A zero-base budgeting process with goal programming feedback

Comput. Environ. Urban Sysrems Vol. 8, No. 2, pp. 93-108, 1983 Printed in Great Britain

A ZERO-BASE BUDGETING GOAL PROGRAMMING FRANK

0198-9715/83 sO3.00+0.00 Pergamon Press Ltd

PROCESS WITH FEEDBACK*

P. BUFFA

Department of Business Analysis & Research, College of Business Administration, Texas A&M University, College Station, TX 77843, U.S.A. Abstract-This paper describes the decision process used to establish the annual budget for allocating general fund revenues to non-revenue generating service activities of a city. This process combines zero-base budgeting (ZBB) and goal programming. The goal programming model formalizes the relationship between the ZBB decision packages specified by city departmental needs and the planning issue goals identified by either the city council, the city administrative staff or a citizens’ survey. A budget committee reviews input data, forms the model and uses its output to revise budget inputs. The goal programming model provides a format for (1) effectively evaluating budget assumptions, (2) consistently representing the relationships between the ZBB decision packages and the city planning issues, and (3) quantifying and evaluating the contribution made by the decision packages toward satisfying the planning issue goals.

INTRODUCTION

describes a goal programming model of the zero-base budgeting (ZBB) process that was used in Denton, Texas, which is a mid-size city approximately 35 miles north of Dallas. Organizationally speaking, this model is a single level model, since the city focuses the ZBB process with its ranking of planning goals and budget decision packages in a budget committee. The model formalizes the linkage between budget decision packages and planning issues, thus providing a measure of goal achievement for the planning issues. These results, together with the selection of decision packages, provide feedback to the budget committee which uses this information to revise budget inputs. By using the model to revise budget inputs and restructuring the budget, the committee refines the ranking of planning issue goals, eliminates inconsistencies among these goals, and ultimately specifies a budget that comes closest to satisfying these goals. Many cities use ZBB as an effective approach to resolve funding issues when budgeting for public services [l, 23. The ZBB format specifically requires the ranking of programs. Such ranking forces the city administration to establish criteria for setting priorities. This is often complex because multiple, perhaps difficult to quantify criteria must be used and, in complex organizational settings, conflicting criteria can be established. Another difficulty with broad managerial implications is the problem of measuring and analyzing the organizational-wide effects of any proposed budget allocation. This is a direct result of the ZBB format that specifies that decision packages be identified with a single department or division. This difficulty compounds when external issues originating in the city’s political, legal, or economic environments constraint the budget process and cross-over departmental boundaries. The goal programming model of the ZBB budget process that is presented here overcomes these managerial problems. The advantage of this model is its format that provides a detailed analysis of budget related issues resulting from external restrictions, or proposed alternative funding criteria, or established planning objectives. The impact of the model upon the managerial effectiveness of ZBB increases as the number of budget programs, criteria, and issues increase. Analyzing budget-related questions using the model improves the effectiveness of the entire ZBB budget process. For more information about goal programming in general, the reader can refer to [S-6]. Two other studies have reported the use of a goal programming model in a ZBB-like environment. Unlike the model discussed here, these studies dealt with a multi-level decision process. Ruefli [7,8] addressed the organizational aspects of a program planning and budgeting system and presented a generalized goal decomposition model of the

THIS ARTICLE

93

94

FRANK P. BUFFA

process where there were multiple levels in the organizational structure. In his model, the process of setting goals and selecting programs was an interactive one in which a lower organizational level generated alternative proposals for a higher level in response to goals generated by that higher level. Chaudhuri [9] also used a goal decomposition approach in a multiple-level organization where top-level goals were first transformed into lower-level goals. At the lowest organizational level he used the zero-one linear goal programming model to select budget packages that satisfied lower-level goals. He then grouped these packages into portfolios of activities that were evaluated at the intermediate level using the zero-one algurithm, Those selected portfolios were submitted to the highest level where a final selection was made using a zero-one goal pro~amming model that satisfied overall organizational goals. DENTON’S

ZBB

PROCESS

In this section we first briefly present a general background on ZBB, then we discuss the ZBB process used in Denton, with particular emphasis placed upon the interface between the process and the goal programming model.

