述分支界限法分配該訂單中商品的配送之後,得到關於商品分配的第一級解。 In one embodiment, the above-mentioned use of the branch-and-bound method to find the order delivery combination that satisfies the space limitation is to arrange the commodities in the order according to the weight of the commodities in descending order, and then use the branch-and-bound method to allocate the delivery of the commodities in the order, After allocating the delivery of the commodities in the order using the above branch and bound method, a first-level solution for commodity allocation is obtained.
以一實施例而言,其中每個該商品分配的第一級解透過置換得到關於該商品分配不同的第二級解。 In one embodiment, each of the first-level solutions for the commodity allocation obtains different second-level solutions for the commodity allocation through permutation.
以一實施例而言,上述計算該系統的可靠度是利用不相交乘積遞歸和(RSDP)算法來評估。 In one embodiment, the reliability of the system is evaluated using a recursive sum of disjoint products (RSDP) algorithm.
以本發明的另一觀點而言,本發明提出一種餐飲線上配送系統之系統可靠度評估方法,該方法包含下列步驟:構建網路模型並輸入時間閥值、 外送人員空間限制、餐廳等待時間、各路線配送時間等參數;計算滿足該空間限制之最低該外送人員的數量;利用分支界限法求出滿足該空間限制之訂單配送組合,根據該訂單中商品的權重由大到小將商品排列然後以該分支界限法分配該訂單中商品的配送,利用上述分支界限法分配該訂單中商品的配送之後,得到關於商品分配的第一級解;利用該商品分配的第一級解經由互換(permutation)產生關於該商品分配的第二級解;計算上述該商品分配的第二級解的運輸時間,並且刪除不可行的該第二級解;利用上述關於該商品分配的第二級解獲得容量向量;計算該系統的可靠度。 From another aspect of the present invention, the present invention proposes a system reliability evaluation method for an online catering distribution system, the method comprising the following steps: constructing a network model and inputting a time threshold, Parameters such as space limitation of delivery personnel, restaurant waiting time, delivery time of each route, etc.; calculate the minimum number of delivery personnel that meet the space limitation; use the branch-and-bound method to find the order delivery combination that meets the space limitation. The weights of the commodities are arranged from large to small, and then the distribution of the commodities in the order is allocated by the branch and bound method. After the distribution of the commodities in the order is allocated by the above branch and bound method, the first-level solution about commodity allocation is obtained; using the commodity The first-level solution of the distribution generates a second-level solution for the distribution of the commodity through permutation; calculate the transportation time of the second-level solution for the distribution of the commodity above, and delete the second-level solution that is not feasible; use the above-mentioned about The second-level solution of the commodity allocation obtains the capacity vector; the reliability of the system is calculated.
以一實施例而言,上述網路模型係考慮上述外送人員之隨機性將該餐飲線上配送系統轉換為一個網路拓樸。 In one embodiment, the above-mentioned network model converts the catering online distribution system into a network topology considering the randomness of the above-mentioned delivery personnel.
以一實施例而言,上述網路拓樸包含複數個節點、連結該複數個節點的複數個傳輸邊、商品、該商品的空間權重、該商品的等待時間、以及傳輸該商品的行駛時間。 In one embodiment, the network topology includes a plurality of nodes, a plurality of transmission edges connecting the plurality of nodes, a commodity, a spatial weight of the commodity, a waiting time of the commodity, and a travel time to transmit the commodity.
以一實施例而言,其中計算上述該商品分配的第二級解的運輸時間,並且刪除不可行的該第二級解更包含以下步驟:創建兩集合分別儲存可實行和不可實行的該商品分配;列出該第二級解中的每個配送(courier)並計算運輸時間;以及列出所有可實行的該第二級解。 In one embodiment, calculating the transportation time of the second-level solution of the commodity distribution, and deleting the infeasible second-level solution further includes the following steps: creating two sets to store the feasible and infeasible commodities respectively Allocate; list each courier in the second level solution and calculate the transit time; and list all feasible second level solutions.
以一實施例而言,上述計算該系統的可靠度是利用不相交乘積遞歸和(RSDP)算法來評估。 In one embodiment, the reliability of the system is evaluated using a recursive sum of disjoint products (RSDP) algorithm.
100:多階狀態網路 100: Multi-Order State Networks
201、203、205、207、209、211:步驟 201, 203, 205, 207, 209, 211: Steps
300:預測系統可靠度之裝置 300: Devices for predicting system reliability
301:輸入裝置 301: Input device
303:記憶體 303: memory
305:處理器 305: Processor
307:輸出裝置 307: Output device
3031:演算法 3031: Algorithms
3032:SODS網路拓樸 3032: SODS network topology
圖1顯示根據本發明的一個實施例所提出食品外送平台之多階狀態網路示意圖。 FIG. 1 shows a schematic diagram of a multi-level state network of the proposed food delivery platform according to an embodiment of the present invention.
