Effectiveness of OR in real-life applications for better returns.

Kumar, Santosh ; Kapur, P.K. ; Jha, P.C. 等

Introduction

Operations Research (OR) is concerned with scientific and technological thinking on aspects of human affairs with respect to usage of resources in day-to-day human activities arising in commerce, government and industry. In OR, solely the aim has been to improve the utilization of resources to maximize profits. Number of situations have been discussed by Ahuja et al., (1993), Checkland and Scholes (1991), Fang and Puthenpura (1993). Another independent field dealing with maximizing returns is revenue maximization (RM), a concept from the field of commerce. For a detailed account of RM has been provided by Browning and Kumar (2003). The OR and RM have developed their own methodology, strategies and both have many success claims. Since they share a common goal, there must be room for OR methodology to enrich RM or alternatively. There is a need for better integration of these two fields. Mathematical optimisation and quantitative approaches of OR may provide better insight to RM and similarly concepts of RM may contribute further to the development of OR and its applications. Visible progress of OR is imminent in management of public and private sectors arising from activities relating to government, commerce and industry.

Blackett (1962) observed and remarked that real-life systems do interact with other systems and consequently all associated parametric values frequently change in an OR model but OR has mostly been dealing with a compromised situation that hardly account for changes arising due to system interactions. It is true that changes in a real-life situation can be so complex that an accurate account of all possible changes might be an impossible task, yet possibility of incorporating changes in a model is worth investigation. Statistical models involving uncertainties usually account for changes depicting some pattern and have been discussed by Fuller (1966). Thus a great deal of attention has been directed towards analysis of interaction free models and success has been achieved in maximizing use of the limited resources and developing quantitative measures for those returns, little attention has been given to the changing environment that arises due to interactions and quantitatively assess their consequences. These changes are experienced at a pace that was never experienced before. Software industry is a good example, where changes are often experienced. Thus the other aspect of this paper is to introduce analysis of the changing systems. Therefore, threefold objectives of this paper are:

(i) To bring RM to the attention of operations researchers.

(ii) To identify and illustrate a method developed in OR, which has a potential for application in RM and to identify revenue leak in a real life application.

(iii) To investigate OR models as protean systems and develop information recycling approach for their analysis.

The Revenue Maximization (RM)

The RM is relatively a new idea that has immersed in parallel with developments in OR. It also known as 'Revenue Assurance or Revenue Assurance Management' in telecom industry, 'Revenue Integrity' in airline industry, 'Revenue Cycle Enhancement' in healthcare industry. 'Total Quality Management' is also a term used by many for RM. The main idea behind RM is to develop strategies and tactical skills to prevent revenue leaks in an organization.

RM has developed strategies to collect the revenue in a correct quantity that has been generated by the company without any pilferage and leakage. In a perfect world, all systems would have generated and collected their due revenue automatically. However, the real world is complex, each system survives in an interacting competitive environment and not in isolation. All systems interact with other systems, within the organization and also with the systems that are external to it. In real-life environment, interactions come fast and unpredictable. The management has to operate constantly in the face of these unwanted ugly challenges. Therefore RM and OR concepts are vital for survival, profitability and meeting challenges in the modern world. The RM helps companies to grow, improve profitability and integrity because:

(i) RM projects improve earnings, which is good for the organization, shareholders, and growth.

(ii) RM is a low-risk, high-return activity.

(iii) RM improves company integrity due to financial reporting.

The awareness of leaks has indirect benefits for the organization. For example, revenue understanding may alter 'employees and managers' relationship from 'mistake prevention role' to 'an active contributor to profit role'. This is a concept common to both OR and RM, as knowledge and purpose based employees will always be more effective to the organization.

