As Cheerwine looks to expand to all 50 states, there are 7 possible warehouse si
ID: 360772 • Letter: A
Question
As Cheerwine looks to expand to all 50 states, there are 7 possible warehouse sites: Alpha, Beta, Gamma, Delta, Epsilon, Zeta, and Eta.
Each warehouse site has a fixed operating cost per month, and a maximum capacity to supply soda. Note: If a warehouse location is selected, at least 80% of its maximum capacity must be used by the overall distribution solution. Do not address this sequentially in your model but at the same time everything else is considered.
The distribution costs between the distributors (A-J) and the potential warehouse locations are shown below. We will use these costs as both a per-unit cost and a per-truck load cost.
The distribution system needs to deliver exactly the following number of units to each location per month. Note: A distributor can be served by multiple warehouses.
Determine how to best meet demand at the distributors to minimize overall costs by determining where warehouses should be located.
Solve this problem under a number of different scenarios:
1. Overall costs consist of the monthly warehouse costs (accrued only if a warehouse is used) plus the distribution costs of the soda, calculated by the total number of units sent from the warehouse/distributor pair times the cost given in the table.
2. Overall costs consist of the monthly warehouse costs (accrued only if a warehouse is used) plus the distribution costs of the soda, calculated by the total number of units sent from the warehouse/distributor pair times the cost given in the table. Limit the maximum number of units of Cheerwine that can be sent from any one warehouse to any one distributor to a maximum of 80.
3. Overall costs consist of the monthly warehouse costs (accrued only if a warehouse is used) plus the distribution costs of the soda, calculated by 60 times the cost given in the table IF the path (pair) is used. Zero otherwise. As with 2) assume that the maximum truck size (or the maximum number of units of Cheerwine that can be sent from any one warehouse to any one distributor) is 80 units.
Max Costs Alpha 300 9900 Beta 250 7965 Gamma 275 8280 Delta 325 11250 Epsilon 295 9603 Zeta 270 8100 Eta 290 7965Explanation / Answer
Let us define our decision variables as the quantity (number of units) to be transported from ith warehouse to jth distribution center as Xij.
Objective in to minimize Total cost which includes fixed operating costs of warehouses (selected) and the cost of distribution between the warehouses and distributors.
Constraints are about the capacities of warehouses and demands of the distribution centers.
Formulation is as follows:
Solution using excel solver is as follows:
There is no feasible solution with the given constraints
Decision variables Xij Dist. A Dist. B Dist. C Dist. D Dist. E Dist. F Dist. G Dist. H Dist. I Dist. J Sum Max Min Yi=S-(S-1) Costs OperCost Alpha 0 0 0 0 0 0 0 0 0 0 0 300 240 9900 0 Beta 0 0 0 0 0 0 0 0 0 0 0 250 200 7965 0 Gamma 0 0 0 0 0 0 0 0 0 0 0 275 220 8280 0 Delta 0 0 0 0 0 0 0 0 0 0 0 325 260 11250 0 Epsilon 0 0 0 0 0 0 0 0 0 0 0 295 236 9603 0 Zeta 0 0 0 0 0 0 0 0 0 0 0 270 216 8100 0 Eta 0 0 0 0 0 0 0 0 0 0 0 290 232 7965 0 Sum 0 Total operating cost 0 Demand 76 100 90 88 78 66 50 70 56 60 Total distribution costs DijXij SumProduct Dij,Xij = 0 Total overall cost (operating+distribution) 0Related Questions
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