Using the learning curve to maximize IT productivity; a decision making analysis model for timing software upgrades, the main focus is in Ojelanki Ngwenyama, Aziz Guergachi, & Tim McLaren.

This paper  describes the problem most managers have in deciding whether to upgrade or not, the time for upgrading, the level of productivity before, during and after upgrade, and provide the mathematical model that help in this  decision.

In the present age, all companies use computers in one way or another. The difference is the magnitude of its use. Whatever the level of use, these computers use programmes or soft wares that need to be upgraded once in a while depending on their lifecycles (Kevin 2006 p. 69).

The claim highlighted in this paper is that decision making is problematic to organisations regarding the perfect time to upgrade IT soft wares. After an announcement of a new version of the software, should the organisation upgrade immediately, should they wait, or postpone it for a while? These are the dilemmas a company is faced with. As such, this claim is an advancement of Information system theoretical knowledge and professional practice (Barry 2006 p. 74).

The research done in this paper is predictive, explanatory and prescriptive. It qualifies as predictive because it proposes a model (mathematical model) that if utilized, can predict outcomes in different situations. As will be seen, the case studies are dividing into Situations 1-4. It's also explanatory because the framework explains the behaviour of productivity in comparison to labour and investments. The S curve also explains the behaviour of learning and production. Finally it is prescriptive because the method can be use to achieve desired outcomes if observed well (Douglas 2007 p.274).

Key word to observe in this paper includes:

IT - Information Technology

Information Systems

Software, refers to computer programmes

Labour unit, value and rate

Software upgrades

Learning curve S curve)

Instantaneous learning

1.  Introduction

Firms spend a lot of money buying soft wares, upraising and implementing them with the hope of attracting an increase in productivity levels productivity is achieved by a complete maximization of performance. It is proven that investing in IT labour produces high profits in terms of productivity. This is because labour is the variable directly related to profits. There has been past empirical studies on ways to improve productivity in an organisation, i.e., increasing capital and employee motivation. However the learning curve was ignored for some time till recently when it became apparent that it could be a major tool for effective decision making (Nancy & Susan 2003 p. 213).

Every organisation has a learning/experience curve, witnessed by past performance and behaviour with implementation of a new software. If studied well, it is evident that there is a relationship between the learning curve, the timing of investment and the organisations productivity. It is therefore very important abd should be taken serious. Studies prove that there is always a drop in productivity for while when technology is first implemented, before a rise again. This rise is usually above the previous level of production before implementation. This is explained by the resistance new technologies receive from employees before they understand its importance and learn how to use it. It could also be due to the amount of learning required to understand the new technology.

The problem of upgrading software

Upgrading new software is problematic in terms of making decision as to the time when this should be done. Most IT soft wares used in the market have life cycles. For it to remain effective and beneficial to the organization, the soft wares need to be upgraded regularly to maximise their profits , software vendors put time limits for the viability of soft wares after which they are not as effective as before. They later come up with revised versions of old soft wares and requires organisations to upgrade the old version or face technical support discontinuation (Adler& Alexander 2004 p.332).

Apart from this limitation, companies still need to upgrade their soft wares or loose productivity to competitors. Sometimes upgrading is compulsory especially if one upgraded application is no longer compatible with the existing ones. This case requires all the application soft wares upgraded, this brings significant cost to the organisation. The costs incurred involve software purchase costs, by buying the new soft wares, training and implementation costs,, for the employee and end users to familiarise themselves with the version, and the cost of loss productivity. Loss productivity is the production time consumed learning the new version. The best time to upgrade is when there is peak efficiency and the old version is becoming less effective (James 2004 p. 184).

The warrant of the claim

A warrant is an explanation supporting a claim to prevent rebuttals. Scientific researches provide warrants as there claims are tested and proven. The following mathematical model describes and helps in understanding of hoe these curve is useful in the decision making, timing and productivity level (Hinkel 2005 p. 39).

Frame work of analysis

Learning is defined differently both at individual and organisational level.. at organisational level. It involves mass learning (by all those involved) of new routines, structures and mechanisms. Because this paper focuses on the organisation as a whole we will concentrate in organisation and an individual within the organisation. The organisation uses the learning curve to illustrate improvement rates after the _learning process Wright (1936) equated the relationship between labour and the learning (productivity time consumed while learning).  It showed that an increase in the rate of learning resulted to a decrease in rate of improvement. The equation explaining this is;

y ¼ ax_b,

y is the unit of labour require to produce x, which is the unit of output.

Long linear curves show that performance gets a steady increase through practice. The most substantive improvements are witnessed at the onset of learning, increasing steadily, till a plateau is reached.

The backing of the warrant

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To back our warrant we look at practical situations where the claim was warranted and it produced the required results. With the below example of the S curve and application of the mathematical model, an organisation is sure to get tangible results that aid in making the right decision (Nancy , Deanna & Florence 2009 p. 278).

