A systems approach to integrate manpower planning and operation

Socrrr-hnn P/onSciVol 19.No 6.pp 371-377. 1985 PnntedI"GreatBntann

0038-0121/85 $300+ 00 Cl1985Pergamon PressLtd

A SYSTEMS APPROACH TO INTEGRATE MANPOWER PLANNING AND OPERATION-/TIMOTHY Navy Personnel

Research

T. LIANG

and Development

Center, San Dlego. CA 92 152. U.S.A.

and

Cahforma (Received

SHAO-JU LEE State University. Northridge, 20 .Ipril 1984. in rewed

CA 91330, U.S.A.

/imn 26 .Iprrl

1985)

Abstract-Manpower planning frequently involves aggregated planmng. This paper addresses the Importance of linking manpower planning with operatlonal process. We developed a systems approach to Integrate the gross level of manpower planning and the detailed level of policy execution. This integrated system could improve the effectiveness of policy making

1. INTRODUCTION Manpower planning to the distribution

plies and demands. Lacking an ability to generate all possible decisions and to compare one decision with another. decision makers find it difficult to determine the best decision in terms of policy goals attained. When multiple and conflicting policy objectives are involved. decision makers at the operational level may incorrectly execute policies unless the relative importance among policies is clearly established. Without a clear statement of policy relationships, the relative importance of the policies could vary from one decision maker to another. from one case to another, and from one time to another. The decision makers at the operational level are unable to execute manpower and other policies simultaneously and consistently. As a result, the manpower planners can neither accurately measure the impact of all policies nor the impact for an individual policy.

frequently involves issues related and utilization of personnel re-

sources. Considerable effort has been devoted to analyzing manpower supply and demand at very aggregated levels. Less effort has been devoted to studying the relationship between macro-level planning and micro-level operations. Planners tend to assume that manpower policies are properly executed and their impacts accurately measured. There are good reasons to doubt the validity of this assumption. In almost all cases, there are other policies and constraints at the operational level that affect the execution of global manpower plans. Effective manpower planning is difficult, if not impossible, unless the policies and constraints of the operational process are carefully considered. Figure I shows the information flow for generalized manpower planning and operational processes. It indicates that matching the demand for personnel with supplies is a decision process that considers many factors simultaneously. The decision to use a unit of resource to meet a unit of demand is based on the mdividual’s capability as well as on the macro and micro policy goals. The macro goals may be a set of policies to guide the allocation of available personnel resources to various demand sectors to achieve certain overall manpower balances. The micro goals may be a set of policies or procedures to determine the feasibility of matching specific supplies to specific demands and to determine the most economical or desirable way of utilizing personnel resources. Figure 1 indicates that macro policies, micro policies. and information about specific demands and supplies all contribute to personnel decisions. However, we have observed no feedback relationships among these factors. Under this condition, decision makers can only consider pohcy goals as a general guideline to sequentially match sup-

2. THE CONCEPT OF SYSTEMS INTEGRATION The lack of a systems approach to link macro and micro information decreases the effectiveness of manpower planning. To remedy this deficiency, we developed a systematic approach to integrate the planning and operational processes as shown in Fig. 2. We established a set of feedback relationships to include all information related to the planning and operational processes. Based on all possible ways to match specific supplies and demands, and with the capability of iteratively feeding back the tentative decisions of matching supplies and demands to the policy levels, the impact of a decision is repeatedly assessed and better alternatives are pursued. The decision is considered final only when there are no feasible alternatives that could better satisfy the policy goals. It makes policy planning and operation integrated and consistent. To make this concept work, a technique to develop overall quantitative linkages for all detailed information is required. Smce it is a large scale system, a large scale quantitative method is needed to integrate planning and operations.

t The viewpomt and the concluskon expressed In this paper are those of the writers and are not to be construed as official or as reflecting those of the Navy Department or the Naval Services. SEPS

19:6-A

3. QUANTITATIVE

APPROACH

Linear programming is frequently used for resource allocation problems. However, the manpower planning 371

T. T. LIANGand S.-J. LEE

372

MANPOWER (MACRO)

I

I

Fig. I. The non-integrated

I plannmg

and operatlonal

I processes.

