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Oke, S.A., Ukwuegbu, U.V., Akanbi, O.G. & Oke, O.O. (2008). Personnel Cost Minimisation Through Effective Scheduling in a Developing Country: The Nigerian Experience, Research and Practice in Human Resource Management, 16(1), 60-77.

Personnel Cost Minimisation Through Effective Scheduling in a Developing Country: The Nigerian Experience

S.A. Oke, U.V. Ukwuegbu, O.G. Akanbi & O.O. Oke


The growing business competitiveness worldwide places great challenges on organisations to improve company-customer relationship, quality, and welfare schemes for staff. In Nigeria, the generator servicing industry, which consists of firms that provide alternative sources of power through generator plants and supporting services, is large and continually strives to provide competitive services. Generator servicing organisations in contemporary times require effective and timely allocation of staff and resources to demanding companies who may sometimes require around the clock technical assistance. This paper presents a staff scheduling intervention programme in which the number of staff to be assigned to respective shifts each working day is determined according to the volume of work to be done in order to optimise the total personnel cost for the company. The application of the programming model is to a company operating in Nigeria that provides generator plants and supporting services to clients in diverse businesses. Overall, the paper is an attempt to link application of a theoretical programming model to the practical world of management and HR in a developing country. The problem, which is developed as a linear programme and solved, using Microsoft Excel software, shows that five shifts are required to avoid inefficiencies with a maximum manpower requirement of 41 people, and a cost range from N1,100 to N1,200 for all the shifts. Adequate staff availability is ensured and the cost of wages is minimised at N 135,950 per day. In an endeavour to control inefficiencies, loss of income and goodwill in a generator servicing company, decisions on staff scheduling that are based on analytical techniques are likely to show benefits and advantages. Although this problem is solved for a developing country, it could also be useful for human resources management (HRM) in developed countries where the HRM policies and practices being administered are quite different. The relevance of the study findings for HRM policies and practices is that it provides a mechanism for effective utilisation of human resources, and an opportunity to make the company competitive and effective in its operational activities through a time savings control mechanism.


Globally, there is a growing business competitiveness. This phenomenon has placed great challenges on organisations for improving company-customer relationship, sustainability, staff welfare schemes, quality, flexibility, variety, responsiveness to customers, and reducing costs (Proudlove, Vadera & Kobbacy 1998, Vries & Conradie 2006). Indeed, many businesses have responded to these issues by introducing management philosophies that are impacting the way industry will meet these challenges and the needs of future customers (Holdsworth 2003). There is mounting evidence to suggest that ISO certification is one of the tools that is being increasingly used to face challenges in the marketplace (Yeung, Lee & Chan 2003). And Holleran, Bredahi and Zaibet (1999) noted that the competitiveness in companies depends upon their ability to adopt production processes, which meet quality requirements. Also, proper scheduling of staff could aid in meeting these challenges through personnel cost minimisation, particularly in developing countries and in the advanced HRM countries that are experiencing different systems. For instance, in the generator servicing business, the quest for excellence in performance is driving organisations to explore all possible options for system improvement, particularly with respect to selective recruitment decisions such that the ‘best brains’ are hired, trained and retrained in order to optimise a company’s potential despite the increasingly complex and unpredictable pattern of service demand by customers (Claggett, Hollas & Stansell 1995). This contention is based on the premise that the further development of business needs new and greater requirements in structure and quality of working staff. Therefore, research into personnel optimisation becomes vital. A key point being raised in this paper is that HRM policies and practices are of considerable interest to practitioners and researchers who are in advanced HRM countries experiencing different systems. Thus, a strong feature of this work is that Nigeria is the context of the paper.

In Nigeria, personnel cost monitoring is extremely important, particularly in situations where the dwindling organisational fortune of organisations has become a challenge to organisational survival. With the enormous power outage experienced in Nigeria, the generator servicing business is profitable, and attracts sizeable investments from business. However, rising wages and strong competition in the generator industry has motivated investors to closely monitor company activities and ensure that personnel cost is minimised. For example, during budget implementation, many managers readily remove training cost, which is believed to bring about a non immediate benefit to the organisation. Thus, managers seek to optimally allocate the human and non human resources in organisations so as to minimise idleness through proper scheduling.

In many parts of Nigeria, power supply is erratic, unreliable, and often does not support both manufacturing and service activities. Most times, businesses run on the power supplied by generator sets. This situation is based on the premise that downtime could result in loss of man hours and resource wastages, thereby causing a huge loss for the organisation. Businesses, therefore, require the support of alternative power sources for survival. Generator services seem to be the most available and reliable option. This boosts the activities of service providers in the industry in view of the unpredictable pattern of customer patronage by clients whereby extensive usage of generators is made and gives rise to the need for unpredictable calls for service by clients that are likely to lose income (due to generator breakdown) until the situation is attended. Also, there is the possibility of clients switching to other service groups for generator maintenance. The procedures employed to organise the workforce, optimally, is the focus of this paper.