Leaks are inevitable in a changing environment due to technology and process aging. They do not occur through a defined revenue hole in a single revenue collection pipe. Leakage finds its way and can mean loss of millions of dollars through a single source. Leakage does not necessarily mean a mistake or laziness on part of employees. For example, a sales marketing person may insist on a pricing plan of a new service launched by the company. Since company does not fully understand implications, they may offer a plan that they may not be able to sustain in the best interest of the organization. This kind of situation is very common when companies offer extended warranties for promotion. Thus a conscious new plan is desirable to avoid leaks due to pricing and promotion. Further when special promotions are introduced the existing revenue collection system may not be capable to handle new requirements. Commonly leaks are associated with billing, yet they also arise elsewhere. For example, see details of leaks given in healthcare industry in Browning and Kumar (2003). These details clearly indicate that leaks can be within, between and across functions of the organization. For example, hospital management may enter in a complex contract, which the existing IT is unable to handle, resulting in a leak. This situation is not only common in health industry, but such difficulties are experienced in other large organizations where automation and computerisation have not integrated well to maintain the interest of the organization.

To put a stop on a leak is not the same as elimination of a service. For example, reduction or elimination of a company managed facility for its employees is not going to result in generating a regular income but it is reduction in cost by reducing facilities. Such decisions may be desirable for other reasons but is not a capturing of a revenue leak. Sustainable increments in revenue will result only by capturing direct leaks, such as correct premium rate will increase recurring revenue. Identification and prevention of a direct leak is usually the first step towards RM and prevention of opportunity leaks is the next step in RM.

The concept of prevention of opportunity leaks is similar to preventive maintenance in OR. Similar concepts have been used by airlines to fill empty seats on an aircraft by offering various price structures. The tour operators in Japan have used a similar idea to fill their buses to full capacity. They have created an extra column of folding seats in the bus between each row of permanent seats, creating room to accommodate over booking. In case of cancellations, they have very high probability of operating to their full capacity and when cancellations are not as many, some people are requested to sit on these seats at a heavy discounted rate. Every one remains happy. Similarly there is a need for other ideas and opportunity to improve revenue collection in a business facing uncertainty. Cost and revenue have a sibling relationship. RM is also possible by cost minimization, a commonly used concept in OR. This cost minimization concept in OR leads to better utilization of limited available resources. Thus OR methodology may have applications in RM.

It has been pointed out that revenue leaks arise due to the changing environment, technology change and competition. A change is inevitable in any organization as discussed by Kumar (1995). All industries experience changes at a pace that was never experienced at any time previously. These changes are resulting in mergers and acquisitions to face the challenges caused by competitiveness. Consequently more and more challenges are arising for rapid adoption of new technologies, accelerated pace of product development and marketing strategies and thereby resulting in revenue leaks due to protean behaviour of real-life systems. Although every company operates under a changing environment, yet its susceptibility to leaks and management of changes differs for each company. Similarly some models may be more readily adaptable to changes and others may display a rigid behaviour with respect to a change. It is desirable to incorporate in a model, when possible, ideas to cope with a change affecting revenue.

Information Recycling in Protean Environment

Recycling is a concept from waste management, where motivation is to reduce the bulk of solid waste and also to create a useful resource from waste as given by Grover et al., (2002). This 'waste-to-resource' journey has taken so long in waste management and hardly been attempted in mathematical modelling and analysis. Although the concept of information recycling can be identified in many mathematical methods, for example, solution of a recurrence equation in dynamic programming is nothing but the information recycling, see Bellman (1957). In fact all iterative methods fall in the same class, they can be classified as information recycling methods. Similarly, many other methods can be traced elsewhere. The solid waste is a transient state until its usefulness is discovered. Likewise in mathematical analysis, converting available information from solution of a problem before change as a useful resource to solve the new problem, see Kumar (2004a, 2004b). The aim is to extract available information as a resource for obtaining the new required solution.