Any ZBB process includes in the annual budget review jns~i~~ation for all previously funded programs, as well as any newly proposed programs. Breaking down each program into different levels of service and identifying the funding needed at each level yields a set of decision packages that are the basic ZBB units. A budget staff ranks the various decision packages and then funds them starting with the highest priority package. Funding continues until the predetermined budget ceiling is reached. At this point, the budget staff considers the highest ranking, unfunded decision package (or set of packages) to determine if the costs vs the benefits of funding this package justify raising ad~tional budget funds, or if the lowest ranking funded package should be abandoned in favor of this package. This for~tion of decison packages and their ranking is a departure from traditional budget preparation, For more details related to the ZBB process and how it is implemented, the reader can refer to [N-12]. When ZBB is applied in governmental environments, it is usually modified since it is not economically feasible to always consider the elimination of operating departments or essential programs. It is important to eliminate unnecessary waste or excess costs within these programs, To accommodate these considerations, the services and funding level associated with any basic decision package are expressed as a percentage of the previous period’s level for the package. This percentage usually varies between 75 and 95%. Numerous examples of ZBB applications at both the municipal and state government level are outlined in [G-19]. Denton’s process Denton uses ZBB to allocate general fund revenues to decision packages that include non-revenue generating services. Packages containing revenue generating services such as utilities are budgeted separately. Figure 1 is a descriptive model of the Denton ZBB process, On the left in Fig. 1 are the inputs to the process. Denton begins the ZBB process at the department level where the department manager formulates decision packages related to the services provided by the department, links service delivery to cost, and measures the impact on the delivery of services at three &nling levels: the reduced level, the current level, and the supplemental level. Figure 1 presents the information that a~ompanies each funding level requests. The order of funding is always the reduced level, then the current level, and finally the supplemental level. The department manager is not required to prepare any supplemented packages; however, if he chooses to do so, a supplemental package is required for each service to be restored or added. When preparing multiple supplemental packages, the department manager must also rank the packages across all divisions in his depart-

.,,,,

Funding Levels

(B)

* Reduced level: Service delivery is 95% of present year. Contents:Summary of decision packages * Current level: Service delivery is 100% of present year. Contents:Summary of decision packages with inflation adjustment * Supplementallevel: Service delivery above that contained in current level. Contents;Single decision packages for each service-either a restored service or new service; package ranks

DecisionPackages, Services, PerformanceMeasures, Resource Needs, Staffing Needs

(A)

DecisionPackages by Departments

,,,,

“,,,

(C)

(B)

(A)

,. ,,.” “,,, “,,

.,I

,.,

~,

.”

Budget Committee

Review decision packages Rank decision packages Establishpackage ranking sum Establishrevenues Review planning issues and goals Coordinateranks of issue goals

ikDecision package recommendations

* Links decision packages and planning issues Q Reflects impact of decision package on planning issues

Goal ProgrammingModel

* * * * * *

ZBB Process

Fig. 1. Descriptive model of Denton’s budget process.

* Constituentplanning issues, goals, and ranks

Citizen Survey

* Manageriallyrelated planning issues, goals and ranks

City AdministrativeStaff

* Legal/contractual * Planning issues, goals, and ranks

City Council

(II) Planning Issues

3)