The presented paper has five sections. Their order of presentation is: (a) the cost minimisation framework, which follows the personnel scheduling opening gambit, (b) methodology, (c) results, (d) discussion, and (e) a conclusion. The section for the cost minimisation framework builds an argument to express what the theoretical pillars are, and which ones the paper supports or challenges. The strategic use of Microsoft Excel platform is in the modelling and implementation activities. Since employees are to be rewarded according to the shift demands, information based on wages per shift is also determined. The methodology section presents information about the subjects, and the study sites. The results section presents the outcomes of the analysis that were obtained from an effort to practically use a linear programming technique in solving a technical staff scheduling problem such that an organised plan is made in allocating technical staff to different locations, which would reduce inefficiencies. The results also indicate the number of staff to be assigned to respective shifts each working day, which is determined based on the volume of work to be done in order to optimise the total personnel cost for the company. The discussion section outlines the practical and operational elements of the model. The last section of this paper gives concluding remarks on the model and its benefits. Some possible future extensions of the model are also suggested.

Personnel Scheduling

A great deal of literature that has been concerned with personnel scheduling has focused on minimising labour costs (Thompson 1997, Mathirajan & Ramanathan 2007). For instance, linear programming based heuristics has been applied to situations where the workforce size necessary to satisfy forecast demand is estimated (Brusco & Johnss 1995). This work has resulted in a near optimal solution with complex procedures. Furthermore, Duffuaa and Al-Sultan (1999) cast the maintenance personnel scheduling problem in a stochastic framework albeit their work centres were in manufacturing systems. Unfortunately, it would take enormous coding time to run the model on a microcomputer, and some specialised skills may be required for its operation and maintenance. Moreover, Kim, Park, Parle, and Chun (2005) developed a game theoretic framework for analysing strategic behaviours of generating companies with maintenance scheduling under competitive market environments. The work is complex, particularly in the generation and interpretation of results. Also, no guidance is provided on the coding approach to adopt for practical use. In another relevant stream of the literature, Mohanta, Sadhu and Chakrabarti (2004) proposed a fuzzy model for power plant maintenance scheduling optimising safety and reliability. While their paper considered scheduling as well as personnel scheduling the latter did not feature in the analysis. Thus, its application in generator servicing organisations is limited. An additional perspective was provided by Zhang, Love and Song (2007) who formulated a finite state semi Markov decision process model to optimally allocate the server’s time to jobs. But their work considered only a server while multiple servers were not considered.

More recent endeavours have been reported. For instance, Yang, Bai and Qui (2007) investigated resource allocation using decentralised resource allocating policy. While this study presents useful information on scheduling, the application of the concept to personnel scheduling is limited, requiring a major rework of the model. And an investigation into the hierarchical structure of the pancake network and a derivation of a job allocation scheme for assigning processors to incoming jobs was carried out by Bennes, Latifi, and Kimura (2007), but the case of multiple jobs and multiple servers is not considered. The study by Guironnet and Peypoch (2007), which quantified a salary based approach to measure the impact of the general lengthening in the duration of studies on private sector productivity, is limited as it did not address multiple servers and multiple customer situations.

From the reviewed literature, it could be inferred that research documentation on personnel scheduling, although extensive, seems to have provided only partial solutions to various problems. Much of the qualitative literature on the subject has only offered descriptions, which provides little guidance for implementation. Others have considered highly technical mathematical derivations, which are mainly theoretical with very little practical value. Thus, a strong need arises to assist managers with a practical tool that is relatively easy to understand and to apply in solving the technical personnel scheduling problem in a generator servicing company.

The focus of this study is to develop and test a staff scheduling intervention programme that permits a specified number of staff to be assigned to respective shifts each working day. This resolution is dependent on the volume of work to be done so that the personnel cost could be optimised. It seems that managers and researchers are having their interests skewed towards understanding the key benefits and advantages from the findings reported in the literature, but these users of information are interested in how the overall outcomes of existing studies have benefited businesses. Managers and researchers also desire knowledge of the implication of the existing literature for the theory and practice of HRM. Users of literature information may be inclined to understand certain critical issues such as efficiency, effectiveness, and contribution the scheduling problem had for organisational competitiveness. In ensuring effective scheduling of the technical staff, the organisation stands to benefit in many ways, such as effective utilisation of human resources, optimisation of personnel costs, effective implementation of training and retraining activities, and maintenance of good employee succession programmes. The alignment between HRM techniques, business strategies, and personnel scheduling costs is central to the wide acceptance of existing and future studies on personnel scheduling cost.

Cost Minimisation Framework

An Overview

The current section discusses the theoretical underpinning for the theme of the paper, which provides evidence and persuasive argument for the foundations of this work. The Nigerian business environment in which Dynamics Limited (DL) engineering company operates is highly competitive. The deregulation of the telecommunication industry by the government, the recapitalisation programme in Nigerian banks and the insurance industry, which has led to mergers and acquisition of component banks, has posed much pressure on performance driven management in these sectors of the economy (Thomas 2004). Consequently, service providers to these institutions are much pressed for performance driven services (Meyer, Krueger & Mathews 2006).

The generator servicing industry is expected to perform optimally. Indeed, the generator servicing industry has a primary function of ensuring regular power supply to businesses in view of the unstable electricity supply from the government. Nevertheless, there are daily calls and complaints by customers on the inefficiency of DL engineering company staff performance. These complaints are usually treated with care and courtesy in view of the sensitivity of business and the possibility of losing customers to competitors. On several occasions some of the staff on duty have been found idle, waiting for their next assignment. This situation poses a great deal of concern to the management since enormous man hours can be wasted when human resources are poorly utilised. This contention is consistent with the findings of a study by DuCote and Malstrom (1999) that established relationship among personnel scheduling, materials requirement planning, and capacity requirement planning in developing software to manage the personnel in manufacturing systems. And as most businesses borrow loans from bank for running their activities the challenge is to address waste reduction through elimination of redundant periods to more fully utilised human resources.

