The company produces navels at three plants, which can be delivered directly to the two customers or it can first be shipped to the two warehouses and then to the customers. Shipments between plants are allowed. This also applies to between warehouses and between customers. The cost of producing the navels is the same at each plant; as a result, the company is only concerned with minimising the total shipping cost incurred in meeting customer demands. The production capacity of each plant (in tons per year) and the customer demand are summarised in the table below: Plant Capacity Plant 1 400 Plant 2 375 Plant 3 350 Customer Demand Customer 1 500 Customer 2 450 The cost (in thousands of dollars) of shipping a ton of the product between each pair of locations is listed in the table below where a blank indicates that the company cannot ship on that route: From node To node Plant 1 Plant 2 Plant 3 Warehouse 1 Warehouse 2 Customer 1 Customer 2 Plant 1 1 1 6 7 15 15 Plant 2 1 1 5 6 16 16 Plant 3 1 1 7 6 14 15 Warehouse 1 3 6 8 Warehouse 2 3 7 7 Customer 1 2 Customer 2 2 The management has set the maximum flow between nodes (in tons) as shown in the table below: From node To node Plant 1 Plant 2 Plant 3 Warehouse 1 Warehouse 2 Customer 1 Customer 2 Plant 1 200 200 250 250 200 200 Plant 2 200 200 250 250 200 200 Plant 3 200 200 250 250 200 200 Warehouse 1 250 250 250 Warehouse 2 250 250 250 Customer 1 200 Customer 2 200 Since sometimes the demands are fluctuated, the company plans to have safety stock of 100 tons at Warehouse 1 and 50 tons at Warehouse 2. The company wantsto determine a minimum-costshipping strategy.
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.
The company produces navels at three plants, which can be delivered directly to the two customers
or it can first be shipped to the two warehouses and then to the customers. Shipments between plants
are allowed. This also applies to between warehouses and between customers.
The cost of producing the navels is the same at each plant; as a result, the company is only concerned
with minimising the total shipping cost incurred in meeting customer demands. The production
capacity of each plant (in tons per year) and the customer demand are summarised in the table below:
| Plant | Capacity |
| Plant 1 | 400 |
| Plant 2 | 375 |
| Plant 3 | 350 |
| Customer | Demand |
| Customer 1 | 500 |
| Customer 2 | 450 |
The cost (in thousands of dollars) of shipping a ton of the product between each pair of locations is
listed in the table below where a blank indicates that the company cannot ship on that route:
From node To node
Plant 1 Plant 2 Plant 3 Warehouse 1 Warehouse 2 Customer 1 Customer 2
Plant 1 1 1 6 7 15 15
Plant 2 1 1 5 6 16 16
Plant 3 1 1 7 6 14 15
Warehouse 1 3 6 8
Warehouse 2 3 7 7
Customer 1 2
Customer 2 2
The management has set the maximum flow between nodes (in tons) as shown in the table below:
From node To node
Plant 1 Plant 2 Plant 3 Warehouse 1 Warehouse 2 Customer 1 Customer 2
Plant 1 200 200 250 250 200 200
Plant 2 200 200 250 250 200 200
Plant 3 200 200 250 250 200 200
Warehouse 1 250 250 250
Warehouse 2 250 250 250
Customer 1 200
Customer 2 200
Since sometimes the demands are fluctuated, the company plans to have safety stock of 100 tons at
Warehouse 1 and 50 tons at Warehouse 2. The company wantsto determine a minimum-costshipping
strategy.
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