*FIND THE FOLLOWING: - Objective function 1 (total transportation costs) - Objective fu nction2 (total opening costs...
Fantastic news! We've Found the answer you've been seeking!
Question:
*FIND THE FOLLOWING:
- Objective function 1 (total transportation costs)
- Objective function2 (total opening costs of plants)
- balance constraint (enough raw material should be sent from the supplier to each plant)
- The capacity constraint of plants
- The capacity constraint of supplier
- Demand satisfaction constraint
Transcribed Image Text:
Q1) A company has a contract with several retailer to satisfy the demand of a specific product. For this reason, the manager of the company decided to establish some plants in some candidate locations. The final product is made using raw materials that can be provided by a set of supplies. The following figure shows a schematic overview of the corresponding supply chain network. MIMAMON suppliers Notations: indices: 1 k m { e₁ رات parameters: by 01 Cim da Cjx Given the notations defined below, formulate a two objective mathematical model to minimize the total transportation costs and the total opening cost of plants in a way that the demand of retailers is satisfied. Write your model in an algebraic form in the table given on the next page. Iml/ Yjk Cmij plants by 0₂ index for suppliers (i=1,2,....) index for plants (-1.2...) index for retailers (k=1,2,....K) index of raw materials (m=1,2,....) decision variables: production capacity of plantj opening cost of plant/ supply capacity of supplier i for raw material m demand of retailer k cik retailers k dz number of raw materials of type m required for manufacturing a single product transportation cost of sending one unit of raw material m from supplier (to plant/ transportation cost of sending one unit of product from plant / to retailer k number of raw materials of type m sent from supplier ( to plant/ number of products to be transported from plant/ to retailer k =1 if plant j is opened: 0 otherwise Q1) A company has a contract with several retailer to satisfy the demand of a specific product. For this reason, the manager of the company decided to establish some plants in some candidate locations. The final product is made using raw materials that can be provided by a set of supplies. The following figure shows a schematic overview of the corresponding supply chain network. MIMAMON suppliers Notations: indices: 1 k m { e₁ رات parameters: by 01 Cim da Cjx Given the notations defined below, formulate a two objective mathematical model to minimize the total transportation costs and the total opening cost of plants in a way that the demand of retailers is satisfied. Write your model in an algebraic form in the table given on the next page. Iml/ Yjk Cmij plants by 0₂ index for suppliers (i=1,2,....) index for plants (-1.2...) index for retailers (k=1,2,....K) index of raw materials (m=1,2,....) decision variables: production capacity of plantj opening cost of plant/ supply capacity of supplier i for raw material m demand of retailer k cik retailers k dz number of raw materials of type m required for manufacturing a single product transportation cost of sending one unit of raw material m from supplier (to plant/ transportation cost of sending one unit of product from plant / to retailer k number of raw materials of type m sent from supplier ( to plant/ number of products to be transported from plant/ to retailer k =1 if plant j is opened: 0 otherwise
Expert Answer:
Answer rating: 100% (QA)
OBJECTIVE FUNCTION 1 TOTAL TRANSPORTATION COSTS The objective function to minimize the total transportation costs can be formulated as Min da xam dx x... View the full answer
Related Book For
Introduction to Operations Research
ISBN: 978-1259162985
10th edition
Authors: Frederick S. Hillier, Gerald J. Lieberman
Posted Date:
Students also viewed these economics questions
-
Consider the following objective function for a linear programming model: (a) Draw a graph that shows the corresponding objective function lines for Z = 6, Z = 12, and Z = 18. (b) Find the...
-
Show how the following objective function can be presented in equation form: Minimize z = max {|x1 - x2 + 3x3|, | - x1 + 3x2 - x3|} X1, x2, x3 0 (Hint: |a| b is equivalent to a b and a - b.)
-
The following diagram shows the flow process, raw material costs, and machine processing time for three products: A, B, and C. There are three machines ( W, X, and Y) used in the production of these...
-
8. Be able to discuss how economic growth was differed across the three eras we discussed prior to WWI.
-
Suppose that another bank branch, located in a residential area, is also concerned with the noon- to- 1: 00 p. m. lunch hour. The waiting time, in minutes, collected from a sample of 15 customers...
-
Art, an executive with Azure Corporation, plans to start a part-time business selling products on the Internet. He will devote about 15 hours each week to running the business. Arts salary from Azure...
-
The quality of Pinot Noir wine is thought to be related to the properties of clarity, aroma, body, flavor, and oakiness. Data for 38 wines are given in Table B. 11 . a. Fit a multiple linear...
-
Use computer software to develop a regression model for the data in Problem 4-19. Explain what this output indicates about the usefulness of this model.
-
Royal Lawncare Company produces and sells two packaged products-Weedban and Greengrow. Revenue and cost information relating to the products follow: Product Selling price per unit Weedban $ 9.00...
-
Spring Manufacturing Company makes two components identified as C12 and D57. Selected budgetary data for 2022 follow: The firm expects the average wage rate to be $25 per hour in 2022. Spring...
-
Suppose that on October 24 you buy 10 March gold futures contracts for $250 per ounce. At 11:00 am on October 25 you buy 8 more contracts for $259.0 ounce. At the close of trading on October 25, gold...
-
A dwarf planet moves around the Sun on an elliptical orbit with semi-major axis \(a\), semi-minor axis \(b\) and period of revolution \(T\). Determine the speed when its direction is perpendicular to...
-
Halley's comet is visible when it is close to perihelion, which is \(0.586 \mathrm{AU}\) from the Sun. The last perihelion passage was in 1986 and the next one will be in 2061. Determine the distance...
-
A quantity of mass \(M\) in space splits into two fractions, of mass \(\alpha M\) and \((1-\alpha) M\). Assuming fixed separation \(D\) between the two fragments, for what value of \(\alpha\) is the...
-
Calculate the radius \(R_{S}\) of the orbit of a geostationary satellite using the lunar period, \(T=27.3\) d, and the Earth-Moon distance, \(D_{T L}=3.810^{5} \mathrm{~km}\), as data.
-
Show that if the sum and difference between two vectors are perpendicular, then the magnitudes of the two vectors are equal.
-
What impact would each of the following have on real GDP? Would economic well-being increase or decrease as a result? a. On average, people in a country decide to increase the number of hours they...
-
Trade credit from suppliers is a very costly source of funds when discounts are lost. Explain why many firms rely on this source of funds to finance their temporary working capital.
-
There are two biased coins with probabilities of landing heads of 0.8 and 0.4, respectively. One coin is chosen at random (each with probability 1/2) to be tossed twice. You are to receive $100 if...
-
Work through the revised simplex method step by step to solve the model given in Prob. 4.7-5.
-
Consider the following quadratic programming problem: Maximize f (x) = 2x1 + 3x2 x12 x22, subject to x1 + x2 2 and x1 0, x2 0.
-
Explain the building blocks of accounting: ethics, principles, and assumptions.
-
On May 1, 2025, Park Flying School Ltd., a company that provides flying lessons, was started with an investment of 45,000 cash in the business. Following are the assets and liabilities of the company...
-
The historical cost basis results in: a. initially recording assets at cost and adjusting when the current value changes. b. keeping activities of an entity separate and distinct from its owner. c....
Study smarter with the SolutionInn App