Theoretical Underpinning for Cost Minimisation

The problem of personnel cost minimisation is serious when several technical crew members are employed and postings of staff to clients’ offices are done by intuition and at the discretion of the management. This scenario has generated into a situation in which some technical staff are assigned to certain clients’ offices without any scientific guide. Hence, other members feel that there is discrimination (Dobson & Jones 1998, Jonsson 2001, Loureiro, Carneiro & Sachsida 2004). Their argument, which is unofficially raised, is that those who were employed through the influence of members of the MD’s nuclear family, friends, and relations are treated specially in situations where experience or financial compensation is to be gained (Leutwiler & Kleiner 2003, Grün 2004). Therefore, when staff have the option of not coming to work, such as on public holidays, they usually elect to stay away from work, particularly if choices are to be made with respect to the staff to be deployed to a particular location of the client. Fortunately for the management, some of the staff who were relieved of their jobs made this allegation and complained to the management that the unfair and unequal treatment of staff have in the past motivated them to exhibit unethical behaviour that led to their dismissal (Peterson 2003, Cardy & Selvarajan 2006, Small 2006). Scheduling personnel in this situation could be aided by the approach proffered by Hao, Lai and Tan (2004) that introduced a neutral network modelling to solve a real rostering case by converting a mixed integer programming formulation to a neutral network model and then compared the results with simulated annealing, tabu search, and genetic algorithm.

For the study company it is usual that no plans are made for new employees (Karuppan, 2004). In practice they are usually recruited and made to join the pool. Unfortunately, these new employees, who possess different skills from those already in the company, are not given the opportunity to pass their knowledge to others in the company. Over time such employees lose interest in the company and may seek other work places where teamwork exists and where there are opportunities to share job relevant knowledge. The company management, having understood the challenges invited a consultant to help solve this problem. In addition to many other solutions, the consultant suggested a scheme where assignments of staff to locations may be made according to skill and experience of staff.

The increasing business expansion and growing business competitiveness on a global basis, particularly in Nigeria, places high pressure on human resource practitioners in generator servicing companies. These professionals are expected to provide an effective schedule of technical personnel in their organisations despite the unpredictable nature of service demand by clients. In other words, management is responsible for the company’s technical staff ability (to meeting customer demands) by the effective scheduling of target oriented, proactive, and assigning technical staff to various sites on demand. These demanding clients are strongly disposed to be attended to at anytime they make service requests. The essential and high demand nature of these customers’ businesses creates the need to pursue continuous availability of their generators for support activities. For example, in the newly deregulated telecommunications industry in Nigeria, generators that power equipment need to be monitored. The downtime of generators in this environment would be devastating, causing a loss of goodwill to the telecommunication company since customers become frustrated when failure to get call destination places due to telecom industry equipment downtime exists. The case of petrol stations, particularly during festive periods is also supportive of the need for good condition of generators. Other cases in meat shops and fire stations that need generator services also suggest the need for proper monitoring of generator conditions.

The marketing personnel of generator servicing companies would like to ensure that contracts won for implementation are carried out on time, and within budgeted costs. Unfortunately, difficulty exists in scheduling technical staff in an environment where job requests by clients are unpredictable both in volume and pattern. This is similar to the problem addressed by Mathirajan and Ramanathan (2007) on the scheduling of a marketing executive’s tour of a large electronics manufacturing company in India using (0 – 1) goal programming (Wagner 1969, Daellenbach & George 1978) with 802 constraints and 11 67 binary variables. Thus, there is a strong need to schedule personnel for generator servicing scientifically such that personnel costs to the generator servicing company is minimised while satisfying the consumers. It should, therefore, be noted that despite the availability of capable technical staff, scheduling based on intuition by managers without due regard for scientific based principles may fail to address the problem of optimising personnel cost while satisfying customers in a generator servicing situation. With this scientific support, it may be possible to satisfy the unpredictability for servicing requests by customers.

There are a number of other foundation papers that strengthen the theoretical theme for the current paper. The work by Bechtold and Brusco (1995) discussed an approach to working set generation for personnel scheduling problems using two phase heuristic labour scheduling solution procedures implemented on a computer. The study by Mabert and Raedels (1977) revealed a rigorous attempt at solving the teller staffing problem of three decades ago. Numerous other models have been developed over the years, which include Thompson (1993, 1997), and Li and Aickelin (2006), which points to the expanding range of personnel scheduling applications in teller services and nursing activities.

Organisations normally have the potential to identify, evaluate and implement control measures and regularly assess its performance and effectiveness (Yang, et al. 2007). These functions are performed by contemporary generator servicing organisations, which require effective and timely allocation of staff and resources to demanding companies, which may be located in different parts of the town. Consequently, technical staff scheduling in an unpredictable customer service demand environment is one of the classical topics that continue to pose great challenges to staff in personnel, marketing, and operations departments of generator servicing companies in contemporary times. But at present, scholars mainly focus on the theoretical analysis of the scheduling problem. Thus, the purpose of this paper is to bridge the gap by providing theoretical and empirical analysis in generator servicing personnel cost minimisation.