and operational problem under consideration is a multlple objective one. with a very large number of variables. An integer solution to a large-scale multiple objective problems is required. The conventlonal single objective linear programming approach IS insufficient for solving this problem. In the early 1970s. Malone et (11.[l] developed a computer-asslsted personnel assignment model for the Navy. A mathematical programming approach was used for the model. The model was not implemented due to its substantial computer resource requirements and its limited capability in handling large populations and myriad manpower policies. At about the same time, Hatch c’t al. [2] developed a personnel assignment model for the Marine Corps. A multiple objective mathematical programming approach was used but no manpower policies were included. A problem in using this mathematical programming approach is its difficulty in determining the numerical weights for each objective. Goeffrion TVa/ [3], Steuer and Schuler 141, and Zionts and Wallenius [5] have developed alternative methods to estimate the numerical weights. Their approaches were applied to problems in educational plannmg [6], and production planning. among others. However, their methods are still too cumbersome for a large operational problem. Later, Clover ct ~11[7] and Glover and Klingman [8] developed a model to improve the mathematical algorithm for the personnel assignment problem. Their approach has significantly reduced the computer storage requirement. In the mid 1970s. there was a breakthrough in the computational capability of network optimization techniques developed by Bradley rt a/ [9]. and Klingman and Russel [IO]. It enables the large scale network problems to be solved with a reasonable amount of computer resources. Recently. Charnes and Cooper [ 1i], and Klingman and Phillips [ 131 used goal deviation variables to study large scale manpower problems. In our opinion, the goal programming approach poses problems for operational use in terms of the demands it places on the decision maker for setting weights and interpreting results. A simpler and more accurate method was developed by Liang [ 131. This paper describes a new approach for integrating manpower planning and operational processes. The network method is used to quantify and integrate all macro and micro information.

We developed a micro model to quantify the operatlonal procedures of matching specific supplies and demands according to the policies involved at the operatlonal level. A set of network flows were developed. A network contains a set of nodes and a collectlon of arcs connectmg them. We use a node to represent a specific supply (i.e. individual or person) or demand (i.e. posltion or job). An arc between a supply node and a demand node represents personnel flow. Associated with each arc (variable) are the unit cost (coefficient) of the flow, and the upper and lower capacities restrictmg the flow on the arc. A minimum-cost flow problem IS the one which seeks a least cost solution for the flows and which satisfies the demand. supply. and capacity restrictlons. Figure 3 IS a network representation of the micro model. A set of nodes {Pi = j P,. P2. . P,,,‘,idenotes acallable personnel resources. and a set of nodes / I .I _ I ‘,,j represents all personnel demands. ~ ;r;.rl?.... An arc exists between a supply node P, and a demand node l; If the supply meets the requirements of the demand sector. The diagram shows that there IS no arc between P, and I .,. It indicates that P, does not meet the requirement for I ‘, The network also shows that there are arcs from P, to 11. I _7.and I ;_ hence It is feasible to use resource P, for 1;. 1;. or 1j. The arcs represent all possible matches. The final selection of matches will be made among these feasible alternatives. In Figure 3, a node S and a node II are used to represent total supply and total demand. In addition. two nodes I’,,,+, and r,+, are created to represent all unmatched supply and demand. Every supply node IS hnked to the unmatched demand node I ,+, Indicating that the supply might not be used. Every demand node IS connected to the unmatched supply node P,,, indicating that the demand might not be met. After establishing the network to represent the feasibility of matching supplies and demands. we then must determine a procedure to search for the “best” set of arcs (matches) among all possible alternatives

MANPOWER

PERSONNEL

DECISION 4 +. OPERATIONAL POLICIES AND CONSTRAINTS

Fig 2. The Integrated planmng and operatlonal system

Integrate

manpower

planmng

and operation

373

DEMAND SECTORS

SUPPLY SECTORS

Fig. 3. The micro model

regarding micro policies. We give a “cost” (coefficient) to each arc to represent the benefit or the cost of matching a supply with a demand. The cost could be a natural one such as relocation costs. or an imputed one such as a utility index. In the former case. cost coefficients may be developed to seek a least-cost solution for total relocation costs. In the latter case, the coefficients may be designed to search for a solution maximizing utility. Similar to the general linear programming formulation. the mathematical expression of the network micro model shown in Fig. 3 is:

minimize 2 = cx

(1)

subject to .4X = B where represents an n X 1 vector of arc flow variables, represents an tn X n node-arc incidence matrix for all feasible matches. represents an tn X 1 vector of the limit of supplies and demands, represents a 1 X t2 vector of coefficients for X3 represents the value of the objective function.

Through this equation. a set .Y is obtained such that total cost is mimmized and all constraints are satisfied. Although the equation describes a minimization problem, it can be used to solve a maximization problem by reversing the signs of the coefficients of the objective function. In addition. eqn (I) is not limited to solving a single objective problem. Using a set of numerical weights, multiple objective functions are combined into a composite utility function. Coefficients C represent the coefficients of the composite objective function.

