物流运作优化-实验课ppt课件

1、 有两家面包店B1, B2)以及四个客户C1, C2, C3, C4)。面包店B1每天最多消费800个面包，而面包店B2每天最多消费600个面包。客户C1, C2, C3, C4) 对于面包的需求分别为150, 250, 350 and 450 个/天，面包店至客户的单位运输本钱如以下图所示，请问最廉价的运输方案是怎样的？简单配送问题举例运输问题数学模型Transportation ProblemMathematical model3面包店i的产量 。我们定义为ai面包的销售j的销量，我们定义为bj练习 试经过Xpress 软件编写程序，处理以下问题，目的为总运费最小？Cij B1B2B3B4

2、产量A13113512A2698720A342141032销量261887运输问题计算机解法关于Xpress IVE (basic features for student restricted version)经常用于优化问题的处理。 Maximum number of constraints 限制条件 (rows): 400 Maximum number of variables 变量 (columns): 800 Maximum number of matrix coefficients 矩阵的元素(elements): 5000 Maximum number of binary and

3、 integer variables二元变量, etc (global elements): 400FICO Xpress-IVE Start Programs Xpress Xpress IVEFICO Xpress-IVE FICO Xpress-IVE FICO Xpress-IVE FICO Xpress-IVE Mosel Xpress-IVE Writing a model in Mosel model Transportation uses “mmxprs定义模型称号变量声明declarations a: array (1.2) of integer b: array (1.4)

4、 of integer c: array (1.2, 1.4) of integer x: array (1.2, 1.4) of mpvarend-declarationsforall(i in 1.2,j in 1.4) x(i,j) is_integerinitializations from example of text.txt a b cend-initializations !引入数据Writing a model in Mosel 目的函数与限制条件! 设置总本钱函数Cost:=sum (i in 1.2, j in 1.4) c(i,j)*x(i,j)! 设置限制条件fora

5、ll (i in 1.2) sum (j in 1.4) x(i,j) = b(j)minimize(Cost) !设置目的函数，本钱变量不需求声明Writing a model in Mosel Output & results! 输出目的函数 getobjval 表示优化后的值writeln(“Total cost: “, getobjval)! 输出各个变量的值forall (i in 1.2, j in 1.4) writeln(“x (,i,j,) = “,getsol(x(i,j)How to write a model in Mosel Xpress-IVEName of the

6、 modelDeclarations (decision variables, arrays, etc.)Data inputObjective functionConstraintsOutput & results15How to write a model (1) Name of the modelmodel ModelNameuses “mmxprs16How to write a model (2) Declarations (variables, arrays, etc.)declarations Variable(变量名 : mpvar VariableArray (变量名 : a

7、rray() of mpvarend-declarations17How to write a model (3) Data input optional sectioninitializations from “Filename UnitCost;end-initializations18How to write a model (4) Objective functionCost:=2*x1+3*x2 !.constraintsminimize(Cost) !you dont need to declare CostorProfit:=2*x1+3*x2 !.constraintsmini

8、mize(Profit) !you dont need to declare Profit19How to write a model (5) Constraints! simple constraintX1+3*X2-5*X3=8! multiple constraints using loopforall(i in 1.10) Z(i)=1! sum constraintsum(i in 1.10) X(i)=B! multiple sum constraints using loopforall(i in 1.5) sum (j in 1.10) X(i,j)=120How to wri

9、te a model (6) Output & results! Value of objective function - getobjvalwriteln(“Objective value: “, getobjval)! Vlue of decision variablewriteln(“X1 = “,getsol(X1)! Values of decision variables in array using loopforall(i in 1.M) writeln( Y(“, i,) = “, getsol(Y(i)21What should be answered in this l

10、esson?Which decisions are made when a distribution system is designed? Which costs must be taken in consideration, if we want to reach the most efficient performance of the system? How to describe the distribution design problem, which is to be solved by computer? Distribution SystemA distribution s

11、ystem is a composition of primary sources of goods, customers, warehouses and stores and a transportation system.A distribution system satisfies customers demands for goods from a set of primary sources. The activities, which cause the move of goods from a primary source to a customer, form logistic

12、 chains. Distribution System StructureHow many echelons (levels) should have the distribution system?How many warehouses, if any, should be located and where should they be placed?How many buffer stores, if any, should be run and where?Which facility should supply a customer?Which warehouse or prima

13、ry source should supply a buffer store?What does the system structure design contribute? Dont you believe me?Money! Follow the next toy example!Let us consider one producer P and four customers, which are supplied each day with one item of product each. Customers can be supplied only by trucks and e

14、ach truck can carry exactly one item of the product at transportation cost 2 RMB per unit distance. What does the system structure design contribute? Producer PCustomers11111111If the customers are supplied directly from P, two items are delivered along the distance of 4 units and another two items

15、are carried along the distance of 5 units. The total distance traversed is 18 units and the associated cost is 36 RMB. What does the system structure design contribute?Producer PCustomers11111111But, there is a railway, which starts from P and goes near to the customers through two places, where tra

16、nsshipment places may be constituted (each for six RMB per day) . This transportation means is able to transports one item at one RMB per distance unit. What does the system structure design contribute?Producer PCustomers11111111Now, three other possibilities have arisen. The transshipment places ca