圖2顯示根據本發明的一個實施例所提計算餐飲線上配送系統之系統可靠度評估方法的流程圖。 FIG. 2 shows a flowchart of a method for calculating the system reliability of an online catering distribution system according to an embodiment of the present invention.
圖3顯示根據本發明的一個實施例所提出之用於預測預測系統可靠度之裝置的示意圖。 FIG. 3 shows a schematic diagram of an apparatus for predicting the reliability of a prediction system according to an embodiment of the present invention.
此處本發明將針對發明具體實施例及其觀點加以詳細描述,此類描述為解釋本發明之結構或步驟流程,其係供以說明之用而非用以限制本發明之申請專利範圍。因此,除說明書中之具體實施例與較佳實施例外,本發明亦可廣泛施行於其他不同的實施例中。以下藉由特定的具體實施例說明本發明之實施方式,熟悉此技術之人士可藉由本說明書所揭示之內容輕易地瞭解本發明之功效性與其優點。且本發明亦可藉由其他具體實施例加以運用及實施,本說明書所闡述之各項細節亦可基於不同需求而應用,且在不悖離本發明之精神下進行各種不同的修飾或變更。 Herein, the present invention will be described in detail with respect to specific embodiments of the present invention and its viewpoints. Such descriptions are used to explain the structures or steps of the present invention, and are for illustrative purposes rather than limiting the scope of the present invention. Therefore, in addition to the specific embodiments and preferred embodiments in the specification, the present invention can also be widely implemented in other different embodiments. The embodiments of the present invention are described below by specific embodiments, and those skilled in the art can easily understand the efficacy and advantages of the present invention through the contents disclosed in this specification. Moreover, the present invention can also be applied and implemented by other specific embodiments, and various details described in this specification can also be applied based on different requirements, and various modifications or changes can be made without departing from the spirit of the present invention.
本發明領域為與「運算科技」相關的領域,首先建模一多階餐飲線上配送網路,並提出一包含時間閾值和空間限制之新演算法,針對多階餐飲線上配送網路計算其系統可靠度。系統可靠度(system reliability)為評估該網路效能之重要指標,其定義為系統中配送人員數量可滿足訂單之機率。 The field of the present invention is related to the field of "computing technology". First, a multi-level catering online distribution network is modeled, and a new algorithm including time thresholds and space constraints is proposed to calculate the system for the multi-level catering online distribution network. reliability. System reliability is an important indicator for evaluating the performance of the network, which is defined as the probability that the number of delivery personnel in the system can satisfy the order.
由於餐飲線上配送系統之配送人員可自行選擇工作地點和時間,故多階餐飲線上配送網路需考量系統內配送人員之隨機特性,使得每個區域的配送人員數量呈現多階狀態(multi-state),因此該系統可建構成一多階狀態網路(multi-state network)。 Since the delivery personnel of the catering online distribution system can choose their own work location and time, the multi-level catering online distribution network needs to consider the random characteristics of the delivery personnel in the system, so that the number of delivery personnel in each area presents a multi-state state (multi-state). ), so the system can be constructed as a multi-state network.
本發明利用網路分析模型將上述考慮配送人員之隨機特性之多揭狀態網路,亦即隨機餐飲線上配送系統(stochastic online-food delivery system,SODS)轉換為一個網路拓樸(network topology)。然後提出一演算法,用以評估SODS系統可靠度。 The present invention uses a network analysis model to convert the above-mentioned multi-state network considering the random characteristics of delivery personnel, that is, a stochastic online-food delivery system (SODS) into a network topology (network topology). . Then an algorithm is proposed to evaluate the reliability of SODS system.
本發明著重於研究具有空間和時間限制的SODS,其中隨機容量 (stochastic capacity)表示每個地區可用的送餐人員數量。我們評估系統可靠度,即SODS在特定的空間和時間限制內成功交付商品以滿足每個客戶需求的機率。 The present invention focuses on the study of SODS with spatial and temporal constraints, where random capacity (stochastic capacity) represents the number of food delivery personnel available in each region. We evaluate system reliability, which is the probability that SODS will successfully deliver goods to meet each customer's needs within specific space and time constraints.
