There is no single "best" theory but a set of situations when organizational culture fits or does not fit to implementation of particualr strategies. Look at Burton, R., Obel, B., deSanctis. G. Organizational Design: A Step-by-Step Approach. 2nd ed. 2011 to get an overview of that approach.
Strategic approach to people management, focused on knowledge, skills, abilities and capacities possessed by people in an organization in order to innovate and to compete comprises the development of all people-related issues impacting on organization’s strategic and operational objectives.
One of the great thinkers on the link between organisational context and strategy was the duo Sumantra Ghoshal and Chris Bartlett. Their theorising has been branded variously as the quality of management model, the individualised corporation model, the managerial theory of the firm.
In setting the framework for the quality of management model, it was argued that three behaviourial elements were central for an organisation to be dynamic and enjoy sustained competitive advantage; distributed and self-generated initiative, mutual cooperation and collective learning. These three central tenets of the quality of management model proposed that (1) successful firms are able to inspire individual initiative, innovation and creativity in all its people (2) successful firms are able to create and leverage knowledge and so build out organisational learning founded on individual expertise, and (3) successful firms are able to ensure continuous renewal and regeneration.
They opine that managerial action determined and shaped the climate within the organisation. Managers of organisations that were able to establish trust, discipline, support and stretch as attributes of their organisational context would motivate and enable outcomes that were aligned with the objectives and interests of the organisation.
From Strategy to Practice, available at http://www.adb.org/publications/strategy-practice, argues that strategic reversals are quite commonly failures of execution. In many cases, a strategy is abandoned out of impatience or because of pressure for an instant payoff before it has had a chance to take root and yield results. Or its focal point is allowed to drift over time. To navigate a strategy, one must maintain a balance between strategizing and learning modes of thinking. This said, On Organizational Configurations, available at http://www.adb.org/publications/organizational-configurations, notes that what configuration an organization has should tell us a lot about what purpose it aims to fulfill. Toward this, what strategies any organization formulates had better make the most of what strengths and minimize what weaknesses are intrinsic to its structure. I would second Silburn Clarke's reference to Sumantra Ghoshal and Chris Bartlett. At the onset, an organization is a social arrangement to accomplish a collective intent. But, past a critical mass, bureaucracy eventually rears its ugly head and the erstwhile energizing corporate purpose is hijacked. Organizational silos multiply, harden, and task the organization with the challenge of connecting the very subsystems it has contrived to enhance specific contributing functions. Individuals, the very glue that binds the organization, find it ever harder to derive fulfillment.
The institutional-based view can be undertaken for this problem:
«The strategic management setup, which is a purposeful institutional change under such an approach, appears to be a separate task. The set of instruments and methods could be used in order to ensure the efficiency of such transformation process – the gradualness of implementation of developed rules; compensations; application of formal institutional alternatives consistent with the internal informal institutional environment».
You can find the link to corresponding article below. Unfortunately in Russian.
Article Strategic Management Setup via Institutional Change
This is more of an observation than a definitive list of sources, but as you are working and researching within the public sector, it is important to appreciate that the culture is often very different to the culture in progressive and flexible private sector organizations, many of which have become adept at managing change in order to deal with turbulent organizational environments.
Often the issue is the built in rigidity of the public sector. Modern organizations have reduced hierarchy and chains of command, dismantled excessive processes and procedures, and embraced autonomous 'self-managing' teams that design and execute work, acting as internal customers and/or suppliers to other teams, with a supportive culture that empowers the worker. Decision-making is often pushed lower down the organization, and employees are committed, trusted, and allowed to deviate from planned activity where it is deemed necessary to retain organizational agility and effectiveness.
The fact is that public sector organizations are just not good at this. the culture is often one of mistrust and structure and hierarchy are maintained. The 'mindset' of the public sector organization is usually 'different', because being 'competitive' in order to survive is just not the way these organizations are put together. they have guaranteed budgets, rigid procedures to 'protect' public funds, and layers of audit to ensure that expenditure can be justified and authorized.
This means that the public sector organization looks at risk in a completely different way, and this, together with the organizational rigidity, means that cultural norms are deeply embedded and risk-averse.
There are a few exceptions to this in the public sector, but change is slow, and these issues have to be taken into account in researching in the public sector.
I hope this helps - but it is only opinion, albeit gained over some years of researching change.
All the prior input is great... I think that Eero Vaara's work is particularly relevant to your question... specifically that organizational culture influences not simply strategy implementation but the practice of strategy making. Great research question.
The above contributions are interesting. In looking at the factors affecting strategy implementation in the public sector in island economies. I considered institutional, resource dependency and stake holder theories.
These have the potential to impact on the organisations culture.