The methodology section provides a description of the system so that managers and researchers may visualise what was done to analyse the study site. In addition the subjects and the methodological framework is given. Considerations are given to the sample size definition, how the sample was chosen, and how the respondents were studied. This approach concerns choice among focus groups, interviews, and survey. The methodology presented here also deals with what questions and issues were raised by interested parties.


The subjects for this research concern the various categories of staff, including artisans, foremen, supervisors, and engineers. This group of company representatives are technically sound to be independent in solving technical problems. As such, only on a few occasions are these respondents likely to consult the head office and other group members servicing other companies in different locations of the town. The operations are conducted so that each team has a running budget from which it could purchase needed components, parts, or resources for emergencies. Such a situation may exist if stocks of parts, components, or resources to be utilised are not available in the store or else a significant time would be lost in pursuing the release of the stock from the head office stores. However, such purchases must be justified and authorised by the most senior member of the group, and approved by a superior at the head office.

Most of the subjects are professionally qualified, and each posses different qualifications and with an ability to speak and write in the English language. This requirement is to create an avenue for easy communication between clients and the technical staff. The engineers are degree qualified, with the minimum qualification being a first degree. However, a number of these engineers have master’s degree. The supervisors are mainly Higher National Diploma (HND) qualified. The minimum requirement for the foremen is Ordinary National Diploma (OND), while many of the artisans have City and Guide Certification. Other artisans, who may not have certificate qualification, are highly skilled in the actualisation of the various jobs.

Normally, employment in the organisation is strongly influenced by the experience profile of the subject. This gives an opportunity to a wide age gap for employment in the organisation. Many of the workers in the organisation are below 40 years in an age profile of 20 years to 55 years. However, special cases exists in which the skills required are not available, but only possessed by the experienced, who perhaps left their former organisations for ‘greener pasture’ or have been retrenched in view of business policy. In the company, females are rarely assigned for fieldwork because of the belief of the management that females are better in non-field related work.


The case studied relates to a practical situation of a company located in Lagos, Nigeria, christened Dynamics Limited (DL) Engineering Services that engages in generator servicing. DL is not the original name of the company, but labelled as such to protect the identity of the private company which is based in Lagos, Nigeria with branch offices in major states of the country. It was established 38 years ago, and presently employs over 300 persons. DL serves a diversity of markets in the provision of power supplies to various industrial and service sectors such as hospitals, banks, federal and state governments of Nigeria and other West Africa countries. For instance, a Federal Ministry invited DL to carry out a survey of diesel generators in operations for more than five years and an assessment of economic life experience. A client in the hospital sector commissioned DL to review fault levels and unrestricted over current and earth fault protective relay setting covering the hospital’s 6.6KV 50Hz ring system. A government client invited DL to carry out engineering services relating to the modification of four independent 500KVA 415V standby diesel generators for parallel operation with automatic start, synchronising and load control.

DL owns its own factory/office complex, which covers a total area of about 40,000 square feet in Lagos, Nigeria. This provides a meeting point for all the team members, and a location where faults are reported and requests for services made. Effectiveness in the delivery of services is aided by the excellent communications that DL has with the rest of the country and the whole world. In order to ensure high technical services to clients, DL embarks on quality certification, which earned it EN ISO9002 BS 5750 Part 1 quality assurance standard in Nigeria. DL activities mainly involve offering equipment from basic power generating plant, Transformer HT/MV electrical equipment, mechanical pumps and industrial equipment to the most complex applications. Dynamic Engineering launched initiatives in the areas of power generation, transmission, distribution and sales to cope with the emerging challenges in the Nigerian power sector. This is aimed at participating in the provision of equipment/services for constant uninterrupted electric power supply in the country. In addition, DL offers a variety of engineering services and also supply products such as welding equipment, irrigation pumps, traffic lights, street lighting, taxi meters, measurement instruments, hand tool kits, water treatment plants and machinery spare parts. In order to support the fieldwork, the company has a computerised design office and workshop facilities, which include comprehensive equipment for the testing of plant and various electrical equipment, drilling machines with adequate tooling and lifting equipment.


The study measures cost of maintaining personnel by scheduling them in various locations. The information utilised was obtained through record vetting and the use of questionnaires directed at both the management and the technical staff of the company. It is important to examine several ways in which the proposed system leads to greater coordination of people to do a better job. Since such a system is scientifically determined, it is expected that if employees are placed in locations where their skills have potential for optimal utilisation a better coordinated system will be demonstrated by information about what employees are responsible for what tasks. Historical records, which assists in understanding the previous tasks carried out on generators at the locations, are usually easy to trace and utilise.

A second issue with effective scheduling is that it promotes the goodwill of the servicing company. Since deployment of employees to locations is planned, it takes short response time to emergencies, which removes frustration that may set in if the service crew do not respond on time to calls. Thirdly, since there is a continuous stream of services, the client server relationship has the potential for being healthy. Cases of huge time losses as a result of plant downtime are likely to be avoided or reduced. The result of this is that set standards in terms of profit goals are achieved both by the client and also the server.

This part of the work considers the sample size and its choice. The population that is investigated consists of artisans, foremen, supervisors, and engineers who carry out field work. However, due to time and resource constraints, a certain percentage of this population that captures the sought information was interviewed. Thus, 20 per cent of the population, which is 40 staff out of about 200 were interviewed and closely studied. These 40 staff are now spread among all the categories of the population studied. Thus, 10 artisans, 10 foremen and 10 supervisors and 10 engineers were chosen for the analysis. Since the clients serviced by the company are diverse and spread across Lagos, and the distance covered on a daily basis may be such that it would be difficult to visit all clients, information on clients was obtained from the head office through documentation files on customer complaints and interviews with clients’ representatives.