Inputs

* Reconnnendation

96

FRANK P. BUFFA

ment. Department managers submit their budget request to the six-member budget committee, chaired by the City Finance Director. The other major inputs to the budget committee are data related to planning issues that have been identified by either the city council, the city administrative staff, or the citizens’ survey. These data include a description of the planning issue, its desired goal and the rank reflecting its importance. Following the ZBB process the committee reviews all decision packages, meets individually with each department manager to eliminate inconsistencies, correct errors, identify omissions, and guarantee that budget forms accurately reflect the department manager’s request, and reviews the department manager’s ranking of his supplemental packages. Each budget committee member individually ranks each supplemental decision package as mandatory (a rank of 6 or 5), first to omit if the need arises (a rank of 4), first to add if possible (a rank of 3), and non-essential (a rank of 2 or 1). The finance director then consolidates the rankings into a ranking sum for each decision package. During this ranking process the committee considers the various planning issues that have been identified for consideration in the next fiscal year. The goal programming model provides the format for this consideration. Using the model requires the committee members to identify the decision packages that address each planning issue and to measure the contribution that each decision package makes toward the achievement of each planning issue goal. The resulting ranking assigned to each decision package by each budget committee member reflects the original ranking submitted by the department manager, whether the package is related to a planning issue, and the contribution the package makes toward achieving the goals set forth by the planning issue. The committee then matches the estimate of revenues from the general fund against the request made in the decision packages. When the general revenue estimate is greater than the total funds requested by all reduced and current level decision packages, there is no need to rank these packages. Typically, general revenues are large enough to fund these packages. As a result, the budget committee uses the goal programming model to prescribe an allocation of funds to the supplemental packages. In addition to requiring that the budget committee formalize and quantify the relationship between departmentally generated decision packages and overall city related planning issues, the goal programming model provides output that the committee uses to refine the entire budgeting process. The output of the model includes the listing of decision packages recommended for funding and the measures describing how effective these decision packages are in meeting the goals set for the planning issues. The second part of the output, the effectiveness of the decision packages, would not be explictly accounted for if only the ZBB process was used to identify the decision packages. Using the model output, the budget committee identifies and corrects inconsistencies in the budget process related to the planning issues, the decision packages, and their rankings, reinforces its understanding of the linkage between decision packages and planning issues, describes the budget related impacts resulting from stated planning issue goals, and suggests revisions in either the planning issues, their goals and ranks or the decision packages. In Fig. 1 this interface between the ZBB process and the model is represented as a feedback loop to the budget committee.

THE

GOAL PROGRAMMING OF DENTON’S ZBB

(GP) MODEL PROCESS

Model variables

The sixteen city department managers submitted 157 decision packages for review by the budget committee. These included 16 reduced level packages at 95% of last year’s allocation, 16 current level packages adjusted for inflation, and 125 supplemental packages composed of 42 restoration and 83 new packages.

A ZBB process with goal programming feedback

97

The ZBB priority structure requires that first all reduced level packages and then all current level packages are funded before any supplemented packages are considered. The estimate of available revenues for the next fiscal year exceeded the total amount requested in all reduced and current level decision packages by $1871,358. Thus, there is no need to include these packages in the model, since there is no question of their funding. Omitting the higher priority decision packages that would be funded because of the preemptive goal structure conforms with the suggestions made by Ignizio and Perlis [20] and Arthur and Ravindran [21]. Ignizio and Perlis present a sequential linear goal programming algorithm that first considers only goals, constraints, and objective function terms relating to the highest priority level. They solve this problem using linear programming, then procede to the next highest priority level where they set up the equivalent linear programming model containing goals, constraints, and objective function terms for both levels. Arthur and Ravindran present a partitioning algorithm where constraints are partitioned to form a nested series of goal programming problems. They then solve the smallest subproblem containing goal constraints and corresponding objective function terms assigned the highest priority. If alternative optimal solutions exist, then the algorithm procedes to the next priority level adding goal constraints and objective function terms while eliminating from the model those non-basis variables from the previous level. An additional reduction in decision packages is possible by considering the ranking sum of the packages. In this application, a supplemental decision package is included in the model if its ranking sum is at least 24 or if the decision package is related to a planning issue. Eliminating decision packages that have no chance of funding due to their ranking sum below 24 reduces the model size. Since estimated available revenue for funding supplemental decision packages is approximately $1.87 million as opposed to the 84.06 million requested by these packages, and since the funding decision is made on a priority basis, it is acceptable to make these exclusions of low ranking decision packages. The resulting model contains 80 decision package variables, composed of 36 restoration packages and 44 new packages, requesting a total of $3,076,799. Table 1 lists for each of the 80 supplemental decision packages included in the model the department and division submitting the package, its status+either new or restoration, the number of existing or new employee positions involved, the amount of funds requested, its ranking sum assigned by the budget committee, its variable number, priority, and weight used in the model. The variable Xj in the model is a continuous variable representing the percentage of requested funds allocated to the jth decision package. Although each decision package is presented as an integral unit, the budget committee can fund decision packages at less than the amount requested by either eliminating part of the decision package or by scheduling it for only a fraction of the fiscal year. There are 7 decision packages for which partial funding is specifically allowed for in the problem statement because of their specific nature, while all other packages would be partially funded only if the model results so indicate. Treating the decision packages as continuous variables is significant from the model perspective. Solution algorithms for models with only continuous variables are faster than those containing integer variables. This difference in solution speed increases when a large number of variables are involved. Ruefli also used continuous variables in a similar context when analyzing a program planning and budget system using a mathematical programming model [7,8]. Model constraints

