The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units. Product is shipped to regional distribution centers located in Boston, Atlanta, and Houston. Because of an anticipated increase in demand, Martin-Beck plans to increase capacity by constructing a new plant in one or more of the following cities: Detroit, Toledo, Denver, or Kansas City. The estimated annual fixed cost and the annual capacity for the four proposed plants are as follows: Plant Number Proposed Plant Annual Fixed Cost Annual Capacity 1 Detroit $150,000 10,000 2 Toledo $275,000 20,000 3 Denver $400,000 30,000 4 Kansas City $475,000 40,000 The company's long-range planning group developed forecasts of the anticipated annual demand at the distribution centers as follows. Distribution Center Number Distribution Center Annual Demand 1 Boston 20,000 2 Atlanta 30,000 3 Houston 30,000 The shipping cost per unit from each plant to each distribution center is as follows. Distribution Centers Plant Site Boston Atlanta Houston Detroit 5 2 3 Toledo 4 3 4 Denver 9 7 5 Kansas City 10 4 2 St. Louis 8 4 3 (a) Formulate a mixed-integer programming model that could be used to help Martin-Beck determine which new plant or plants to open in order to satisfy anticipated demand and minimize total cost (in thousands of dollars). (Let xij = units shipped in thousands from plant i to distribution center j with the existing plant in St. Louis being plant number 5. Let y1 = 1 if a plant is constructed in Detroit and 0 if not, y2 = 1 if a plant is constructed in Toledo and 0 if not, y3 = 1 if a plant is constructed in Denver and 0 if not, and y4 = 1 if a plant is constructed in Kansas City and 0 if not.) Min s.t.Detroit Capacity Toledo Capacity Denver Capacity Kansas City Capacity St. Louis Capacity Boston Demand Atlanta Demand Houston Demand xij ≥ 0 for all i and j and y1, y2, y3, y4 binary (b) Solve the model you formulated in part (a). What is the optimal cost (in $)? $ What is the optimal set of plants to open? (Select all that apply.) DetroitToledoDenverKansas City
Critical Path Method
The critical path is the longest succession of tasks that has to be successfully completed to conclude a project entirely. The tasks involved in the sequence are called critical activities, as any task getting delayed will result in the whole project getting delayed. To determine the time duration of a project, the critical path has to be identified. The critical path method or CPM is used by project managers to evaluate the least amount of time required to finish each task with the least amount of delay.
Cost Analysis
The entire idea of cost of production or definition of production cost is applied corresponding or we can say that it is related to investment or money cost. Money cost or investment refers to any money expenditure which the firm or supplier or producer undertakes in purchasing or hiring factor of production or factor services.
Inventory Management
Inventory management is the process or system of handling all the goods that an organization owns. In simpler terms, inventory management deals with how a company orders, stores, and uses its goods.
Project Management
Project Management is all about management and optimum utilization of the resources in the best possible manner to develop the software as per the requirement of the client. Here the Project refers to the development of software to meet the end objective of the client by providing the required product or service within a specified Period of time and ensuring high quality. This can be done by managing all the available resources. In short, it can be defined as an application of knowledge, skills, tools, and techniques to meet the objective of the Project. It is the duty of a Project Manager to achieve the objective of the Project as per the specifications given by the client.
| Plant Number | Proposed Plant | Annual Fixed Cost | Annual Capacity |
|---|---|---|---|
| 1 | Detroit | $150,000 | 10,000 |
| 2 | Toledo | $275,000 | 20,000 |
| 3 | Denver | $400,000 | 30,000 |
| 4 | Kansas City | $475,000 | 40,000 |
| Distribution Center Number |
Distribution Center |
Annual Demand |
|---|---|---|
| 1 | Boston | 20,000 |
| 2 | Atlanta | 30,000 |
| 3 | Houston | 30,000 |
| Distribution Centers | |||
|---|---|---|---|
| Plant Site | Boston | Atlanta | Houston |
| Detroit | 5 | 2 | 3 |
| Toledo | 4 | 3 | 4 |
| Denver | 9 | 7 | 5 |
| Kansas City | 10 | 4 | 2 |
| St. Louis | 8 | 4 | 3 |
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