Apart from information obtained through records kept by the company, the authors raised a number of questions and issues. These questions, which relate to the competitiveness of dynamics, quality of service, efficiency and effectiveness of the current structure of the servicing company, were asked of the sampled groups and information complemented from the clients’ representatives in order to ascertain the completeness and correctness of the responses by the service groups.


The methodology upon which the current work hinges is the linear programming framework, which consists of an objective function and constraints (Hillier & Lieberman 2001). The objective function is expressed as minimisation of personnel cost subject to the constraint of the minimum number of staff that is required at each timeframe. In the particular case solved, Xj represents the number of staff assigned to shift j, where j representing the number of shifts which ranges from one to five. Thus, essentially, five shifts are convenient. Then, the eight time slots with which there are a minimum number of staff required for each slot should be reduced to five time slots. The linear programming model formulated and solved using Microsoft Excel solver is shown by equations (1) to (10).

Minimise Z = 1200X1 + 1150X2 + 1150X3 + 1100X4 + 1100X5 (1)
Subject to: X1 23 (06:00 – 08:00) (2)
X1 + X2 41 (08:00 – 10:00) (3)
X1 + X2 51 (10:00 – 12:00) (4)
X1 + X2 + X3 56 (12:00 – 14:00) (5)
X2 + X3 + X4 52 (14:00 – 16:00) (6)
X3 + X4 46 (16:00 – 18:00) (7)
X3 + X4 41 (18:00 – 20:00) (8)
X4 25 (20:00 – 22:00) (9)
X5 23 (22:00 – 06:00) (10)

Where Xj 0 for j = 1, 2, 3, 4, 5

The explanation of the model is that given five shifts, as indicated in j = 1 to 5, the total cost incurred for all the shifts is likely to be minimised. This is indicated by the Xj and its various coefficients, as indicated in the objective function. Each constraint, representing a time slot, indicates the minimum number of staff required. For instance, it is shown in Table 1 the first constraint equation states that 23 technical staff are at least needed between 06:00 and 08:00, 41 technical staff needed between 08:00 and 10:00, and 51 technical staff are needed between 10:00 and 12:00. The convenient shift periods are as shift 1 to shift 5.

Shift 1:   06:00 – 14:00
Shift 2:   08:00 – 16:00
Shift 3:   12:00 – 20:00
Shift 4:   14:00 – 22:00
Shift 5:   22:00 – 06:00

Having obtained this data it is necessary to arrange it in a tabular form so as to facilitate easy input into the Microsoft Excel platform, which has a tabular structure. Table 1 shows the format obtained. Some explanations of Table 1 is necessary. The first column indicates the time slots for which customer demands for service are made. The second section of Table 1 is divided into five columns, each indicating the shift wages (shown below). For these columns, check marks are shown, indicating the variables marked as X2 to X5 in the original framework. The right most column of Table 1 shows the minimum number of technical staff required for the given time period shown in the first column. The number of technicians that is required for each time period varies with the amount of work to be done at that period. Wage differentials exist between shifts according to customer demand at that time slot. Thus, it is observed that shift one has the highest wage rate, followed by shifts two and three since a high number of requests are made during office hours.

Table 1
Structure for Dynamics Limited for the Personnel Scheduling Problem
Time period Shift Minimum #
1 2 3 4 5
Daily cost per staff in Naira (N) 1,200 1,150 1,150 1,100 1,100
06:00 – 08:00 23
08.00 – 10:00 41
10:00 – 12:00 51
12:00 – 14:00 56
14:00 – 16:00 52
16:00 – 18:00 46
18:00 – 20:00 41
20:00 – 22:00 25
22:00 – 06:00 23

Note. Minimum # = Minimum number of technical staff needed.

From equations (1) to (10), it seems that this framework could be transferred to Table 1 for analytical purpose. A close observation at the contribution of the linear equations reveals that equations (1) to (10) serve as the framework on which the model is built. With close observation of the model, it may be noted that constraints equations 2 and 3 as well as 6 and 7 are identical (Table 1). For instance, what makes the difference between constraint equations 2 and 3 is the number of technical staff, which is higher in constraint equation 3. Thus, constraint equation 3 is representative of constraint equation 2. Again, the difference between constraint equations 6 and 7 is the number of staff required. In this manner also, constraint equation 6 is preferred since it is higher in value of constraint than constraint equation 7. Thus, the second constraint equation and the sixth constraint equation are not necessary, and may be omitted from the sets of equations.

Table 2 shows a similar structure to Table 1, but with three additions. These amendments are (a) Row 15 labelled ‘solution’, to store the values of the decision variables; (b) Column H labelled ‘totals’; and (c) Column I, the inequality condition. For each functional constraint, the number in column H is the numerical value of the left hand side of the constraint. Excel calculates the value of the left hand side of each constraint using formulae entered in each cell. The constraint for non-14:00 p.m. is X1 + X2 + X3 56. In Excel, the equivalent equation for the number in cell H9 is H9 = C9*C15 + D9*D15 + E9*E15. Cell H14 will contain the objective function, and thus, the formula for the objective function is entered there. The lower right hand side of Table 2 shows all the formulae that need to be entered in the ‘totals’ column (column H) for the DL engineering scheduling problem.