The above micro model will help decision makers to obtain an optimal decision with respect to multiple policy goals and constraints at the operational level. However, the micro model is not sufficient to handle manpower planning goals at the macro level. To incorporate the more global manpower policies, the micro model must be expanded. Based on Fig. 3. Fig. 4 was developed to demonstrate the expansion of the network flows for a manpower planning policy to achieve manpower balance between two regions. Let I ‘l to I ; represent the demands in the first region. El, and I b to TL represent demands in the second region, El. Each demand node I,’ is umquely connected to either El or E2 by an arc. To control the manpower distribution between the two regions. it is necessary to

T. T. LIANGand S.-J.

374 DEMAND SECTORS

n

REGIONS

v.

Fig. 4. The macro section of the integrated model.

construct a duplicate set of nodes, F, and F2 and a set of multiple arcs between nodes E and nodes F. These arcs represent the flows of personnel resources at each region and are used to determine the priority sequence of meeting demands between the two regions if supphes are available. In essence. they represent all possible ways of allocating supplies to meet demands. An example helps to clarify the conceptual scheme. Suppose there are 100 additional people available to meet the demands and the manpower policy is to make the number of personnel in each of two regions equal. Based on the existing number of personnel in the two regions, we are able to determine the sequence of allocating personnel one by one. Assuming the existing number of personnel in Region 1 and Region 2 are 500 and 496, respectively. we can calculate all possibilities of distributing 100 available personnel as shown in Table 1. The first arc represents the first person, the second arc the second person, etc. The first arc indicates

LEE

that if only one person is available, he should be allocated to E2 to raise the staffing of the second region to 497. The second arc indicates that if two people are available. with the first arc already given to the second region, the second person should be allocated to E2 to raise the staffing of the second region to 498. After the first four people are distributed, the manpower of the two regions achieves a balance at 500 each. Beyond this point. we will distribute people differently. The fifth and sixth arcs represent the fifth person. We give these two arcs the same priority sequence (coefficient) to make them indifferent. We may either use the fifth arc to allocate him to Region I or use the sixth arc to allocate him to Region 2. However. if SIX people are available, the fifth person should go to Region 1 and the sixth person to Region 2. FolIowIng this heuristic procedure, after the 100th person is allocated, the staffing for both regions reaches its highest value, 548. However. when this highest value for regional balance is carried over to the operational level, there are microlevel restrictions which may prevent decision makers from achieving the global objective of 548. In our approach, instead of just deriving a single macro goal. we incorporated a process of sequentially deriving every possible macro goal into the operational process as it is shown in Table 1. By optimizing the micro policies and constraints. as well as the prioritized macro goals. we will obtain a solution satisfymg all policies and constraints. The final solution could be well below the highest goal of 548. Our integrated macro and micro model always attempts to make staffing for the two regions equal under any possible condition. Figure 4 and Table I show the development of the multiple arcs based on two regions. Additional nodes and arcs can be developed for more regions. Similarly, additional type of manpower policies can be Included in the decision process by expanding the network. Figure 5 is an expansion of our example to include an additional macro policy. Nodes E and Fin Fig. 5 are the same as they are in Fig. 4. Nodes .3 and B are introduced to represent a manpower policy which seeks to distribute personnel to two types of professions before distributing them to regions. In Fig. 5, let .-II .42

represent represent

Profession Profession

I in Region 2 in Region

Table 1. Numerical illustration of macro goals Total After Allocation

Allocation Arc Sequence

Region I @I. Fd

1St

Region 2 (Ez. Fz)

500

I 1 0 1 0 I 0 I

500 500 500 501 500 502 501 503 502

497 498 499 500 500 501 501 502 502 503

i

548

548

US>F2) I 1

2nd 3rd 4th 5th 6th 7th 8th 9th 10th IO&h

Region I WI. FJ

Region 2

0

Priority Sequence

51

1, I.

Integrate manpower planning and operation

375

T. T. LIANG and S.-J. LEE

376 .43

“14 E, EZ

represent represent represent represent

Profession 1 in Region 2. Profession 2 in Region 2. both professions in Region I, both professions in Region 2.