首先,隨機餐飲線上配送系統(SODS)是由節點(nodes)、傳輸邊(arcs)、商品(commodities)、商品的空間權重(commodity's space weight)、等待時間、行駛時間等組成,其中每個節點表示配送區域中的一個區域並且與每個節點不重疊;每個傳輸邊(arc)表示與一對節點連接的路徑。在每個節點上,它可能包含幾個餐廳以及食品配送人員為商品的配送提供服務。商品由一名送餐員配送,也可以由一名送餐員配送多件商品。商品的空間權重是餐廳給定的一個比例(0≦權重≦1)。令D={d|d=1,2,…,r}是一組餐廳,其中d表示每個餐廳的索引(index)。第d家餐廳的等待時間用t d 表示,會根據餐廳的實際情況而有所不同。節點a到節點b的行駛時間是由軟體(例如Google Map)取得,用t a,b 表示。SODS涉及的參數包括節點容量、空間約束s、時間約束T。每個網路拓撲由G≡( N , A , D ,M, O ,W)表示,代表具有發貨節點和到達節點的SODS,其中N={i|i=1,2,…,m}表示節點的集合,A={a i,j |i,j=1,2,...,m}表示連接節點i和節點j的傳輸邊集合,M={M i |i=1,2,...,m}表示每個節點的最大容量集合,表示商品的集合。每個節點代表一個區域(例如,一個交付區域)。節點n i 的當前容量,用x i 表示,是一個從0到M i 的整數。容量向量X=(x 1 ,x 2 ,…,x m )。商品用O a,b c,d 表示,索引a表示該商品的發貨節點a,索引b表示該商品的到達節點b,索引c表示該商品的編號,索引d表示該商品是由第d家餐廳製作的。商品的空間權重用W=(w 1 ,w 2 ,...,w v )表示,v為商品數量。等待時間用t d 表示,t d 是第d家餐廳的準備時間。行駛時間用t a,b 表示,t a,b 是從節點i到節點j所消耗的時間。為建構SODS,作出以下假設: First, the Random Catering Online Distribution System (SODS) is composed of nodes, transmission edges (arcs), commodities, commodity's space weight, waiting time, travel time, etc., where each node Represents an area in the delivery area and does not overlap each node; each transit edge (arc) represents a path connecting a pair of nodes. At each node, it may contain several restaurants as well as food delivery personnel servicing the delivery of goods. Items are delivered by one courier, or multiple items can be delivered by a courier. The spatial weight of the product is a ratio given by the restaurant (0≦weight≦1). Let D={ d | d = 1,2,…, r } be a set of restaurants, where d represents the index of each restaurant. The waiting time of the dth restaurant is represented by t d , which will vary according to the actual situation of the restaurant. The travel time from node a to node b is obtained by software (such as Google Map), represented by t a, b . The parameters involved in SODS include node capacity, space constraint s , and time constraint T . Each network topology is denoted by G ≡( N , A , D , M , O , W ), representing SODS with outgoing and arriving nodes, where N = { i | i =1,2,…, m } represents the set of nodes, A ={ a i,j | i,j =1,2,..., m } represents the set of transmission edges connecting node i and node j , M ={ M i | i =1,2 ,..., m } represents the maximum capacity set of each node, Represents a collection of items. Each node represents an area (eg, a delivery area). The current capacity of node ni , denoted by xi , is an integer from 0 to Mi. The capacity vector X=( x 1 , x 2 ,…, x m ). The product is represented by O a,b c,d , the index a represents the delivery node a of the product, the index b represents the arrival node b of the product, the index c represents the serial number of the product, and the index d represents the product from the dth house. Made by the restaurant. The spatial weight of commodities is represented by W = ( w 1 , w 2 ,..., w v ), where v is the number of commodities. The waiting time is denoted by t d , where t d is the preparation time for the d -th restaurant. The travel time is denoted by t a,b , where t a,b is the time it takes to get from node i to node j . To construct SODS, the following assumptions are made:
1.每個節點的容量是一個隨機變量(random variable),它的機率基於給定的機率分佈。 1. The capacity of each node is a random variable whose probability is based on a given probability distribution.
2.行駛時間t a,b 可能與t b,a 不同。 2. The travel time t a,b may be different from t b,a .
3.每個節點的容量在統計上是獨立的。 3. The capacity of each node is statistically independent.
4.每個節點和傳輸邊都非常可靠(perfect reliable)。 4. Each node and transmission edge is perfectly reliable.
向量操作係根據以下所描述規則: Vector operations are performed according to the rules described below:
I. X Y(x 1 ,x 2 ,…,x n )(y 1 ,y 2 ,…,y n ):x i y i 對於每個i=1,2,…,m。 I.X Y ( x 1 , x 2 ,…, x n ) ( y 1 , y 2 ,…, y n ): x i y i =1,2,…, m for each i .