Three types of constraints represent the different restrictions placed upon the revenue allocations to the decision packages. These constraints relate to both ZBB restrictions and to environmental restrictions. The constraints are classified as structural, issue related, and resource related.

Civil defense Civil defense Civil defense

Community developments/admin. Community development/ad~n. Community deveiop~nt/ad~n.

Word processor and printer Vehicle maintenance Radio maintenance

Planning and zoning services ~velopment review services Planning assistance service

Finance/customer service Finance/customer service Finance/accounting Finance/purchasing Finance/customer service Finan~/customer service Fin~~/purchasing Finance/administration

Public Public Public Public Public Public Public Public

Engineering services Unicorn radio

Customer service Service connection Restore clerical and training Purchasing service Replacement vehicles Additional vehicle Word processor and furniture Long range planning

Street lights Labor and Materials Labor Building inspector Vehicle maintenance Vehicle Crack seal Street patching

works/street lighting works/street patching works/street sweep and drain works/inspections works/street patching works/traffic works/street construction works/street patching

Data processing/administration

Airport/administration Airport/administration

Software licenses

:: R R R R N

R

R R R R R N N N

N N

R R R N

N R N

0 1 1 1 0 0 0 0

8 0 0 0 0 0

0

0 0

0

2 0 0

0 0 0

I: 0 0 2

0 0 0

:: 0 0 1

0 0 0

::

0

8 0 0 0 0

0 0.5 0

0

0.5 0 0

0

R R N R

Legal/administration

Personnel/administration Personnel/administration Personnel/administration

ti 0

i 0 0

: N N

0 0

2

0 0 0.5

New

0

0 0 0 0

Exist

R

Restore departmental budget Administrative support M.P.A. intern Employee training

operations operations operations operations operations

Building Building Building Building Building

R R N N

Office space lease Service center lease operation Building superin~ndent Energy conservation modifi~tions Roof replacement

govt/administration govt/administration govt/administration govt/administration

Status

Gen. Gen. Gen. Gen.

Department/Division

Office supplies Management training Clerical support Office of productivity services

Package title

Positions

65,000 30,072 26,580 21,653 18,590 8050 25,000 175,000

26,435 6950 8934 4300 31,361 8908 5000 8033

2.59400 9000 1880

3500 265 500 40,147 4400 5585

9892 1833

27,250

35,187 109,598 19,368 2746 16,000

3000 6400 6699 76,846

Amount

33 32 31 29 28 29 31 27

28 32 30 29 27 25 27 28

36 26 29

28 31 31 35 33 27

33 26 30

29

36 35 22 25 28

34 26 30 27

Budget committee ranking sum

Table 1. Description of general fund supplemental decision packages by department

31 32 33 34 35 36 37 38

;; 30

;: 26 27

23

20 21 22

14 15 16 17 18 19

11 12 13

10

1 2 3 4

Variable number

2 2 2 2 2 2 2 4

; 2 4 4 4

2 2

t 4 4

f 2

4 2 4

2 4 2

2

2 1 4 4 4

2 2 4 4

Priority

33 3200 3100 2900 28 29 31 2700

28 32 30 29 27 2500 2700 2800

2600 2900

1

3500 33 27

2800 31 3100

3300 2600 30

29

36 1 2200 2500 2800

34 26 3000 2700

Weight

Street renovation

N

Fire Fire Fire Fire

Parks/parks Parks/parks Parks/recreation Parks/recreation Parks/ath~etic Parks/parks Parks/parks Parks/administration Parks/parks