Using the method described in Table 1 and Fig. 4, we developed a set of multiple arcs between Nodes :I and B to distribute personnel by professions and regions based on desirable manpower goals. The optimization of the network containmg these two macro policies, the micro policies. and the constraints produces an operational decision representing the efficient execution of all manpower policies. Although the network structure has been expanded to cover the additional policy, the general mathematical expression of the problem (eqn (I )) remains the same. To combine all multiple objecives into a composite utility function. we may subjectively assign a weight to each objective according to the relative importance of the policy objectives. By optimizing the expanded eqn (1) to represent a composite utility function. we may obtain a solution in accordance with the relative importance of the policies. 4. APPLICATIONS We would like to give two cases. in the pubhc sector and private sector. to demonstrate the capability of this technique for problems in manpower planning and operations.

In the Navy. a large number of military personnel are available for new assignments every month: that is. they are scheduled to rotate from one job to another and from one region to another. Every rotation action creates a vacancy that needs to be filled by the personnel who become available for a new assignment. In addition to personnel rotation, many personnel leave the Navy, creating additional job vacancies. Also. after new personnel receive training from Navy training schools. they become assets for assignment. On average, the Navy makes over 20,000 assignments a month. In matching people to jobs. the decision makers at the operational level must consider numerous rules and regulations to determme people-jobs eligibihty. A person might be eligible for numerous jobs and a job might be suitable for many people. Matching people to jobs among so many alternatives is a difficult decision process. There are many policies involved. For example. to maximize the use of its personnel resources. the Navy has always tried to assign as many people to jobs as possible. To conserve funds, the Navy maintains a policy of filling jobs with personnel such that long range movements are minimized. With over one-half milhon military personnel, reducing unnecessary moves and the distances of the moves can save the Navy millions ofdollars of annual moving costs. In addition. the Navy wishes to assign its personnel to the locations of their choice whenever possible. The purpose of this policy is to satisfy individual preferences and thereby increase retention. With these multiple and often conflicting policies included in the decision process. it IS unlikely that the decision makers can satisfy all these goals and requirements without a systems approach. Our micro model suits this type of apphcation.

The Navy is also concerned about more aggregatelevel or macro level pohcies. These policies are intended to improve aggregate manpower distribution. Mannmg. defined by percentage of positions filled. IS frequently used to measure manpower balance. Some policies are designed to achieve an equal manning between the Pacific Fleet and the Atlantic Fleet. Other policies are developed to control manning for sea duty and shore duty. not usually equal. At the operational level, personnel are assigned to jobs to meet these macro goals as well as the micro goals. However. already burdened by policies and requirements at the micro level, it is very difficult to make optimal decisions. By applying our integrated macro and micro approach, the opportunity to satisfy both macro and micro goals could be increased.

Prllnte

Jcctot

In manpower planning in the private sector, macro policy goals are often derived without the micro operational considerations, resulting in a disjoint system. For example. at the macro level. let’s specify two goals. The first goal is to achieve a female representation of some fixed proportion in the managerial ranks within the next five years. The second goal is to achieve a proper balance of skilled and experienced personnel allocated to various operating divisions. These two goals may be in conflict. Furthermore, the macro goals may be unachievable at the operational level unless the micro operational policies governing the promotion, personnel management. and qualification standards are modified. which m turn may nullify other macro or micro policy goals. Macro policy goals that are not integrated into the operational implementation WIII hamper the effort to assign and allocate personnel in an optimum manner. The approach we have suggested so far should alleviate the problem.

5. CONCLUSION We conclude that in some cases, manpower planning which ignores operational pohctes and constraints results in misallocation of resources. Without including factors affecting the operational process. it is not known for sure if the manpower policies can be executed properly. If a policy cannot be executed properly, the results of the policy execution would not provide a valid base to justify the effectiveness of the policy. It might impair the capability for policy making. To remedy this deficiency, we developed an integrated system. We established a complete quantitative linkage between the planning and operational processes. In searching for a mathematical solution, we found the conventional mathematical programming approaches incapable or inefficient in solving this large scale problem. Taking advantage of the recent development of efficient network computer codes, we developed a network formulation to handle the large scale multiple objective problem. Our system is less complex than the goal programming approach and is capable of achieving a precise goal without large deviations. This paper is concerned with large scale multiple objective optimization problems related to manpower planning and policy execution, However. the approach could be applied to study similar problems in other

Integrate manpower planning and operation areas. We ning and operation also could

believe that a system integrating both planoperatlonal processes not only could make more efficient in terms of time and cost, but make planning and analysis more effective.

.~t,~no~t/ed~m~~~~-The authors are indebted to Joe Sdverman. Thomas Blanco. Mllton Chen. and Glenn Ifuku for their improvements on this paper.

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Dlslrr-

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