II. X<Y(x 1 ,x 2 ,…,x n )<(y 1 ,y 2 ,…,y n ):X Y且x i<y i ,對於至少一個i。 II. X < Y ( x 1 , x 2 ,…, x n )<( y 1 , y 2 ,…, y n ): X Y and x i < y i for at least one i .
III. X不大於或小於Y:XY既不成立,X<Y也不成立。 III. X is not greater or less than Y : X Neither Y holds, nor does X<Y.
在商品分配階段,每個送餐員必須滿足約束條件(1),即每個送餐員的商品總空間權重(commodity's total space weight)不能大於設定的空間約束s。 In the commodity distribution stage, each delivery person must satisfy the constraint condition (1), that is, the commodity's total space weight of each delivery person cannot be greater than the set space constraint s .
在我們分配商品之前,我們必須計算出最小送餐人數h。最小送餐人數可以根據約束條件(2)得到。 Before we distribute the items, we must calculate the minimum number of people to deliver, h . The minimum number of people delivering meals can be obtained according to constraint (2).
分支定界法用於分析系統的所有可能情況。在獲得最小送餐人數後,我們可以透過約束條件(1)來分配商品,並使用建議的分支定界方法(branch and bound method)來分配商品。H f 代表第f個送餐員的商品,對於f=1,2,...,h, 。首先,根據商品的空間權重從大到小將這v種商品排列成H*。然後,透過具有約束條件(3)和(4)的所提出的分支定界方法來分配商品。 The branch and bound method is used to analyze all possible cases of the system. After obtaining the minimum number of delivery people, we can allocate the items through constraint (1) and use the proposed branch and bound method to allocate the items. H f represents the item of the f -th deliveryman, for f = 1, 2,..., h, . First, arrange the v commodities into H * according to their spatial weights from large to small. Then, the commodities are allocated by the proposed branch and bound method with constraints (3) and (4).
使用以上所提出的分支定界法(branch and bound method)對商品進行分配後,可以得到有關商品分配的第一級解(first-stage solutions)C=(H f |f=1,2,…,h)。每個有關商品分配的第一級解C可以透過置換(permutation)得到不同的有關商品分配的二級解(second-stage solutions)R β =(H f |f=1,2,…,h),即第β個二級解。對於每個R β ,R β 中每個送餐人員的運輸時間由約束條件(5)和(6)計算。約束條件(5)用於計算在R β 中花費時間最多的送餐員的運輸時間,將送餐員的運輸時間設為R β 的運輸時間(transportation time)。約束條件(6)用於計算R β 中每個送餐人員的運輸時間,運輸時間為開車時間加上等待時間。於R β 中所有發貨節點和到達節點的索引的向量中沒有第一個索引的向量用U β 表示。作為R β 中所有存儲索引的索引的向量由W β 表示。 After allocating commodities using the branch and bound method proposed above, the first-stage solutions for commodity allocation can be obtained C=( H f | f =1,2,… , h ). For each first-level solution C related to commodity allocation, different second-stage solutions related to commodity allocation can be obtained through permutation. R β =( H f | f =1,2,…, h ) , which is the βth second-order solution. For each R β , the transit time of each delivery person in R β is calculated by constraints (5) and (6). Constraint (5) is used to calculate the transportation time of the delivery person who spends the most time in R β , and the transportation time of the delivery person is set as the transportation time of R β . Constraint (6) is used to calculate the transportation time of each delivery person in R β , and the transportation time is the driving time plus the waiting time. A vector without the first index among the vectors of indices of all dispatching nodes and arriving nodes in R β is denoted by U β . The vector that is the index of all stored indices in R β is denoted by W β .
S(R β )=Max(H f ),對於R β 中的H f (5) S(R β )=Max(H f ) for H f (5) in R β
S(H f )=Σt a,b +Σt d ,對於i=U β ,j=L β ,以及l=W β (6) S ( H f )=Σ t a,b +Σ t d for i = U β , j = L β , and l = W β (6)
然後,本發明提出兩個集合F和F'分別存儲可實行和不可實行的商品分配Hj。以上兩組用於快速計算可實行R。 Then, the present invention proposes two sets F and F' to store feasible and infeasible commodity allocations Hj, respectively. The above two sets are used to quickly compute feasible R.