Parks/parks Parks/parks Parks/athletic Parks/recreation Parks/parks Parks/recreation Parks/recreation

Library/tech process Library/adult services Library/children/youth Transfers and non-departmental Transfers and non-departmental Transfers and non-departmental Transfers and non-departmental

Firefighters Motor pool vehicle replacement Motor pool vehicle replacement Fire inspector

Mowing program Mowing equipment replacement Summer playground program Youth sports donation Ballfield clay Irrigation system, north lakes Chemical and fertilization Comprehensive master plan Irrigation system conversion

Truck replacement Playground renovation Wind screens Pool improvements Picnic pavilion Basic years course Ceramics program

Additional library clerk Books for adult services Children’s supplies and materials

Salary reserve Sycamore street bridge County-wide tax district Contingency reserve

Animal control Animal control Animal control

Bird control program Animal control officer Additional patrol unit operations operations administration prevention

N N N

Police/patrol Police/administrative Police/administrative

N R R N R R N

R R N N N N N

R R R R R N N N N

R N N N

:

R

z 0

: N

:: 0

0

0 0 0

0 0 0 0 0 0 0

: 0 0 0 0 0 0

4

:: 0

4

0 0 0

::

0

:

2

0 0 0

R R R

N N

PoIice/adm~istrative Police/criminal investigation Police/patrol Police/police admin. Poli~/patrol Police/criminal investigation

Public works/street construction Public works/ins~~ions Public works/tra~c

TWOpolice officer positions One juvenile officer and six vehicles Sworn personnel overtime (holiday pay) Computer system update (lea~/purch~) Four additional police officers Four additional certified officers Traffic enforcement and accident investigation unit Crime prevention vehicle Crime prevention program (op. extra-eye)

Code enforcement Traffic engineer

0 0 0 0

1 0 0

0 0 0 0 0 0 0

0 0 I 0 0 0 0 0 0

0 0 0 1

0 1 2

4 0 0

:: 4 4

0 0

2 1

0

700,000 50,000 40,Mx) 20,000

10,097 9305 2796

61,885 12,000 2500 35,000 12,000 1600 1423

7585 25,061 25,775 26,100 6000 12.500 10,762 40,OOfl 5000

73,914 13,137 7481 13,256

lO$QO 13,659 40,848

89,340 13,677 6500

49,735 11,735 31,710 3934 72,322 123,285

125,000 53,414 21,220

36 35 36 31

26 22 22

25 20 22 17 19 22 26

33 30 24 14 27 30 32 17 30

34 29 28 18

27 24 13

13 18 35

:: 16

3.5 32 36

2.5 2.5 9

74 75 76 17 78

: f. 73

67 68 69 70

58 59 60 61 62 63 64 65 66

54 55 56 57

:f 53

48 49 50

2 47

2

42

39 40 41

p: K

I 1 1 1 1

1

2600 22 22

1700 1900 2200 2600

g 20 2200

$ E 8. B

r! r; 3‘ 3 c a

61 w

*

27 3ooo 3200 1700 3000 25

3400 2900 2800 1800 3300 30 2400 14

27 2400 1300

1300 1800 3500

3500 3200 36 3200 2500 1600

2500 2500 900

4 2 2

2 2 4 4 4 4 4

: 2 2 2 4 4 4 4

2 4 4 4

2 4 4

4 4 4

5 4 4 4

2

4 4 4

100

FRANK P.