The intent is to create a 'path' that joins solutions of two problems; one of them is a problem for which the solution is known and the other one is that, which is required to be solved. In the context of a protean system some input values change in a mathematical model. Since one set of analysis was completed before changes, the old problem plays the role of the problem we have a solution for and the new problem after changes plays the role of the problem that has to be solved. The model structure is essentially the same but is different with respect to its input parameters. Thus in the pathway approach, one is essentially finding a path that joins the solution of the old problem to the solution of the new problem. Garcia and Zangwill (1981) have called this a 'path-way method'. Kumar in 1987 coined the term protean. The idea is that a given real-life mathematical model may remain valid for relatively longer periods but its associated input parameters are likely to change due to interactions with other systems. Thus a given mathematical model may have to be analysed again and again when changes are experienced in the form of input parameter. Similar analysis would have to be carried out again and again for obtaining new results for different input parameters. Since one is dealing with a familiar OR model, its analysis is not an issue, but the issue is to make use of available information for obtaining the new solution when some input values might have changed in the mathematical model. This is similar to post-optimal analysis, but in protean systems changes are beyond the control as they arise due to system interaction. The information recycling approach attempts using the existing information to get to a new solution see Kumar (2005, 2006), Kumar and Bappoo (1999) and Kumar et al. (2007). Changes also arise due to thrust for growth, see Graff (2007) and also an application of vehicle routing for supply of a soft drink company, see Cheong et al., (2002). Thus information recycling idea may prove useful for analysis of mathematical models in a protean environment.

The information recycling methods are more appropriate for models to be analysed in a 'protean environment', see Kumar (1995). In these models the input changes but broadly speaking model structure remains unchanged. The word protean is used to reflect an environment that changes. Changes in any real-life system are natural. These changes might be experienced due to interactions with other internal and/or external systems. Thus input data associated with various aspects of the model may change. This 'repeated use of the same model with changed input values has been described as a protean environment. The authors believe that applied mathematical models should attempt to incorporate changes and where possible develop methods to solve these problems in a protean environment. The expectation is that the recycling information may result in more efficient solution methods that may reduce computational efforts to solve problems arising in a protean environment. More work is required to make a meaningful statement. This in our opinion is a philosophy and a challenge to create new mathematics for various methods to meet the demand of the changing time.

Conventional discussion on sensitivity and postoptimality analysis of a mathematical model is broadly an information recycling approach, however, in those discussions generally it is assumed that changes take place in a defined structured way. Such an assumption is unrealistic as real cause of a change is an interaction of a given system with other systems. Since these interactions are beyond control of any one, so are the changes arising from those interactions. For example, in a network model, G (N, E), let N represents the set of nodes which is a kind of infrastructure and it is safe to assume that infrastructure may hold on for a considerable time but the set of edges represented by E is a set of relationships between various nodes which may experience changes frequently due to interactions. For example, travel time on a particular link may change due to blockage created by an accident, but it goes back to its normal time once the accident has been cleared.

Thus, this concept from waste management to mathematical modelling and analysis of a real life system in a protean environment attempts to search for a path between an existing solution and the required new solution. In summary, "a mathematical problem of interest is to find a path joining a solution of a given model before changes to its new solution after changes". Note that we are dealing with changes, which have: (1) No restriction in the manner they may arise, and (2) the aim is to obtain the new solution by using the existing information from the available solution obtained earlier before changes.

An application of an OR Model to RM

The Economic Order Quantity (EOQ) and its variants in OR have found extensive applications in inventory control and many other situations. An analogy may be identified between an inventory situation and a loan on a credit card. This analogy helps us to pose a problem that has revenue implications in RM. Consider a financial institution that extends credit card facilities to a typical cardholder. For example, the situation may be described as follows:

(i) Annual demand rate, denoted by D, for loan on a credit card of an individual is assumed deterministic and known.

(ii) The loan amount increases at a constant rate with time.

(iii) When the credit facility provider places a demand note on that individual for clearing the outstanding loan, an ordering cost is incurred.

(iv) The bank is expected to offer a specified lead-time to the cardholder to take action to clear the existing loan amount within the prescribed limits.

(v) Shortages are allowed at a specified penalty cost in the form of interest. It means full loan amount is not demanded, however, the balance would attract interest.