根據約束條件(7)和(8),計算容量向量X=(x 1 ,x 2 ,…,x m ): According to constraints (7) and (8), calculate the capacity vector X = ( x 1 , x 2 ,…, x m ):
X i =(x 1 ,x 2 ,...,x m ), (7) X i =( x 1 , x 2 ,..., x m ), (7)
系統可靠度R o 定義為SODS在空間和時間限制內成功交付v種商品的機率。索引l表示容量向量的數量。因此,系統可靠度可以由約束條件(9)計 算。 System reliability R o is defined as the probability that SODS will successfully deliver v items within space and time constraints. The index l represents the number of capacity vectors. Therefore, the system reliability can be calculated by constraint (9).
幾種可用於計算系統可靠度的方法,例如狀態空間(state-space)分解、包含-排除(inclusion-exclusion)、不相交事件(disjoint-event)方法和不相交乘積的遞歸和(recursive sum of disjoint products,RSDP)。基於不相交乘積原理(disjoint product principle,SDP)的RSDP算法比其他方法更有效。所以在本文中,我們使用RSDP方法來計算系統可靠度。 Several methods can be used to calculate system reliability, such as state-space decomposition, inclusion-exclusion, disjoint-event methods, and recursive sum of disjoint products disjoint products, RSDP). The RSDP algorithm based on the disjoint product principle (SDP) is more efficient than other methods. So in this paper, we use the RSDP method to calculate the system reliability.
本發明提出了一種評估SODS系統可靠度的演算法,演算法敘述如下。 The present invention proposes an algorithm for evaluating the reliability of the SODS system, and the algorithm is described as follows.
輸入(Input):網絡拓撲G、時間約束、空間約束、等待時間t d 、行駛時間t a,b 。 Input (Input): network topology G, time constraints, space constraints, waiting time t d , travel time t a,b .
Step 1:使用分支定界法計算商品分配的第一級解C。 Step 1: Calculate the first-level solution C of commodity allocation using the branch and bound method.
1.1)根據約束條件(10)計算最少送餐人數。 1.1) Calculate the minimum number of people to deliver meals according to constraint (10).
1.2)利用H*得到有關商品分配的第一級解C,其中H*為根據商品的空間權重從大到小將這v種商品排列。 1.2) Use H * to obtain the first-level solution C about commodity distribution, where H * is to arrange the v commodities according to their spatial weights from large to small.
Step 2:利用有關商品分配的第一級解C經由互換(permutation)產生有關商品分配的第二級解R。 Step 2: Use the first-level solution C about commodity distribution to generate a second-level solution R about commodity distribution through permutation.
Step 3:計算R的運輸時間並刪除不可行的R。 Step 3: Calculate the transit time of R and delete the infeasible R.
3.1)創建兩個集合F和F'。設和。 3.1) Create two sets F and F' . Assume and .
3.2)列出R中的每個配送(courier)並計算運輸時間。 3.2) List each courier in R and calculate the shipping time.
3.3)列出所有可實行的R。 3.3) List all feasible R.
Step 4:利用R獲得容量向量。然後移除重複項和更大的容量向量。 Step 4: Use R to obtain the capacity vector. Then remove duplicates and a larger capacity vector.
4.1)生成容量向量(capacity vector)X。 4.1) Generate a capacity vector X .
4.2)移除重複項和更大的容量向量。 4.2) Remove duplicates and larger capacity vectors.
Step 5:利用RSDP方法計算網絡可靠度。 Step 5: Calculate the network reliability using the RSDP method.
輸出(Output):Ro Output: R o
為了幫助理解如何執行所提出的算法,下面展示了一個簡單的多階狀態(multi-state)餐飲線上配送網路。以圖1之食品外送平台之新竹服務地區為例之多階狀態網路100,本發明亦可利用於其他實務系統中。針對該服務地區可劃分成不同外送區域,此案例之多階狀態網路100採用Activity on Arrow網路拓樸圖以架構各外送區域間之相對位置,其中a α 表示劃分出之第α個外送區域,P β,ε 表示β到ε之外送區域中心的最短直接路徑,外送平台中外送人員可自行選擇上班地點,因此每一外送區域中之外送人員數量視為多階狀態。在本發明中,考量每一外送區域之外送人員數量為多階狀態以及考量時間閾值和空間之限制,以評估外送平台當前外送人員數量可成功配送訂單之機率,而此機率稱之為系統可靠度。
To help understand how the proposed algorithm is implemented, a simple multi-state online food delivery network is shown below. Taking the
透過歷史資料可歸納出每一外送區域之外送人員容量機率表,如下表一所示。若系統收到5張訂單,其中出發地及送達地都已預先知道,外送公司設定在20分鐘和一個外送箱之限制下運送,相關訂單資訊如表二所示,外送區域i到外送區域j之花費時間可透過外送公司的外送系統得知,詳細資料如表三所示。 Through historical data, the probability table of delivery personnel capacity for each delivery area can be summarized, as shown in Table 1 below. If the system receives 5 orders, of which the origin and destination are known in advance, the delivery company sets the delivery within the limit of 20 minutes and one delivery box. The relevant order information is shown in Table 2. The delivery area i to The time spent in delivery area j can be known through the delivery system of the delivery company. The details are shown in Table 3.