Table 2
Structure of Data Input Into Excel Spreadsheet
Containing the Linear Programming Data
1 Time DL Scheduling Problem Staff
5 Shift
6 1 2 3 4 5 Totals
7 06:00–08:00 1 0 0 0 0 0 >= 23
8 10:00–12:00 1 1 0 0 0 0 >= 51
9 12:00–14:00 1 1 1 0 0 0 >= 56
10 14:00–16:00 0 1 1 1 0 0 >= 52
11 16:00–18:00 0 0 1 1 0 0 >= 46
12 20:00–22:00 0 0 0 1 0 0 >= 25
13 22:00–06:00 0 0 0 0 1 0 >= 23
14 Cost per shift 1,200 1,150 1,150 1,100 1,100 0
15 Solution 0 0 0 0 0

Note. Staff = Minimum number of staff needed.

Using the Excel Solver to Solve the Model

The solver can be started by choosing ‘solver’ in the tools menu (Winston 2007, Microsoft Corporation 2000). The ‘target cell’ is the cell containing the value of the objective function. The values of the target and the changing cells are entered with the addresses for the functional constraints added. The location of the values on the left hand side and the right hand sides of the functional constraints are specified in this dialogue box. The cells H7 through H13 all need to be greater than or equal to the corresponding cells in J7 through J13.

Table 2 shows a summary of the solver dialogue box. The dialogue box allows for the specifying of a number of options about how the problem will be solved. The most important of these are the Assume Linear Model option and the Assume Non-negative option, which tells solver that the problem is a linear programming problem with non-negativity constraints for all the decision variables, and that the simplex method should be used to solve the problem. If the model has no feasible solutions or no optimal solution, the dialogue box may indicate that instead by stating that ‘solver could not find a feasible solution’ or that ‘the set cell values do not converge’.


Table 3 illustrates the original value of the decision variable in the spreadsheet with the optimal value after solving the model. The spreadsheet also indicates the value of the objective function, as well as the amount of each resource that is being used. In particular, Table 3 shows the layout of the spreadsheet that is obtained after solving the scheduling problem. The first row and column show the original labels of spreadsheet. Column B shows the various shifts and columns C to G show constraints. In the original equation solved, X1 23, which means that Xi, denoting the no. of staff needed for shift 06:00–08:00 should not be less than 23. Since the coefficient of X1 is 1, this is indicated in cell C7 as 1. Column J consists of the minimum number of staff required. Row 14 shows the cost per shift, while row 15 indicates the solution. The solution shows five shifts and indicates manpower requirements. For each shift, the costs are indicated for each staff.

Table 3
The Spreadsheet Obtained After Solving the Scheduling Problem
1 Time DL Scheduling Problem Staff
5 Shift
6 1 2 3 4 5 Totals
7 06:00–08:00 1 0 0 0 0 23 >= 23
8 10:00–12:00 1 1 0 0 0 51 >= 51
9 12:00–14:00 1 1 1 0 0 56 >= 56
10 14:00–16:00 0 1 1 1 0 74 >= 52
11 16:00–18:00 0 0 1 1 0 46 >= 46
12 20:00–22:00 0 0 0 1 0 41 >= 25
13 22:00–06:00 0 0 0 0 1 23 >= 23
14 Cost per shift 1,200 1,150 1,150 1,100 1,100 135,950
15 Solution 23 28 5 41 23 120

Note. Staff = Minimum number of staff needed.

Table 4 shows answer report provided by Excel Solver Target cell (min) for the DL scheduling problem. The cell, which is named ‘cost per shift totals’, shows that the difference between the final values and the original value is 135,950. For adjustable cells named solution the range of values for the difference between the final value and original value five and 41. For the constraints, cells which are named with time value totals, having status of either binding or not binding with cell value ranging from 23 to 74 and slack also varying from zero to 22, respectively.

Table 4
The Answer Report for the DL Scheduling Problem Provided by the Excel Solver
Cell Name Original Value (N) Final Value (N)
Target Cell (Min) $H$14 Cost per shift Totals 0 135950
Adjustable Cells $C$15 Solution 0 23
$D$15 Solution 0 28
$E$15 Solution 0 5
$F$15 Solution 0 41
$G$15 Solution 0 23
Cell Name Cell Value Formula Status Slack
Constraints $H$7 06:00–08:00 Totals 23 $H$7>=$J$7 Binding 0
$H$8 10:00–12:00 Totals 51 $H$8>=$J$8 Binding 0
$H$9 12:00–14:00 Totals 56 $H$9>=$J$9 Binding 0
$H$10 14:00–16:00 Totals 74 $H$10>=$J$10 Not binding 22
$H$11 16:00–18:00 Totals 46 $H$11>=$J$11 Binding 0
$H$12 20:00–22:00 Totals 41 $H$12>=$J$12 Not binding 16
$H$13 22:00–06:00 Totals 23 $H$13>=$J$13 Binding 0

Table 5 which shows the limits report provided by the Excel solver for DL scheduling problem. For cell with target name cost per shift totals, the final value of N135, 950 is obtained. For Adjustable cell named solution having the same value and lower limit range of 5 and 41, a constant target result of 135,950 is shown.

