Application of stochastic linear programming in managerial accounting. Scenario analysis approach

• Pages: 184-204
• DOI: https://doi.org/10.1108/IJAIM-12-2018-0148
• Date: 29 January 2020
• Published date: 29 January 2020
• Author: Di Wu,Yong Choi,Ji Li
• Subject Matter: Accounting/accountancy,Accounting & Finance

Application of stochastic linear

programming in managerial

accounting

Scenario analysis approach

Di Wu,Yong Choi and Ji Li

Department of Accounting and Finance, California State University Bakersf‌ield,

Bakersf‌ield, California, USA

Abstract

Purpose –This paper aims to focus on applications of stochastic linear programming (SLP) to managerial

accounting issues by providing a theoretical foundation and practical examples. SLP models may have more

implications –and broader ones –in industrypractice than determinis ticlinear programming (DLP) models do.

Design/methodology/approach –This paper introduces both DLP and SLP methods. In addition,

continuous and discrete SLP models are explained.Applications are demonstrated using practical examples

and simulations.

Findings –This research work extends the current knowledge of SLP, especially concerning managerial

accounting issues. Through numerical examples, SLP demonstrates itsgreat ability of hedging against all

scenarios.

Originality/value –This study servesas an addition to building a cumulative traditionof research on SLP

in managerialaccounting. Only a few SLP studies in managerial accounting havefocused on the development

of such an instrument. Thus, the measurement scales in this research can be used as the starting point for

furtherref‌ining the instrument of optimization in managerial accounting.

Keywords Scenario analysis, Data analytics, Deterministic linear programming,

Stochastic linear programming

Paper type Technical paper

Introduction

Operations management focuses on processing general business information for better

decision-making with the aim of achieving a greater degree of eff‌iciency and effectiveness

while managerial accounting uses accounting information as inputs in its decision-making

with a focus on accounting objectives,such as making budgets, planning business activities,

assessing business risks andevaluating business performance. Overlap between operations

management and managerial accounting can be seen in many business operations.

However, differences between these two f‌ields also exist. In some cases, applications of

operations managementmethods may lead to business outcomes that cannot be captured or

measured through internal or external accounting. This work studies an important subject:

sensitivity and scenario analysis in allocations of constrained business resources with an

aim of maximizing prof‌its and contribution margins in production. The subject uses

operations management tools to address important managerial accounting issues (Togo,

2008;Horngren et al.,2015). For example, when companies have limited capital budgets,

labor hours and raw materials, it becomes important to know how to optimally allocate

these resources to manufacturemultiple products.

IJAIM

28,1

184

Received14 December 2018

Revised2 March 2019

26March 2019

Accepted2 April 2019

InternationalJournal of

Accounting& Information

Management

Vol.28 No. 1, 2020

pp. 184-204

© Emerald Publishing Limited

1834-7649

DOI 10.1108/IJAIM-12-2018-0148

The current issue and full text archive of this journal is available on Emerald Insight at:

https://www.emerald.com/insight/1834-7649.htm

Effective allocation of resourcesand its impact on businesses have received a great deal

of attention in both academia and practitioner world. Research shows that effective

allocation of resources in budgeting can help reduce slack, improve business performance

and have effective performanceevaluation (Fisher et al., 2002;Arnold and Gillenkirch, 2015).

It can be particularly importantfor businesses in critical situations, such as scarce resources

and economic crisis (Becker et al.,2015). Similar results can also be found in non-prof‌it and

governmental accounting areas (Anessi-Pessina et al., 2016). Many of these issues can be

approached by linearprogramming (LP) tools and methods, such as simplex method,binary

programming, integer programmingand quadratic programming (Summers, 1972;Chvatal,

1983) that are well emphasized in operations managerial areas. Furthermore, LP can be

extremely useful to CPA f‌irms in staff‌ing plans (Killough and Souders, 1973;Siegel et al.,

1998). Goal programming and fuzzy set approaches are applied to multi-objective planning

tasks (Gardner et al.,1990;Kwaket al.,2003;Krügerand Hattingh, 2006). Applications of LP

methods are also seen in areas of cost–volume–prof‌it analysis, performance-based

budgeting, production, activity-based costing and supply chain management (Tsai and Lin,

2004;Kostakis et al.,2008;Bhagwat and Sharma, 2009;Hung, 2011;Zamf‌irescu and

Zamf‌irescu, 2013). Many of these applications can be facilitated through computer

information technologiesand platforms.

In most cases, these problems are formulated as deterministic models, using either

predicted values or expected valuesof scenarios. Scenarios in practice can be either discrete

or continuous. Scenario analysis, in application of operations management tools, can

def‌initely be useful to companies in planning (Mietznerand Reger, 2005;Drury, 2007). Each

scenario can be formulated as a simple operations research problem and solved with an

optimal solution. However, in practice, a company can have numerous scenarios. When it

comes to decision-making, implementing all these different scenarios can be simply

impossible. One way to consider all scenarios is to use expected values of input variables,

and then a simple deterministic linearprogramming (DLP) problem is solved. However, the

solutions to this problem may not necessarily determine the maximum amount of prof‌itin

the long run and there is certainly a lack of consideration paid to hedging all uncertainties

with potential businessrisks.

A solution to the stochastic linear programming (SLP) problem can be useful to hedge

against various scenarios as well as risks (Kall and Mayer, 2011;Consigli and Moriggia,

2014). It receives much interest from practitioners and researchers (Hoffman et al.,2004;

Geyer et al.,2009;Trusevych et al.,2014;Righetto et al.,2016). Applications of stochastic

programming are found in forest planning(Garcia-Gonzalo et al., 2016), cost–volume–prof‌it

analysis (Yunker, 2001;Chrysaf‌is and Papadopoulos, 2009), production and inventory

planning (Golari et al.,2017). The concept of recourse is a characteristic of SLP, and when a

random event takes place, corrective actionwill then happen. For example, a company may

not know its budget or the price of materials, but once the information is available, the

company then knows how to allocateits resources to maximize its prof‌its or its contribution

margin. Business uncertaintiesare serious challenges to management and operations. In the

meantime, companies and businesses make a great effort to either f‌ind solutions or turn

uncertainties into opportunities (Zhen, 2014;Brink, 2017;Pomerol, 2018). The optimal

solution to one scenario may not be applicableto others. Therefore, applications of SLP and

models may be critical as determiningwhich solution is optimal in the long run requires that

all scenarios are hedged. Hedging is a very important concept and a tool in the f‌ields of

f‌inancial managementand business operations.

Prior literature shows thatthe use of hedging increases f‌irm value and f‌irm performance,

especially during the f‌inancial crisis (Pincus and Rajgopal, 2002;Karim and Didier, 2010;

Stochastic

linear

programming

185