In a mixed economy, planning will always play a role in the allocation of resources. This is because a mixed economy has elements of a command economy -- one in which the government makes decisions about the economy.
Planning clearly does have a role to play in the allocation of resources in a mixed economy. For example, when the United States government institutes a program like the Medicare prescription drug benefit that Pres. Bush promoted, it helps to determine the allocation of resources. It takes money from tax payers and gives it to drug companies. This allocates money in ways that would not happen if the government had not planned it that way.
A mixed economy is whereby an economy consists of both the private firms running in the market as well as the public sector—which is the governments. They share the limited resources in the country, and the private sector would produce goods that are demanded majority as wants from the economy, and try to achieve a profit maximization by selling at the cheapest prices and lowest costs, they produce a lot of demerit goods. Whereas the government will produce goods that they think are needed by the country and that the citizens would benefit by consuming them, they produce mainly merit goods. Resource allocation is the efficiency in allocating products of goods and services to their right areas and firms, so that they can be sold efficiently. Resource allocation is however, influenced by both the private and public sectors.
Recent developments suggest the superiority of market over planned economies, they may be explained in terms of inefficient resource allocations of planning failures and inefficiencies. Private sectors will always be causing externalities in which the government would plan to get rid of them, and always find ways to correct the faults being caused by the private sectors. Mixed systems will however employ some degree of regulation or planning to correct market failures and improve social welfares, these are usually all provided by the government.