Is it right for a Project Manager questioning the prices which purchased by Procurement Dept?

To purchase wisely, you need to buy the right quality and quantity of materials or products at the best possible price and at the appropriate time from the best vendor.

Project manager have no rights to raise question about the prices. The full responsibilty is only for purchasing manager. Purchasing need not be the purchasing manager's sole duty; in fact, your business may not do enough purchasing to require a full-time purchasing manager. You should select an employee who can handle purchasing, as well as the other duties he or she my already have. This individual should be able to communicate clearly with your business's suppliers. Although purchasing duties probably won't occupy all of this individual's time, there is more to purchasing than placing orders. The purchasing manager will have to gather orders, make sure they are complete, and stay within any limits the company may have set on spending, select an appropriate vendor, order the goods, check their condition upon receipt, make sure the invoice is correct, and speed payment of the invoice by forwarding it to the accounting department.

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project manager can about pricing since he is responsible for costing at the same time purchase team need to share the reason for pirce increase for mutual understanding and for completing the project successfully

Project manager can ask for perticular make or with perticular specification. But he should not ask for the price coz he has been provided with what is needed to him. It is role of purchase department to procure best quality material, at best price, at right time and from right vendor. It is purchasers duty to control the cost while discussing the specifications with project manager before it is purchased in order to keep control on project budget.

but once it is purchased, there should not be any differences unless, project manager feels there is vested interest of purchaser.

Project manager has always the right to ask about the pricing of his tools/ materials related to his project to keep truck on his project cost & spend, and be within the budget.

project manager can ask the price for controlling the project budget before purchasing the material.