Table 5
The Limits Report for the DL Scheduling Problem Provided by the Excel Solver
Cell Target Name Final Value (N)
$H$14 Cost per shift Totals 135,950
Cell Name Value Lower Limit Target Result Upper Limit Target Result
Adjustable $C$15 Solution 23 23 135,950 #N/A #N/A
$D$15 Solution 28 28 135,950 #N/A #N/A
$E$15 Solution 5 5 135,950 #N/A #N/A
$F$15 Solution 41 41 135,950 #N/A #N/A
$G$15 Solution 23 23 135,950 #N/A #N/A

The Sensitivity Analysis

Table 6 shows the sensitivity report for the problem. The upper table in this report provides sensitivity analysis information about the decision variables and their coefficients in the objective function. The lower table does the same for the functional constraints and their right hand sides. From the upper table, the ‘final value’ column indicates the optimal.

Table 6
The Sensitivity Report Provided by the Excel Solver for the DL Scheduling Problem
Cell Name Final Value Reduced Cost Objective Coefficient Allowable Increase Allowable Decrease
Adjustable Cells
$C$15 Solution 23 0 1,200 IE + 30 50
$D$15 Solution 28 0 1,150 50 1,100
$E$15 Solution 5 0 1,150 1100 49.99999999
$F$15 Solution 41 0 1,100 49.99999999 1,100
$G$15 Solution 23 0 1,100 IE + 30 1,100
Cell Name Final Value Reduced Cost Objective Coefficient Allowable Increase Allowable Decrease
Constraints $H$7 06:00–08:00 Totals 23 49.99999999 23 22 23
$H$8 10:00–12:00 Totals 51 51 5 16
$H$9 12:00–14:00 Totals 56 56 16 5
$H$10 14:00–16:00 Totals 74 74 22 IE + 30
$H$11 16:00–18:00 Totals 46 46 IE + 30 16
$H$12 20:00–22:00 Totals 41 41 16 IE + 30
$H$13 22:00–06:00 Totals 23 23 IE + 30 23

The solution is that the next column gives the ‘reduced costs’. The next three columns provide the information needed to identify the allowable range to stay optimal for each coefficient cj in the objective function. For any cj, its allowable range to stay optimal is the range of values for this coefficient over which the current optimal solution remains optimal, assuming no change in the other coefficients. The ‘objective coefficient’ column gives the current value of each coefficient, and then the next two columns give the allowable increase and the allowable decrease from this value to remain within the allowable range.

Thus, 1,150 <= c1 is the allowable range for c1 over which the current optimal solution may stay optimal. Similarly, 50 <= c2 <= 1,200 is the allowable range to stay optimal for c2. The ranges for c3, c4 and c5 are (a) 50 <= c3 <= 1,200, (b) 1,100 <= c4 <= 2,250 and (c) 0 <= c5. The fact that both the allowable increase and the allowable decrease are greater than zero for the coefficient of both decision variables provides another piece of information. The lower Table 6 focuses on sensitivity analysis for the functional constraints. The ‘Final Value’ column gives the value of each constraint’s left-hand side for the optimal solution. The next two columns give the shadow price and the current value of the right-hand side (bi) for each constraint. When just one bi value is then changed, the last two columns give the allowable increase or allowable decrease in order to remain within its allowable range to stay feasible. For any bi, its allowable range to stay feasible is the range of values for this right-hand side over which the current optimal BF solution remains feasible, assuming no change in the other right-hand sides. Using Table 6, combining the last two columns with the current values of the right hand sides gives the allowable ranges to stay feasible.

The only optimal solution that satisfies the scheduling problem is summarised in Table 7. With this schedule, adequate staff availability is ensured for every time period and the cost on wages is minimal at 135,950 per day.

Table 7
Optimal Staff Schedule for DL Engineering
Shift Personnel Number Wage () Total ()
Totals 120 135,950
1 (06:00 – 14:00) 23 1,200 27,600
2 (10:00 – 16:00) 28 1,150 32,200
3 (12:00 – 20:00) 5 1,150 5,750
4 (14:00 – 22:00) 41 1,100 45,100
5 (22:00 – 06:00) 23 1,100 25,300


This study presents a framework solution to the problem of technical staff scheduling in a generator servicing company that has a large clientele in the hospital, government, bank, and manufacturing plants sectors in Nigeria. The major services engaged by the company include the sales and maintenance of various electrical equipment, mainly generators. The company is located in the commercial environment of Lagos, usually associated with high level of commercial activities. Many of these clients require immediate repairs of generators and other equipment to prevent excessive loss of money due to downtime of facilities. The arrangement made with company management is such that at the beginning of the week, schedules of work where particular employees are assigned to jobs in specific locations are made. The company, therefore, transports these staff to the various places of assignments. Where a particular job would engage employees for more than one week, this has the potential for being taken care of in the schedule. However, employees have the freedom of reporting to the field directly from home while DL takes responsibility for transport allowance spent by the employees. The amount approved, however, has a limit, which depends on the rating of the employee in the company.

The Nigerian business environment in which DL operates is competitive. A feature of this environment is the demand for a strategic understanding of customer’s needs, and fulfilling such needs that satisfied customers are created. Some of customers keep records of breakdown, which reflect the equivalent amount of income lost to machine unavailability. When this value gets to a threshold, DL is first notified of the problem, but if it persists, the case is taken to the board before the decision to switch to another service groups is taken. If this action is not taken on time, sustainability of the company may be difficult and the company may finally close down.

