Consider the transportation problem (a special kind of network optimization problem with no transshipments nodes) having the unit shipping costs shown in the following table. Destination 1 2 3 Supply Source 1 $6 $7 $4 40 $5 $8 $6 60 Demand 30 40 30 Formulate and solve a spreadsheet model for this problem and determine the following: a) Optimal number of products that can be shipped • from Source 1 to Destination 1 = units • from Source 1 to Destination 2 = units • from Source 1 to Destination 3 = units • from Source 2 to Destination 1 = units • from Source 2 to Destination 2 = units %! • from Source 2 to Destination 3 units %3D b) Optimal Cost = $ 2.

Consider the transportation problem (a special kind of network optimization problem with no transshipments nodes) having the unit shipping costs shown in the following table. Destination 1 2 3 Supply Source 1 $6 $7 $4 40 $5 $8 $6 60 Demand 30 40 30 Formulate and solve a spreadsheet model for this problem and determine the following: a) Optimal number of products that can be shipped • from Source 1 to Destination 1 = units • from Source 1 to Destination 2 = units • from Source 1 to Destination 3 = units • from Source 2 to Destination 1 = units • from Source 2 to Destination 2 = units %! • from Source 2 to Destination 3 units %3D b) Optimal Cost = $ 2.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter5: Network Models

Section: Chapter Questions

Problem 47P

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Two plants supply three customers with medical supplies. The unit costs of shipping from the plants to the customers, along with the supplies and demands, are given in Table below. The company’s goal is to minimize the cost of meeting customers’ demands.            From                                              To Customer 1 Customer 2 Customer 3 Supply Plant 1 55 65 80 35 Plant 2 10 15 25 50 Demand 10 10 10    Formulate a linear programming (LP) model for this problem. Use solver to find the optimal transportation rule    As a management science student, the MD of the company seeks your expert advice on ways in which to determine the optimal                   transportation rule. Advise the MD, providing detailed explanation    using your answer obtain in (b). Write your answer in a form of a report to the MD.
(a) Write the dual of the following linear programming problem: Maximize       Ζ = 3x1 + 5x2 + 4x3, Subject to      2x1 + 3x2 ≤ 8, 2x2 + 5x3 ≤10 3x1 + 2x2 + 4x3 ≤15 x1 , x2 , x3 ≥ 0 (b) Find the optimal solution to the given problem in (a) above, using the simplex method. (c) From the final optimal table in (b) above, find the solution to the dual problem. (d) Give the economic interpretation to the solution in (c) above.
Jefferson Distributing is analyzing distribution networks with either 4, 5, 6 or 7 warehouses to serve 200 major customers in Europe. Relevant costs include transportation cost from the warehouses to customers, fixed facility costs, and inventory costs in the warehouses. The table below shows the annual transportation cost produced by a facility location software tool for locating 4, 5, 6 or 7 warehouses for this company. Suppose that annual inventory cost for the network can be modeled as $800,000 times the square root of the number of warehouses. Thus, if the network has 4 warehouses, then the annual inventory cost would be $800,000 x √4= $1,600,000. Number of Warehouses Transportation Cost 4 8,000,000 5 6,500,000 6 5,000,000 7 4,400,000 a) If the annual fixed cost per warehouse is $1,000,000, how many warehouses should there be to minimize the total (transportation + warehouse + inventory) cost?                   b) Now suppose the…
A beer distributor needs to plan how to make deliveries from its warehouse (node 1) to a supermarket (node 7), as shown in the network below. A graph with 7 nodes and 9 arcs is shown. Node 1 is connected to node 2 by arc of value 3, to node 5 by arc of value 3, and to node 6 by arc of value 11. Node 2 is connected to node 3 by arc of value 4. Node 3 is connected to node 2 by arc of value 4 and to node 4 by arc of value 7. Node 4 is connected to node 3 by arc of value 7, to node 6 by arc of value 5, and to node 7 by arc of value 6. Node 5 is connected to node 6 by arc of value 7. Node 6 is connected to node 4 by arc of value 5, to node 5 by arc of value 7, and to node 7 by arc of value 3. Develop the LP formulation for finding the shortest route from the warehouse to the supermarket. (Let xij represent the flow from node i to node j.) Min s.t.Node 1 Flows Node 2 Flows Node 3 Flows Node 4 Flows Node 5 Flows Node 6 Flows Node 7…
consider the following network representation of a transportation problem:(The image provided) The supplies, demands, and transportation costs per unit are shown on the network. The optimal (cost minimizing) distribution plan is given below. Des Moines Kansas City St.Louis Supply Jefferson City 20 0 10 30 Omaha 10 10 0 20 Demand 30 10 10 Total Cost: $530. Find an alternative optimal solution for the above problem. If required, round your answer to nearest whole number and if your answer is zero enter “0” Des Moines Kansas City St.Louis Jefferson City Omaha Total Cost: $ is?
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In a 3 x 3 transportation problem, let xij be the amount shipped from source i to destination j and let cij be the corresponding transportation cost per unit. The amounts of supply at sources 1, 2, and 3 are 15, 30, and 85 units, respectively, and the demands at destinations 1, 2, and 3 are 20, 30, and 80 units, respectively. Assume that the starting northwest-corner solution is optimal and that the associated values of the multipliers are given us u1 = -2, u2 = 3, u3 = 5, v1 = 2, v2 = 5, and v3 = 10. a) Find the associated optimal cost. b) Determine the smallest value of cij for each nonbasic variable that will maintain the optimality of the northwest-corner solution.
A Company has 3 production facilities S1, S2 and S3 with production capacity of 7, 9 and 18 units (in 100's) per week of a product, respectively. These units are tobe shipped to 4 warehouses D1, D2, D3 and D4 with requirement of 5,6,7 and 14 units (in 100's) per week, respectively. The transportation costs (in rupees) per unit between factories to warehouses are given in the table below. D1 D2 D3 D4 Capacity S1 19 30 50 10 7 S2 70 30 40 60 9 S3 40 8 70 20 18 Demand 5 8 7 14 34 Find initial basic feasible solution for given problem by usingcolumn minima methodif the object is to minimize the total transportation cost.
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Consider the following linear programming model with 4 regular constraints:Maximize 3X + 5Y (a) Draw your graph in the space below:subject to: 4X + 4Y ≤ 48 (constraint #1) 4X + 3Y ≤ 50 (constraint #2) 2X + 1Y ≤ 20 (constraint #3) X ≥ 2 (constraint #4) X, Y ≥ 0 (non-negativity constraints)(a) Which of the constraints is redundant? Constraint #______.Justify by drawing a graph similar to Figure 7.14 on p.263.(b) Is point (9,3) a feasible solution? _____. Explain your answer (by analyzing each of the constraints).Constraint #1: _______________________________________________________________Constraint #2: _______________________________________________________________Constraint #3: _______________________________________________________________Constraint #4: ______________________________________________________________