Suppose that there are two factories, O, and 02, supply laptops in a market. The laptops are delivered to the two retail centers of the market, De and D2, with the objective of minimizing the total distribution cost. For the successful distribution. To deliver the laptops to the retail centers, a series of packaging processes are required, which have been done at the three warehouses, T3, T., and Ts, and factory (in case of direct delivery from factory O, to the two retail centers without passing through the warehouses, packaging processes will be done at the corresponding factory. Otherwise, the processes will be done at the warehouses). Note that every distribution link is associated with a distribution cost cijas given by the below table and supply limits of the factories are given by si = 20 and $2 = 30, respectively. Meanwhile, the retail centers are scheduled to receive do = 15 and d7 = 35 laptops, respectively. A matrix of the (link-based) distribution cost cy is given as follows. 1. Draw a network structure showing the nodes (two factories, three warehouses and two retail centers) and transportation links that connect between the nodes an example is given by Tutorial 5 PDF file). 2. State at least four different types of condition, e.g., operational conditions, that make the above distribution problem feasible. 3. Define decision variables, parameters and sets that you need to formulate a mathematical model of the problem. 4. Formulate a mathematical model (including an objective function and a set of constraints) of the above problem 5. Find a cost-minimum distribution plan (values of decision variables) and its total transportation cost (objective function value) by using Excel solver. 0 02 T 21 Ta To 32 32 31 45 D D 4557 24 14 11 02 T: TA T D D 16 10 12 16 Figure. A matrix of the distribution cost cy Suppose that there are two factories, O, and 02, supply laptops in a market. The laptops are delivered to the two retail centers of the market, De and D2, with the objective of minimizing the total distribution cost. For the successful distribution. To deliver the laptops to the retail centers, a series of packaging processes are required, which have been done at the three warehouses, T3, T., and Ts, and factory (in case of direct delivery from factory O, to the two retail centers without passing through the warehouses, packaging processes will be done at the corresponding factory. Otherwise, the processes will be done at the warehouses). Note that every distribution link is associated with a distribution cost cijas given by the below table and supply limits of the factories are given by si = 20 and $2 = 30, respectively. Meanwhile, the retail centers are scheduled to receive do = 15 and d7 = 35 laptops, respectively. A matrix of the (link-based) distribution cost cy is given as follows. 1. Draw a network structure showing the nodes (two factories, three warehouses and two retail centers) and transportation links that connect between the nodes an example is given by Tutorial 5 PDF file). 2. State at least four different types of condition, e.g., operational conditions, that make the above distribution problem feasible. 3. Define decision variables, parameters and sets that you need to formulate a mathematical model of the problem. 4. Formulate a mathematical model (including an objective function and a set of constraints) of the above problem 5. Find a cost-minimum distribution plan (values of decision variables) and its total transportation cost (objective function value) by using Excel solver. 0 02 T 21 Ta To 32 32 31 45 D D 4557 24 14 11 02 T: TA T D D 16 10 12 16 Figure. A matrix of the distribution cost cy