The decision to minimise personnel cost through effective scheduling hinges on the premise that employees with at least the minimum standard of skill and knowledge, are recruited and trained. In fact, the company seeks to hire the ‘best brains’, train them, and endeavours to develop employees so as to optimise the company’s potential. The unpredictable pattern of service requests also calls for employee commitment. On some occasions service requests are made at odd hours of the day in which only committed employees are likely to respond to such calls. However, in order to minimise idle time among employees proper scheduling of staff to locations is vital.

The overall outcomes of this study, and especially their implications for the theory and practice of HRM, are varied and contain clear benefits and advantages. These are discussed in issues such as efficiency, effectiveness, contribution of scheduling systems to organisational competitiveness, and the alignment between HRM techniques and business strategies. With respect to efficiency, a lot of time is saved. The set up time for organised scheduling is significantly small when compared with the time loss due to imperfections in scheduling with managerial intuition. This time loss should be of major concern to managers. The lost time could be translated into loss of money due to employees’ apportioned salary for the equivalent time, loss of income for the client whose time is spent indiscriminately instead of attending to the generator breakdown in their companies. Energy is also lost. Vehicles that would move the workers about burn fuel for that period of unproductive activity.

The second issue relates to the effectiveness, which emphasises on producing desriable results. Since this proposal is scientific, there is a focus. Workers tend to be target oriented and result focused since they know that their stay at clients’ offices is pre planned and for a specific period. Hence, not attaining results may count against the assigned workers. This may imply incompetence, and may attract penalties such as disengagement from service. Concerning the contributions of personnel scheduling to organisational competitiveness, it is implied that effective personnel scheduling will make the company more competitive since customers would have greater confidence in the firm. Customers also expect that the same high level of satisfaction that others derive from the generator servicing company would be extended to them in order for the receiving company to remain in business and be competitive. Hence, the next consideration is the alignment between HRM techniques and business strategies. Granted that generators are expensive facilities, there is a greater advantage and opportunity in exploring the high quality service in selling additional generators. Satisfied customers are more likely to be willing to respond positively to the requests of their service providers. Thus, the more generators sold has the potential to bring in additional income for the servicing company.


The focus of the paper was to provide a solution to the problem of scheduling technical staff in a generator servicing company. Technical staff, who are engaged in sales, maintenance, installation and repairs of generators, are usually requested by customers for jobs, which may sometimes require round-the-clock technical assistance. The unpredictable pattern of service demand and its complexity motivates proper planning and execution of plans in order to achieve the smooth running of the business. This scenario provides a point of departure for the formulation of a solution to the problem as a linear programme that can be solved on the Microsoft Excel solver platform. Within this framework the activities correspond to shifts and the level of each activity is the number of technical staff assigned to that shift. Based on the obtained results, a mechanism for effective utilisation of human resources is created. Hence, it has been demonstrated that effective scheduling of personnel in a generator scheduling firm could make the company competitive, efficient, and effective in its operational activities, and could also assist in reducing the cost of operations through time savings both from the service provider and the customer who enjoys the service. Also, the implementation of the programme creates a healthy organisational environment where training and retraining of staff is easier in order to plan for staff succession and employee turnover. In a disorganised environment, where intuition and the rule of thumb guide the decision to allocate staff to demanding clients, more or less than enough staff may have been deployed to a site. This arrangement is a difficult situation in which deployed staff may not be easily redeployed to other sites at a particular instance due to time limitations or geographical differences between the two sites.

With respect to personnel costs, excessive amounts are expended. This results in wastage as the extra staff posted to the location would be redundant. Hence, there can be, unnecessary costs for personnel, which could have been channelled to a more useful work. And if a client needs a service, and is not attended to promptly, the client may lose financially as a result of the generator not functioning, and hence, clients may switch over to another service provider. Apart from loosing income from the client, the generator servicing company also loses goodwill.

Although it could be concluded that the programming model proposed in this paper seems effective in the Nigerian context, a limitation of the study is that the rationale is entirely quantitative and apparently does not take into account the human factors that are involved. That is, an experienced supervisor of a generator servicing company might well be able to put together a useful team with only half the mathematically appropriate number of members, if the capabilities of the chosen team were known to be outstanding. The opposite reasoning would apply to a team of under performing, or of the team had problematic members. The paper also assumes that the expertise to apply the model would be readily available, which may not always be the case in a developing country. Basically, it is concluded that in order to control inefficiencies, loss of income, loss of goodwill, proper planning of training and retraining programmes, decisions on staff scheduling may be based on analytical techniques with the use of linear programming approach. This condition is made relatively easy by utilising Microsoft Excel solver facility since it could be programmed and run severally with little or no additional skill requirements other than the presented facts in this paper. Future extensions of the model could seek for the incorporation of fuzzy concepts into the framework in order to capture uncertainties in model elements.


S. A. Oke graduated in Industrial Engineering from the University of Ibadan, Nigeria with bachelor and masters degrees in 1989 and 1992, respectively, and worked for IDM services limited as a consultant. He currently lectures in the Department of Mechanical Engineering, University of Lagos and has published 42 papers in 18 journals.

U. V. Ukwuegbu is an undergraduate mechanical engineering student with interest in personnel scheduling.

O. G. Akanbi, a former General Manager of a manufacturing plant in Ibadan, lectures in the Department of Industrial and Production Engineering, University of Ibadan. He has published extensively.

O. O. Oke is currently a student at the Saint Augustine’s College of Education, Akoka, Lagos.
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