BUFFA

Structural constraints depict the 80 decision packages as variables in the model and link each variable with its ZBB priority. Each of the 80 structural constraints is as follows :

Xj + Dj = 1,

(1)

where Xi is the fraction of requested funds allocated to thejth decision package and Dj is the deviation from the request expressed as a fraction. The constant 1 implies that no decision package can receive more funds than requested. The ZBB priority placed upon the jth decision package is associated with Xj through the variable Dj and is formalized in the objective function of the model. The higher the priority placed upon finding Xj, the more important it is to keep the value of Dj small or, more importantly, to reduce it to zero. There are 15 issue-related constraints, each corresponding to a different planning issue identified by either the city council, the city administrative staff, or the citizens’ planning survey. Some planning issues correspond directly to proposed new supplemental decision packages. These constraints formalize this association. Each of the 15 planning issue constraints is stated as follows:

1 AijXj

+ Gi = 1,

j where A, is a percentage expressing the contribution made by the jth decision package toward achieving the ith planning issue goal and Gi is the resulting deviation from the planning issue goal after summing the contribution made by all decision packages, and 1 is the planning issue goal expressed in relative terms. The value, A,, is a linear combination of the budget committee’s estimate of the impact that the jth decision package has on the ith planning issue and the committee’s ranking sum for the jth decision package. The former is difficult to quantify. The ZBB process does not require this quantification or even that the linkage between the planning issue and the decision package be formally expressed. The latter balances the impact estimate where the assumption is that when ranking a decision package, each budget committee member considers the significance of the package in relation to the proposed planning issue. The importance of achieving the goal for the ith planning issue is associated with the issue through Gi and is reflected in the objective function of the model. The more important it is to achieve the planning issue goal, the higher is the priority placed upon reducing Gi to zero. Part A of Table 2 includes a description of the 15 planning issues considered during Denton’s 1981-82 ZBB process. For each issue, Table 2 lists the planning issue rank set by the budget committee based upon inputs from the city council, the citizen survey, and the city staff, the model constraint number for the issue, the contributing decision packages, their variable numbers, and the estimated contributions made by the decision packages to the planning issues. The resource constraints reflect restrictions present in the budgeting process. The primary resource constraint is the available revenues, while others deal with a hiring ceiling on new employees, and partial funding for some decision packages during the fiscal year. The budget constraint is:

where Bj is the funds requested by the jth decision package and R is the estimate of general fund revenues available for allocation to the supplemental decision packages.

A ZBB process with goal programming feedback

101

The employee hiring constraints is:

where Ej is the number of full-time equivalent man-years of new employee time requested in the jth decision package and N is the maximum allowable number of man-years set by the city. The constraints for the 7 decision packages that can be funded for a fraction of the year are similar to the structural constraints. They specify that no penalty occurs if these decision packages are funded up to the allowable minimum as specified in the constraint. For each of the 7 decision packages the constraint is: Xj

+

Uj

-

Oj

=

0.5,

(5)

where Uj is the fraction by which the allocation to the jth decision package understates the allowable minimum level of 0.5, Oj is the fraction by which the allocation exceeds this level, and 0.5 indicates that the minimum allowable level of funding is for half the fiscal year. Part C of Table 2 presents those decision packages that allow for partial funding without penalty. Model objective function

The budget committee, when ranking decision packages and planning issues, specifies the importance of the decision packages and the planning issues and dictates a funding priority for the ZBB process. The higher the priority, the greater is the hkelihood that the decision package will be funded or the planning issue goal will be achieved. The committee uses both decision package ranking sums and planning issue rankings in order to synthesize in the model two different sets of inputs. One set originates with department heads and relates to the importance of decision packages. Budget committee members use this input to rank decision packages. The other set originates from the city council, city staff, and citizen survey. From this the budget committee ranks planning issues. During the budgeting process, the committee used the model to specify a funding pattern under different priority structures. The committee also used each output to further revise and refine the priority structure. For the purposes of presenting the form of the objective function, the first priority structure is presented. The structure is similar to the ZBB priorities used by the committee in the past. The major difference is that planning issue goals are now included, but at a relatively low priority level. The objective function includes four priority levels. Decision packages relating to contractual, legal, or other established commitments are at the first priority level. Part B of Table 2 identifies these decision packages. At the second priority level are restoration decision packages. Within this level, those packages containing employee positions receive a greater weight than those not including employee positions. The weights assigned to these decision packages are based upon the ranking sum specified by the budget committee. Planning issue goals and their achievement are at the third priority level. A summary ranking based upon the rankings provided by the city council, the city administrative staff and the citizen survey reflects the importance of each planning issue. The fourth priority level is for all decision packages not included at a higher level where a weight based on the decision package’s ranking sum reflects its relative importance. The variables, Dj and Uj, in the objective function link the priority levels and weights to the decision packages, while the variables, G,, do the same for the planning issues. For example, if Xj is a decision package representing a legal commitment, then it is at the first priority level. When minimizing the value of the objective function, the GP model first attempts to reduce the value of Dj to zero. This, in turn, forces the value of Xj to increase to its maximum value as specified in the structural constraint. The objective

