Mr. Stein Khashane as a Director of Logistics & Supply Chain Management for Limpopo Tomato Growers. Limpopo Tomato Growers (LTG) provides over 30% of tomatoes used for making various tomato products in South Africa. The crop is harvested throughout the year and is converted into tomato paste at various farms where they are harvested and transported to various destinations throughout South Africa. The tomato paste is then supplied to various destinations where they are made into various finished products such as ketchup, tomato salad, food colourings, tomato juice, etc. While sales are seasonal, there is steady demand throughout the year. The production pattern for finished product at the conversion plants tend to this steady demand. The raw tomatoes are converted into tomato paste at three orchards in Tchakuma, Tzaneen and Bela Bela. There are five tomato paste conversion plants in Silverton, Durban, Cape Town, Kimberly & Bloemfontein. The table below provide a summary of the unit transportation cost from each tomato paste processing orchard to each conversion station, the unit processing costs at each processing cost at each orchard, the production capacity at each orchard, and the tomato paste requirement at each conversion plant during a given 4-week period. The firm would like to determine a production schedule which has the lowest total production and transportation cost. Table 1. Input Data for LTG Transportation Cost to Destinations Production Capacity Silverton Durban Kimberly Cape Bloemfontein Sources Cost Tonnes Town Tchakuma R5,240 4,600 R250 R480 R540 R670 R750 Tzaneen R5,410 2,900 R110 R440 R570 R610 R810 Bela Bela R6,120 1,700 R570 R330 R320 R100 R360 Amount Required in Tonnes 2,100 1,700 1,600 1,300 2,200 Mr. Stein Khashane, the Director of Logistics & Supply Chain Management has sought your help in determining a production schedule that can help him in obtaining the lowest total production and total transportation costs. Section A [8 Marks Considering the above, a) Represent the above information as a Network Diagram (2 Marks) b) Formulate the scenario above as an LP Model (2 Marks) c) Implement the formulation in Excel following goals/guidelines for good spreadsheet design and solve using solver (4 Marks) Mr. Stein Khashane as a Director of Logistics & Supply Chain Management for Limpopo Tomato Growers. Limpopo Tomato Growers (LTG) provides over 30% of tomatoes used for making various tomato products in South Africa. The crop is harvested throughout the year and is converted into tomato paste at various farms where they are harvested and transported to various destinations throughout South Africa. The tomato paste is then supplied to various destinations where they are made into various finished products such as ketchup, tomato salad, food colourings, tomato juice, etc. While sales are seasonal, there is steady demand throughout the year. The production pattern for finished product at the conversion plants tend to this steady demand. The raw tomatoes are converted into tomato paste at three orchards in Tchakuma, Tzaneen and Bela Bela. There are five tomato paste conversion plants in Silverton, Durban, Cape Town, Kimberly & Bloemfontein. The table below provide a summary of the unit transportation cost from each tomato paste processing orchard to each conversion station, the unit processing costs at each processing cost at each orchard, the production capacity at each orchard, and the tomato paste requirement at each conversion plant during a given 4-week period. The firm would like to determine a production schedule which has the lowest total production and transportation cost. Table 1. Input Data for LTG Transportation Cost to Destinations Production Capacity Silverton Durban Kimberly Cape Bloemfontein Sources Cost Tonnes Town Tchakuma R5,240 4,600 R250 R480 R540 R670 R750 Tzaneen R5,410 2,900 R110 R440 R570 R610 R810 Bela Bela R6,120 1,700 R570 R330 R320 R100 R360 Amount Required in Tonnes 2,100 1,700 1,600 1,300 2,200 Mr. Stein Khashane, the Director of Logistics & Supply Chain Management has sought your help in determining a production schedule that can help him in obtaining the lowest total production and total transportation costs. Section A [8 Marks Considering the above, a) Represent the above information as a Network Diagram (2 Marks) b) Formulate the scenario above as an LP Model (2 Marks) c) Implement the formulation in Excel following goals/guidelines for good spreadsheet design and solve using solver (4 Marks)