因此,根據本發明的技術,首先透過分支界限法求出滿足空間限制之訂單配送狀況,接著針對各訂單配送狀況計算消耗時間並去除超過時間閾值之訂單狀況,後將通過空間和時間閾值限制之訂單狀況轉為最小下界向量,並透過RSDP方法和最小下界向量以估算出系統可靠度為0.9044,評估之系統可靠度表示該系統中外送人員在20分鐘和一個外送箱的限制下,成功配送以下五張訂單的機率為0.9044。系統可靠度可以作為一管理者管理外送系統的一項指標,管理者可運用系統可靠度適當調整各外送區域之外送人員數量,抑或是增減時間閾值區間以滿足設定之服務水準或系統可靠度門檻值,透過適當的外送人員配置可有效降低人事成本和訂單未成功運送之風險成本。 Therefore, according to the technology of the present invention, the order delivery status that satisfies the space limitation is first obtained through the branch and bound method, then the consumption time is calculated for each order delivery status and the order status that exceeds the time threshold is removed, and then the space and time threshold limitations are passed. The order status is converted to the minimum lower bound vector, and the system reliability is estimated to be 0.9044 through the RSDP method and the minimum lower bound vector. The estimated system reliability indicates that the delivery personnel in the system successfully delivered the delivery within the constraints of 20 minutes and one delivery box. The probability of the following five orders is 0.9044. System reliability can be used as an indicator for a manager to manage the delivery system. Managers can use the system reliability to properly adjust the number of delivery personnel in each delivery area, or increase or decrease the time threshold interval to meet the set service level or The system reliability threshold value can effectively reduce the personnel cost and the risk cost of unsuccessful order delivery through appropriate delivery personnel allocation.
參考圖2,其顯示根據本發明的一個實施例所提出的計算餐飲線上配送系統之系統可靠度評估方法的流程圖。本發明針對多階餐飲線上配送網路考量時間閾值和空間限制,利用網路分析方法建構網路模型並輸入時間閥值、外送人員空間限制、餐廳等待時間、各路線配送時間等作為運算參數(步驟201),其中時間閾值可限制配送人員在給定之時間下完成訂單配送,以符合配送公司之服務水準設定,空間限制則約束配送人員之訂單數量,可讓商品在充足的空間下保存並配送,餐廳等待時間、以及各路線配送時間則關係到服務指標與顧客接受服務之滿意度;接著,計算滿足上述空間限制之最低配送人員數量(步驟203);然後,透過分支界限法求出滿足空間限制之訂單配送組合,進而求出 各外送員配送之訂單狀況(步驟205);接下來,計算各配送狀況消耗時間,除去超過時間閾值之訂單狀況(步驟207);緊接著,將訂單狀況轉為最小下界向量(步驟209);最後,透過不相交乘積的遞歸和(recursive sum of disjoint products,RSDP)方法計算系統可靠度(步驟211)。 Referring to FIG. 2 , it shows a flowchart of a method for calculating the system reliability of an online catering distribution system according to an embodiment of the present invention. The present invention considers the time threshold and space limitation for the multi-level catering online distribution network, uses the network analysis method to construct a network model, and inputs the time threshold, the space limitation of delivery personnel, the waiting time of the restaurant, the delivery time of each route, etc. as the operation parameters (Step 201), wherein the time threshold can limit the delivery personnel to complete the order delivery at a given time to meet the service level setting of the delivery company, and the space limit can restrict the order quantity of the delivery personnel, so that the goods can be stored and stored in sufficient space. Delivery, restaurant waiting time, and delivery time of each route are related to service indicators and customer satisfaction with the service; then, calculate the minimum number of delivery personnel that satisfies the above space constraints (step 203); Order delivery combination of space constraints, and then find Order status delivered by each courier (step 205); next, calculate the consumption time of each delivery status, and remove the order status exceeding the time threshold (step 207); then, convert the order status into a minimum lower bound vector (step 209) ; Finally, the system reliability is calculated by the recursive sum of disjoint products (RSDP) method (step 211).