These two situations on the surface may look different but mathematically similar. In the case of a credit card system, a 30day billing is a norm for convenience only. This may have revenue implications. Why not a fortnight or two months or any other period of time more appropriate? Furthermore, if a particular credit card holder has an amount due for payment is less than the expense incurred in collecting that revenue, is it worth for a notice of collection? Why not wait for the loan to grow a bit more before incurring the collection cost? Thus it may be desirable to hold on to a notice until funds demanded justify the associated expense. Thus an optimum amount, when a demand notice must get activated is a reasonable question. This aspect requires data from credit card companies and its analysis. Thus there are several questions that need investigation. The authors could not obtain necessary information due to data confidentiality. However, some information was available from the web that gives interesting insight. The source is: The Credit Card Report: Credit card Spending in Perspective, VISA, Vol. 1, November 2002 Obtained from the internet for the Australian market. Many facts, dealing with credit on Visa card have been mentioned in this report but to single out one fact, the report indicates, "As on June 2002, financial institutions had on issue 9.6 million credit cards". This number must have grown several folds by now. Thus a few cents saving on each account may mean easily in millions of dollars to these financial institutions. It is for this reason; EOQ approach may have applications in RM.

Automation and Revenue: An Illustration of Inappropriate Revenue Collection

It is a real case study of an individual who was renting a house at $265 per week, which is equivalent to $1148 per calendar month and at the end of the current lease the rent was increased to $270 per week, which in terms of a calendar month is equivalent to $1170 per month. This individual didn't renew the lease but to accommodate his other plans he continued on a 28 days notice basis on new rental rate for a couple of months. The new rental was to be effective from May 23, 2004. This individual visited the real estate agent on May 21, 2004 to pay advance rent for a month, however, the computer was down and neither the agent nor this individual remembered the exact new amount that was due. In accordance with Estate Agent's regulations, he also gave a notice of vacating the property on July 3, 2004, thus fulfilling the requirement of 28 days notice. In the absence of a clear picture about the rent, it was agreed that the agent accepts monthly rent at old rate and necessary adjustments to be paid later. The tenant received a letter in the mail that the balance due to clear the rent until July 3, 2004 is $463.14. This individual disagreed with this figure and asked for clarification. The dispute was for a small amount; it was arising as follows:

Demand request from the estate agent

Estate Agent's calculations were based on their Real Estate Software: Number of remaining days for rent from May 23 to July 3, 2004 = 42 days for which rent is (1170X12X42)/366 = 1611.14--1148 (paid already) = $463.14 as was demanded.

Tenant's approach and his justification

Balance for the period from May 23 to June 22, 2004 = 1170--1148(already paid) = $22. Days from June 23 to July 3, 2004 = 11 days Rent for 11 days = (1170X11)/30 = $429 Thus total Balance to be paid is $429+22=$451 as the final figure.

Final collection

Since the computer would not give a clearance on receiving $451, the tenant, as was agreed earlier, paid a cheque for $22.00 to clear the balance from the previous month. Thus the computer updated the rent paid to June 22. The new calculation for the remaining period was calculated using the software, which was $421.96 as follows:

Days from June 23 to July 3, 2004 = 11 days.

Rent for this period was = (1170X12X11)/366 = $421.96

Thus the total amount paid in settlement was = 22+ 421.96 =$443.96 in two separate cheques.

This simple example indicates a possible source of discrepancy that may result in an under or over collection of revenue, depending on the situation, month and period involved. For example, daily rent rate is: For Feb. (nonleap year) > for Feb. (leap year) > April, June, Sept., and Nov> Jan. March, May, July, Aug. Oct., and Dec.

Concluding Remarks

This article has introduced revenue maximisation, a field of study from commerce, to operations researchers. It has been pointed that both Operational Research and Revenue Maximising share a common goal and can enrich each other by adopting each other's methodology and strategies. Therefore, it is desirable for operations researchers to develop familiarity with the field RM and implement their strategies. It has also been pointed out that real-life systems are protean in character, and analysis for these systems may be better achieved by the information-recycling concept taken from waste management area. A real case of software based revenue leak from a rental situation has been cited. These ideas may result in better returns and create new theoretical challenges for research.

References

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Santosh Kumar, Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria, Australia E-mail: santosh.kumar@vu.edu.au

P.K. Kapur, Department of Operational Research, Delhi University, Delhi, 110007, India, E-mail: pkkapur1@gmail.com,

P.C. Jha, E-mail: jhapc@yahoo.com