Preview

Assignment #4: Case Problem “Stateline Shipping and Transport Company”

Good Essays
Open Document
Open Document
1325 Words
Grammar
Grammar
Plagiarism
Plagiarism
Writing
Writing
Score
Score
Assignment #4: Case Problem “Stateline Shipping and Transport Company”
Assignment #4: Case Problem “Stateline Shipping and Transport Company”

1) This transportation model problem consists of 18 decision variables, representing the number of barrels of wastes product transported from each of the 6 plants to each of the 3 waste disposal sites: [pic]= Number of Barrels transported per week from plant ‘i’ to the j-th waste disposal site, where i = 1, 2, 3, 4, 5, 6 and j = A, B, C.
The objective function is to minimize the total transportation cost for all shipments. So the objective function is the sum of the individual shipping costs from each plant to each waste disposal site:
Minimize Z = 12[pic]+ 15[pic]+ 17[pic]+ 14[pic]+ 9[pic]+ 10[pic]+ 13[pic]+ 20[pic] +11[pic] +17[pic] +16[pic] +19[pic] +7[pic] +14[pic] +12[pic] +22[pic] +16[pic] +18[pic]
Let’s assume the constraints are the number of barrels of wastes available per week at each plant and the number of barrels of wastes contained at each waste disposal site. Therefore there are 9 constraints- one for each plant supply and one for each waste disposal site’s demand.
The six supply constraints are: [pic]+ [pic]+ [pic] = 35 [pic]+ [pic]+ [pic] = 26 [pic]+ [pic] +[pic] = 42 [pic] + [pic] +[pic] = 53 [pic] +[pic] +[pic] = 29 [pic] + [pic] +[pic] = 38
For example, let’s say the supply constraint [pic]+ [pic]+ [pic] = 35 represents the number of barrels transported from the plant Kingsport to all the three waste disposal sites. The amount transported from Kingsport is limited to the 35 barrels available.
The three demand constraints are: [pic]+ [pic]+ [pic]+[pic]+ [pic]+[pic] ≤ 65 [pic]+ [pic]+ [pic]+ [pic]+[pic] +[pic] ≤ 80 [pic]+ [pic]+[pic]+ [pic]+[pic] +[pic] ≤ 105 Here the demand constraint [pic]+ [pic]+ [pic]+[pic]+ [pic]+[pic] ≤ 65 represents the number of barrels transported to the waste disposal site Whitewater from all the six plants. The barrel of wastes that can accommodate in the waste disposal site Whitewater is limited to 65 barrels.

You May Also Find These Documents Helpful

  • Good Essays

    The problem basically consists of finding the optimum set of routes that represent the lowest possible total cost and/or total travel time. The plant is dealing with the repositioning of trucks to serve its supply demand and determining a number of transportation units that optimally balance supply requirements against the cost of maintaining the transportation units. In order to increase truck utilization and achieve better performance, the plant has to adequately and efficiently ensure the scheduling of a steady supply of hogs.…

    • 1274 Words
    • 6 Pages
    Good Essays
  • Satisfactory Essays

    Optimization and Brand

    • 846 Words
    • 4 Pages

    30 units of nutrient C are available so the mathematical equation of constraint 1 is…

    • 846 Words
    • 4 Pages
    Satisfactory Essays
  • Powerful Essays

    In linear programming, if there are three constraints, each representing a resource that can be used up, the optimal solution must use up all of each of the three resources.…

    • 1510 Words
    • 7 Pages
    Powerful Essays
  • Satisfactory Essays

    The Goal Essay

    • 822 Words
    • 4 Pages

    The second constraint for the manufacturing plant is material because they have too much inventory on hand. Since they have so much of an excess of material on hand this causes for them to be spending more money than they need to right now on materials that they are not even going to use for another seven months. Also, the manufacturing plant has to spend…

    • 822 Words
    • 4 Pages
    Satisfactory Essays
  • Good Essays

    Let Xij i=1,2,3,4,5,6; j =1,2,3 denote the quantity of waste transported from i-th plant to j-th waste disposal centre. Then the objective function Z representing the cost and different constraints of the problem can be written as…

    • 1284 Words
    • 6 Pages
    Good Essays
  • Satisfactory Essays

    Transshipment Models

    • 403 Words
    • 2 Pages

    The assignment model is for a specific form of transportation model in which all supply and demand values are…

    • 403 Words
    • 2 Pages
    Satisfactory Essays
  • Good Essays

    This objective function is subject to some constraints. These constraints can be classified in to three categories.…

    • 1401 Words
    • 6 Pages
    Good Essays
  • Better Essays

    Case 3.2 Sonoma

    • 1831 Words
    • 8 Pages

    Further, it is given that the proportion of Brand I should be between 40% and 60%. The corresponding constraint becomes [pic]…

    • 1831 Words
    • 8 Pages
    Better Essays
  • Satisfactory Essays

    Biology Test

    • 837 Words
    • 4 Pages

    1) Transportation models may be used when a firm is trying to decide where to locate a new…

    • 837 Words
    • 4 Pages
    Satisfactory Essays
  • Good Essays

    Mathematical Methods

    • 1527 Words
    • 7 Pages

    Select the north west (upper left hand) corner cell of the transportation table and allocate as many units as possible equal to the minimum between available supply and demand.…

    • 1527 Words
    • 7 Pages
    Good Essays
  • Good Essays

    Micoeconomics

    • 649 Words
    • 3 Pages

    The quantity supplied for prices P(a), P(b), P(c), P(d) were calculated based on the MC’s of each type – if the price is below the MC of the firm, the firm would stop its production. The quantities to be supplied for each price level is like below:…

    • 649 Words
    • 3 Pages
    Good Essays
  • Good Essays

    Sonoma Valley Wines Case

    • 1190 Words
    • 4 Pages

    There are four groups of conditions, three with four constraints each and one with two constraints: (i) sales must be less than demand, (ii) sales must be less than production, (iii) sales must be greater than the minimum values given in the case, and (iv) cash balance conditions each year. Thus, the total number of constraints is 14.…

    • 1190 Words
    • 4 Pages
    Good Essays
  • Powerful Essays

    Lp Free Chapter 6 Tmh

    • 14599 Words
    • 59 Pages

    Outline of Graphical Solution Method, 6S-4 Plotting Constraints, 6S-6 Identifying the Feasible Solution Space, 6S-9 Plotting an Objective Function Line, 6S-9 Redundant Constraints, 6S-13 Solutions and Corner Points, 6S-13 Minimization, 6S-14 Slack and Surplus, 6S-15…

    • 14599 Words
    • 59 Pages
    Powerful Essays
  • Satisfactory Essays

    Bio Pharma

    • 992 Words
    • 4 Pages

    *Total Transportation Cost=SUMPRODUCT of each plant’s Highcal production with corresponding transportation costs (TABLE 6-23) plus the SUMPRODUCT of each plant’s Relax production with corresponding transportation costs (TABLE 6-23)…

    • 992 Words
    • 4 Pages
    Satisfactory Essays
  • Good Essays

    As per the CPHEEO norms, the water supply schemes are designed for 135 lpcd for Corporations and ULBs having UGSS. Provisions are also made for fire fighting demands as per CPHEEO Manual. Bulk, Industrial and other demands are considerd as per the TWAD Guidelines. The details of water demands considered for Madurai Corporation is as presented in Table IV.1.…

    • 2010 Words
    • 9 Pages
    Good Essays