請參閱圖3,其顯示本發明實施例中用於預測系統可靠度之裝置300的示意圖。如圖所示,應用於本發明之多階狀態網路(MSN)之可靠度計算裝置可以至少包含輸入裝置301、記憶體303、處理器305以及輸出裝置307。其中,輸入裝置301與記憶體303電性連接,輸入裝置301可包括電腦裝置的各種輸入介面或是檔案的接收裝置,可以藉由輸入裝置301接收有關隨機餐飲線上配送系統(SODS)3032的節點以及傳輸邊的架構(亦即SODS網路拓樸),並將其儲存於記憶體303中。記憶體303可以儲存針對上述餐飲線上配送系統(SODS)所開發之系統可靠度計算方法的演算法3031,演算法3031如同前述實施例所揭露的流程步驟。
Please refer to FIG. 3 , which shows a schematic diagram of an
以一較佳實施例,記憶體303可包含唯讀記憶體、快閃記憶體、磁碟或是雲端資料庫等。
In a preferred embodiment, the
以一較佳實施例,上述處理器305與記憶體603電性連接,處理器305包含中央處理器、影像處理器、微處理器等,期可以包含多核心的處理單元或是多個處理單元的組合,處理器305可以存取記憶體中的SODS網路拓樸3032以及可靠度計算方法的演算法3031,進行系統可靠度估算。
In a preferred embodiment, the above-mentioned
以一較佳實施例,處理器305演算的結果,可由輸出裝置307輸出。輸出裝置307可以為呈現計算結果的顯示器,例如LCD、LED或OLED顯示螢幕,又或者是有線/無線的網路傳輸裝置,將計算結果傳送至遠端之使用者。
In a preferred embodiment, the calculation result of the
簡而言之,本發明將實務系統中每一單位時間內每個區域會有不同配送人員數量的機率變動特性納入考量,並藉由所提出之系統可靠度作為系 統狀態的評估指標,本發明所提供之系統可靠度,可用以評估系統之現有餐飲線上配送系統狀態,以量化系統之負載性並強化管理者的風險控管能力。餐飲線上配送系統中各區域之配送人員數量為一隨機變數,並且不需服從特定機率分配,故可輕易將餐飲線上配送系統中配送人員數量視為多階狀態。以外送平台為例,在外送區域中外送人員數量為隨機變動,在訂單浮動下,系統中的外送員可滿足訂單的機率亦會跟著變動,因此,可透過本專利所提出之系統可靠度來作為系統狀態之量化指標,以實際控管外送人員之數量,以達到成功配送所有訂單之目的。本發明可提供相關配送產業一系統之績效指標,該績效指標可讓管理者作為派遣配送人員之依據,在系統可靠度不足時增派配送人員以降低風險成本。 In short, the present invention takes into account the probability variation characteristics of the number of different delivery personnel in each area per unit time in the practical system, and uses the proposed system reliability as the system. The evaluation index of the system state, the system reliability provided by the present invention can be used to evaluate the state of the existing catering online distribution system of the system, so as to quantify the loadability of the system and strengthen the risk control ability of managers. The number of delivery personnel in each area in the online catering distribution system is a random variable, and does not need to obey a specific probability distribution, so the number of delivery personnel in the online catering distribution system can be easily regarded as a multi-level state. Taking the delivery platform as an example, the number of delivery personnel in the delivery area varies randomly. Under the fluctuation of the order, the probability that the delivery personnel in the system can satisfy the order will also change. Therefore, the reliability of the system proposed in this patent can be achieved through the It is used as a quantitative indicator of system status to actually control the number of delivery personnel to achieve the purpose of successfully delivering all orders. The present invention can provide a performance index of a system related to the distribution industry, the performance index can be used by managers as the basis for dispatching distribution personnel, and when the reliability of the system is insufficient, additional distribution personnel can be dispatched to reduce risk costs.
本發明的保護範圍在於針對一餐飲線上配送系統提出一評估方法,可針對配送人員數量隨機之狀態下,評估在空間和時間閾值限制下的系統可靠度,其定義為在給定之空間和時間閾值限制下,當前系統中配送人員數量可成功配送所有訂單的機率,依據評估之系統可靠度可針對不同區域派遣不同配送人員數量,以降低人事成本及未成功配送訂單之風險成本。因此,該系統可靠度可提供管理者作為一管理指標,可透過該系統可靠度派遣適當配送人員,並了解系統的負載狀況。上述各實施例之一或任意實施例的組合,可儲存於電腦可讀取媒體中,並透過電腦之硬體,例如處理器加以運算、處理、演算、預測、估算等,以達到本發明所欲之目的、功效,而產生不可預期之效果。 The protection scope of the present invention is to propose an evaluation method for an online catering distribution system, which can evaluate the reliability of the system under the limitation of space and time thresholds under the condition that the number of distribution personnel is random, which is defined as the given space and time thresholds Under the limitation, the number of delivery personnel in the current system can successfully deliver all orders. According to the assessed system reliability, different numbers of delivery personnel can be dispatched to different regions to reduce personnel costs and the risk of unsuccessful delivery of orders. Therefore, the reliability of the system can provide managers as a management indicator, through which the reliability of the system can be used to dispatch appropriate delivery personnel and to understand the load status of the system. One of the above-mentioned embodiments or any combination of the embodiments can be stored in a computer-readable medium, and can be calculated, processed, calculated, predicted, estimated, etc. through the hardware of the computer, such as a processor, so as to achieve the goal of the present invention. The purpose and effect of desire, and produce unpredictable effects.