17、n be constituted at both crossings or at one of the two possibilities. What does the system structure design contribute?Producer PCustomers11111111Here, two transshipment places are constituted at price of 12 rmb.Items are carried by railway by two 3 and 4 distance units respectively, what does 14 u

18、nits totally (and 14 RMB).The total distance traversed by trucks is 4 and the cost is 8.The total cost is 34. What does the system structure design contribute?Producer PCustomers11111111In this situation, one places is constituted at price of 6 .Items are carried by railway by 16 distance units tota

19、lly, what does 16 RMB.The total distance traversed by trucks is 6 and the cost is 12.The total cost is also 34. What does the system structure design contribute?Producer PCustomers11111111In this situation, also one places is constituted at price of 6 .Items are carried by railway by 12 distance uni

20、ts totally, what does 12 RMB.The total distance traversed by trucks is 6 and the cost is 12.The total cost is also 30. What does the system structure design contribute?Producer PCustomers11111111This structure with the total cost 30 wins!It is by 6 better than the original direct distribution in thi

21、s case.33Why we build the model if we were able to solve the problem without it?Our toy problem has exactly four feasible solutions given by sets of places, at which a facility is located. A problem with n possible places has 2n feasible solutions.If there are 64 possible locations, then 2n is appro

22、ximately 1.8*1019. When we were able to evaluate one million solutions in one second, determination of the optimal solution would required 1.8*1013 seconds, what is 584*103 years.Relevant Costs of DistributionHolding cost (rent cost for a warehouse, fixed charge fi for locating or keeping a warehous

23、e at given place i).Handling cost (manipulating cost connected with transshipment or storing one unit of goods gi ).Transportation costs (costs connected with way of transport at the particular echelon, e.g. bulk transport cost and distribution transport cost).35Relevant Cost of DistributionPrimary

24、sourceCustomersWarehouse 1Warehouse iTransportation cost of bulk transportFixed charge fiHandling cost giTransportation cost of distribution transportLet us demonstrate the procedure on the toy example Producer PCustomers11111111Nodes of special importance are here the producer P and the crossings P

25、1 and P2. We obtain distances:P1P2C1C2C3C4PP1P2C1C2C3C4P0344455P13011122P24102211Cost of Customers Demand SatisfactionNotice the prime costs e0 and e1 please!Each of them gives a cost of transport of one demand unit along one distance unit.Primary sourceCustomer jWarehouse idsi distance between prim

26、ary source and warehouse idij distance between warehouse iand customer j.gi handling cost at iLet us demonstrate the cost calculation on the toy example Producer P =sCustomers11111111The prime cost e0 is 2 RMB and e1 is 1 RMB。Handling cost gi =0 and bj=1.P1P2C1C2C3C4dijPP1P2C1C2C3C4P0344455P13011122

27、P2410221139Let us demonstrate the cost calculation on the toy exampleCustomersProducer P=s11111111P1P2C1C2C3C4dijPP1P2C1C2C3C4 1P0344455 2P13011122 3P24102211CijPP1P2C1C2C3C4 1P881010 2P15577 3P2886612340Decision Variables for Distribution System Structure DesignDecision on a facility location at pl

28、ace i will be modeled by a variable yi 0,1.y3 0,1Producer P=s11111111P1P2C1C2C3C4y20,1y10,112341Decision Variables for Distribution System Structure DesignDecision on supplying of customer j from place i will be modeled by a variable zij 0,1. Customer j=2z320,1.Producer P=s11111111P1P2C1C2C3C4y10,11

29、2342Decision Variables for Distribution System Structure DesignPrimary sourceCustomer jLocation iyi 0,1 Will ( yi =1) or will not ( yi =0) be a warehouse located at place i ?zij 0,1 Will ( zij =1) or will not ( zij =0) be customer j assigned to location i ?43A Model of the Total CostThis is fixed co

30、st (charge), which will appear at place i depending on the decision yi. If no warehouse is located at i, then yi=0 and also fiyi=0. On the contrary, if a warehouse is located at i, then yi=1 and fiyi=fi.44A Model of the Total CostThis is fixed cost (charge), at all considered places of I.45A Model o

31、f the Total CostThis is cost of customers j demand satisfaction via place i, which will appear depending on the decision zij. If customer j is not satisfied via i, then zij=0 and also cijzij =0. On the contrary, if customer j is satisfied via i, then zij=1 and cijzij =cij .46A Model of the Total Cos

32、tThis is cost of customers j demand satisfaction.It must be supplied via one place from the set I.47A Model of the Total CostThis is cost of demand satisfaction of all customers.48A Model of the Total CostThis is relevant total cost the distribution system over a considered time period.49A Model of

33、Two-echelon Distribution System DesignThese are the constraints, which assure that each customer is supplied via exactly one place from I. Customer j=2z320,111111111P1P2C1C2C3C412350A Model of Two-echelon Distribution System DesignThese constraints ensure that customer j is allowed to be supplied via place i, only if a warehouse is located there, i.e. yi=1. 51A Model of Two-echelon Distribution System DesignCustomer j=2z320,1Producer P=s11111111P1P2C1C2C3C4y10,112352Le