Acquiring knowledge and experience equates the process of learning. Knowledge increases with learning until it reaches a plateau, when it remains static. Learning is initiated with an encountered of a problem. The S curve use, r (value) and t(time). With t, r will increase till it reaches its maximum efficiency. The standard equation for the S curve is

 rðtÞ ¼ r1=ð1 þ ae_btÞ,

 The curve coined its name "S" curve from the S shape it forms when the variables are considered. I.e. with learning, knowledge increase till a plateau is reached. This rise and plateau level when drawn assumes an S shape hence the name S curve (Louis, Manion & Keith 2007p. 76).

Backup for the above warrant

A mathematical frame work is used in making effective decisions as to the perfect timing for software upgrading. This frame work is the backup for the theory that learning and production relate in a S Curve. To explain this concept, we take case studies of different situations that an organisation regarding the timing and an announcement of a new version for soft wares (James 2004 p. 264).

What happens if technology is used immediately it is acquire?

The cost of saving acquired at a particular time (t) will be calculated as:

Cost of ownership will be denoted by C1. Reflective of the above savings, the organisation shall have recovered C1 at a time (t). This statement is defined by the equation:

t1 ¼ C1=r11

To understand the above, the assumptions are made in regard to certain situations.

Instantaneous Learning- This is when the software vendor announces a new version when the ownership cost for the old version is recovered, the maximum productivity is reached. In this case there is no emphasis of the fact that the organisation owned an old version therefore the decision to upgrade depends on other factors like the availability of money, the importance of the task to be completed in the organisation, the rate of learning and costs attached to it, and the need to use this new technology to return investments.

Instantaneous learning- when the ownership costs of the original version are not recovered by the time an announcement is made of a new version. In this case, Maximum productivity is not yet attained.

The ownership cost is denoted as C1, and this decision is dependent on the fraction of C1 recovered, and the amount of the upgrade, in this situation, ownership is denoted as C2, and the time for the upgrade is t0. Therefore the total cost that the organisation shall have paid will be C1 +C2 and the time will be t2. To calculate the time the organisation will take to recover the costs are therefore equated as;

ð1 _ r11=r21Þt0pC1=r11 _ ðC1 þ C2Þ=r21,

For the upgrade to be beneficial to the organisation there must be an emphasis on time. t0 should be less than or equal to time, t  must be greater than 0

If the vendor announces an upgrade at an instant time:t0

The learning curve- The ownership costs of the original version are fully recovered and maximum productivity level is reached. In this case, just like in the instantaneous learning, ownership of original version is irrelevant and the decision to buy does not depend on it

4th Situation in the learning curve

The ownership costs are not recovered and the organisation has not reached maximum efficiency level. Ownership of the old version is taken into account. In this case, the cost, C2 of the software includes both the purchase price (upgrade) and the deployment costs. In addition to C2, the organisation incurs a sharp drop in value. This drop in value is denoted by L. to equate the drop,

½r1ðtÞ _ r2ðtÞ_ dt.

To back this theoretical warrant, an illustrative example is given of Sam Walsh, an IT manager who uses her organisations' S curve to make decisions that are time bound. Five months after implementing system software, the vendor announces an upgrade that promise to increase efficiency compare to the one her organisation uses. She is faced with the choice to upgrade, post pone or continue with the version they use (Green et al 2006 p. 254).

Using the above mathematical model, she takes time comparing the values of the existing system with the values of the upgraded version. She takes into account organisation performances, casts and profit levels, and using the above equations, she is able to determine the nature of the results expected with every decision.

Point of cost recovery

This is the point at which the organisation expects a rise in productivity in response to an upgrade. This point is denoted by t2, and is defined by the equation;

r1ðtÞ dt þ

r2ðtÞ dt _ C1 ¼ ðC1 þ C2Þ _ C1,

If you equateC1 with its equivalent above, you

r2ðtÞ dt ¼

½r2ðtÞ _ r1ðtÞ_ dt _ DC

The paper makes a hypothesis contribution to the organisational decision making in regard to the upgrading of software and the productivity levels.  There is an explanation given in using a mathematical frame work in understanding these timing decisions.  This framework is tested and proven to help indecision making. Offering insight to an assumption that an increase in labour consumption decreases productivity, and increase in rate of labour increases efficiency and productivity.

 As is the case with other assumptions, scientific hypotheses are not reputed as they provide room for testing and proven, and until they are proven, they are not referred to as facts. This qualifies as a scientific research to prove the hypothesis that an upgrade of software et the right time increase productivity within an organisation. The mathematical framework is used to effectively time software upgrade following the learning theory that increase in the rate of learning corresponds to a decrease in the rate of improvement. The learning curve give rise to the S curve which shows that learning occurs after a problem is encountered. This learning leads to a steady rise in knowledge till an optimum level is reached. These curves aid in decision making where a manager is faced with different confusing alternatives.

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