1 costs of shared capacity resources to the various

1    
Theoretical foundation

This chapter aims to provide an understanding of capacity
utilization and its role in the cost accounting system. In order to do so, the
relevant concepts of capacity planning, capacity management and ABC systems are
discussed in accordance with the scope of this thesis work. Moreover, an
overview of the simulation-based research work focusing on the issue of
capacity has been given.

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1.1          
Role of product
costs

The function of a product costing system is to allocate the
costs of shared capacity resources to the various products offered by a firm.
This allocation is performed for several purposes. First, cost allocation
enables firms to value their inventories and subsequently compute their incomes
as per the generally accepted accounting principles. Second, the allocations
help managers to make critical decisions pertaining to product and capacity
planning. Finally, cost allocations are used by managers to induce desired
organizational behavior  (Balakrishnan et al. 2012).

The costs of capacity resources allocated to products can be
classified into two broad categories in accordance with the ABC. The first
category consists of costs incurred by a firm pertaining to resources which are
acquired as needed.  Due
to a clear dependence between the supply and usage of these resources in the
short-run, these resources have no idle capacity and are often referred as
“variable costs”.  The
second category of costs known as “fixed costs” comprises of costs pertaining
to resources which are committed or acquired in advance of their usage  (Kaplan, Robin Cooper 1992)Cit typo. In other
words, these resources known as the capacity resources entail up-front cost
commitments and therefore it is uneconomical for firms to acquire them on an as
needed basis. Consequently, firms incur opportunity costs when the installed
capacity is insufficient to meet future market demand and on the other hand,
they incur costs of idle capacity in case the capacity is in excess of the
market demand in a given period. The long-range capacity planning in a firm
aims to determine the optimal capacity by trading off the expected cost from
over- and under-stocking of these resources (Balachandran et al. 1997). As this thesis work deals
with capacity utilization, the capacity costs in the remaining portion of this
report imply the fixed costs/costs incurred for resources in advance of their
usage.

The objective of this thesis work is to analyze the effects
of capacity utilization on product costs. In such an enquiry, it becomes
important to understand the reason why firms might install surplus capacity at
the time of capacity planning. Section 2.1.1
therefore gives an overview on capacity and product planning while section 2.1.2
further details the role of product costs in solving this joint problem.     

1.1.1   ???

2.1.1  
Capacity
and product planningKGM1 

The capacity-planning problem for firms
refers to the decision of determining optimal quantity of resources to be
acquired to meet future customer needs. Along with capacity-planning the firms
must simultaneously solve the product-planning problem, the solution to which
decides the product portfolio of firms. Since the set of products whichproducts, which
a firm decides to produce has an influence on the required capacity levels to
be installed, the two problems are interrelated in nature (Balakrishnan, Sivaramakrishnan
2002).
The solution to the this joint problem theoretically requires solving of a
stochastic optimization program which aims at maximizing the firm profit
subject to market and resource constraints. The formulation of this problem
becomes thereby computationally complex and informationally demanding in itself
(Balakrishnan et al. 2011).

 Let us consider a
single-period capacity planning problem faced by a multi-product firm with N products and M capacity resources. In order to understand the dilemma faced by a
firm regarding underinvesting or overinvesting in resources at the time of
capacity planning, assume the resources impose “soft capacity constraints”.
This implies that the firm has a flexibility to acquire resources at a later
time but against a penalty factor in case the demands on resources exceed the
capacities installed in subsequent time period. Then in accordance to Banker & Hughes, (1994) the firm aims to maximize
their profit as shown in equation (1),
while equations (2)
and (3)
represent the demand and resource constraints imposed on the firm. 

 

(1)

Subject to:

 

 

 

(2)

 

(3)

 

(4)

Where,

Pi: price per unit of product i

vi: variable cost per
unit of product i

 

: anticipated demand for a product i as a
function of its price

cj:
normal cost per unit of cost driver for activity j

Lj:
capacity in cost driver units implied by resources committed to activity j

?j>1:
penalty factor for emergency purchase of resources committed to activity
j

Rj:
total capacity in cost driver units for activity j purchased under
emergency

mij:
number of cost driver units of activity j consumed by each unit of
product i

The penalty factor ?j in equation (1)
implies the trade-off between under-investment and over-investment in resources
at the time of capacity planning, which might lead firms to install surplus
capacities rather than acquiring resources against a high penalty in case of
shortage (Banker, Hughes John S. 1994). In addition, the equations
above reflect the computational complexities associated with determining the
required capacity levels. In order to solve the quadratic problem theoretically
as per equation (1), the firm must anticipate future product prices, product demand
distributions as well as premiums paid for emergency purchase of resources at
the portfolio level.  These complexities induce
firms to adopt simple, implementable rules to plan their capacity and product
portfolios (Balachandran et al. 1997). Product-based capacity
planning is one such rule employed by firms which will be explained in the
following section.