以上實施例僅用以說明本發明的技術方案,而非對其限制;儘管參照前述實施例對本發明及其效益進行詳細說明,本領域的普通技術人員應當理解:其依然可以對前述各實施例所記載的進行修改,或者對其中部分技術特徵進行等同替換;而這些修改或替換,並不使相應技術方案的本質脫離本發明權利要求的範圍。 The above embodiments are only used to illustrate the technical solutions of the present invention, but not to limit them; although the present invention and its benefits are described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that the foregoing embodiments can still be used for Modifications are made to the descriptions, or equivalent replacements are made to some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions depart from the scope of the claims of the present invention.
201、203、205、207、209、211:步驟 201, 203, 205, 207, 209, 211: Steps
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Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104598994A (en) * | 2015-01-23 | 2015-05-06 | 广东易富网络科技有限公司 | An Optimal Scheduling Method for Linked Logistics Transportation with Time-varying Time Window |
| US20170235848A1 (en) * | 2012-08-29 | 2017-08-17 | Dennis Van Dusen | System and method for fuzzy concept mapping, voting ontology crowd sourcing, and technology prediction |
| CN107180276A (en) * | 2017-05-23 | 2017-09-19 | 大连海事大学 | An intelligent scheduling and route optimization method for O2O food delivery platform |
| CN108090601A (en) * | 2016-11-22 | 2018-05-29 | 浙江科技学院 | Food Cold Chain transportation service network robust Optimal methods |
| CN109583634A (en) * | 2018-11-16 | 2019-04-05 | 西北工业大学 | A kind of take-away Distribution path selection method based on Modern Portfolio Theory |
| CN110598946A (en) * | 2019-09-20 | 2019-12-20 | 浙江树人学院(浙江树人大学) | Flood prevention material rescue distribution method based on non-dominated artificial bee colony |
| CN110710852A (en) * | 2019-10-30 | 2020-01-21 | 广州铁路职业技术学院(广州铁路机械学校) | Meal delivery method, system, medium and intelligent device based on meal delivery robot |
| CN111967668A (en) * | 2020-08-17 | 2020-11-20 | 安徽理工大学 | Cold chain logistics path optimization method based on improved ant colony algorithm |
-
2021
- 2021-09-24 TW TW110135682A patent/TWI769928B/en active
Patent Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20170235848A1 (en) * | 2012-08-29 | 2017-08-17 | Dennis Van Dusen | System and method for fuzzy concept mapping, voting ontology crowd sourcing, and technology prediction |
| CN104598994A (en) * | 2015-01-23 | 2015-05-06 | 广东易富网络科技有限公司 | An Optimal Scheduling Method for Linked Logistics Transportation with Time-varying Time Window |
| CN108090601A (en) * | 2016-11-22 | 2018-05-29 | 浙江科技学院 | Food Cold Chain transportation service network robust Optimal methods |
| CN107180276A (en) * | 2017-05-23 | 2017-09-19 | 大连海事大学 | An intelligent scheduling and route optimization method for O2O food delivery platform |
| CN109583634A (en) * | 2018-11-16 | 2019-04-05 | 西北工业大学 | A kind of take-away Distribution path selection method based on Modern Portfolio Theory |
| CN110598946A (en) * | 2019-09-20 | 2019-12-20 | 浙江树人学院(浙江树人大学) | Flood prevention material rescue distribution method based on non-dominated artificial bee colony |
| CN110710852A (en) * | 2019-10-30 | 2020-01-21 | 广州铁路职业技术学院(广州铁路机械学校) | Meal delivery method, system, medium and intelligent device based on meal delivery robot |
| CN111967668A (en) * | 2020-08-17 | 2020-11-20 | 安徽理工大学 | Cold chain logistics path optimization method based on improved ant colony algorithm |
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