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A Chance-Constrained Mixed Integer Programming Model for Internal Control Design.

The Accounting Review 1980 55(4), 578-593
Abstract ABSTRACT: Modeling of the internal control system provides an element of structure and objectivity to the design and evaluation of the system. A model for the design of an internal control system is proposed which minimizes system cost subject to management-set error reduction probability goals for designated error types. The model chooses from a set of preventive controls with given error reduction rates in arriving at the minimum cost solution, and can accommodate multiple combinations of controls and error types, as welt as restrictions on the use of controls. The model is also useful to the external auditor for evaluation purposes, especially since the system is evaluated by error type.

The Use of the Generalized Shapley Allocation in Joint Cost Allocation.

The Accounting Review 1980 55(2), 269-287
ABSTRACT: The simple Shapley allocation has been recently proposed by several authors as a useful allocation scheme in the joint cost allocation problem. However, while satisfying several useful allocation axioms, it does have a least two debilities. First, it is a unique solution and does not permit any flexibility by management. Second, it may fail to satisfy the core conditions in many relevant situations, causing independent action by subcoalitions of divisions which is to the detriment of the corporation. A generalization of the simple Shapley allocation is proposed which maintains most of the favorable properties of the simple Shapley allocation while removing these two weaknesses.

The Use of Core Theory in Evaluating Joint Cost Allocation Schemes.

The Accounting Review 1977 52(3), 616-627
ABSTRACT: The problem of joint cost allocation is examined with particular emphasis on the possibility that some allocation schemes may result in divisional decisions which are suboptimal at the corporate level. Such decisions may arise whenever the marginal cost function for the allocated cost is decreasing, and the joint cost allocation scheme results in a charge to a division (or group of divisions) which exceeds the charge which that division (or group of divisions) could incur by acting independently. The theory of the core is used to establish criteria that any cost allocation scheme should meet if it is to avoid encouraging these suboptimal decisions. Four cost allocation schemes are studied and evaluated using the core criteria. It is shown that three of these schemes, including the activity level allocation scheme, satisfy the core criteria; however, a fourth scheme, which was recently proposed, is satisfactory in only certain cases.