Final answer:
The false statements concerning the transshipment model are options (d) and (e). A transshipment node should not have a negative RHS value, and a supply node should actually have a positive RHS value.
Step-by-step explanation:
The student is asking about the characteristics of nodes within the transshipment model, which is a topic within operations research, a branch of applied mathematics used in the optimization of complex processes or systems. Specifically, the question pertains to understanding the flow balance at various nodes in a transshipment network, crucial for solving optimization problems involving the transportation of goods through an intermediate network.
Let's examine which statements are false:
- Supply nodes: At a supply node, the outflow is greater than the inflow, which is correctly stated in option (a).
- Transshipment nodes: Here, the inflow equals the outflow, meaning they are neither sources nor sinks of the product; thus, (b) is a true statement.
- Demand nodes: These should indeed exhibit a positive RHS value since they represent destinations with certain demands, making (c) a true statement.
- However, option (d), stating that the flow balance for a transshipment node should show a negative RHS value, is incorrect since the inflow equals the outflow at such nodes.
- Additionally, option (e), which postulates that the flow balance for a supply node should show a negative RHS value, is also false. In the case of a supply node, the RHS value should be positive to reflect excess supply.