89

92

93 94 95 96

63 46 18 2

38 47 68

Unranked

Throughfare planning Recreation and leisure activities Code enforcement Computer services

Emergency medical service Centralized bldg maintenance Animal control

Youth sports program

88

22

Street improvements

90 91

86 87

50 6

29 Unranked

83

4

Fire Employee pay productivity

Airport development Planning

Crime prevention

Planning issue

Constraint no. in model

Rank” assigned by city staff Sworn personnel overtime (holiday pay) Four additional police officers Four additional certified officers Traffic enforcement and accident investigation unit Crime prevention vehicle Crime prevention program (op. extra-eye) En~neering services Planning and zoning services Development review services Planning assistance service Fire inspector Management training Office of productivity services Salary reserve Labor and material Crack seal Street patching Street renovation TraBic engineer Comprehensive master plan Code enforcement Word processor and printer Word processing and furniture Computer system update (lease/purchase) Motor pool vehicle replacement Building superintendent Animal control officer Additional patrol unit Youth sports donation Ballfield clay Comprehensive master plan

Decision package contributing to planning issue goal

A: Planning issue constraints

0.058 0.1 0.452 0.164 0.452 0.376 0.186 0.10 0.164 0.186 0.5 0.334 0.292 0.186 0.142 0.031 0.090 0.142 0.208 0.186 0.334 0.23 0.112 0.12 0.058 0.066 0.186 0.090 48 49 50 21 17 18 19 57 2 4 77 32 37 38 39 41

:: 45 55 I 52 53 61 62 65

. .^ ,,”

0.142 0.082

ZI

OS

44

Contribution made by decision package to planning issueA, coefficient

46 47

Decision package (variable) no. in model

Table 2. Data for constraints: planning issues, legal or contractual commitments, decision packages allowing partial funding

,,

.

.

-I

O.fO6 a.112 0.090

68 $ ::

Wind smetm$r Pool improvem~t~

Picnic pavilion Basic years course

3

4% 46 47 4& 53 74

98

99 100 iat 102 IO3 104

LO 1.C X.0

:;s I.0 1.0

Co&Gent (Arif __ ._ __... ..__.

__

Contribution made by decision package to planning issueA, coefficient

* Not ah issues relate to decision packages in the general fund budget, thus there are gaps in the ranks presented here.

Clerical support Traffic engineer Pour additionat police officers Four additional certified officers Traffic enforcement and Accident jnve~tigat~on unit Additional patrol unit Additional library clerk

Package description

Decision Package (variable} no. in model

79 78 20 6 80 77

Constraint number in model

C: Partial Funding Packages

County-wide tax diz+trict Sycamore street bridge Software licenses Service center leax: operation Contingency reserve Salary reserve

Decision package (variable) no. in model

OS 12 0.103

0.120 0.090 0.186

60 ::

Summer piaygronnd program Bailfield clay Comprehensive master plan ~~ygrouad r~ovat~on

B: Legal or ~ontra~tna~ Commitments

97

Appraisal district Bridge renovation Data processing improvements Service center lease ~n~ngeacy reserve Salary reserve

Unranked

Legal or contractual commitments

program

Decision package contributing to planning issue goal

~arks/~iay~ound

Table 2..--cu~ti~ue~

Legal/administration Personnel/administration Personnel/administration Per~nnel/administration Civil defense Civil defense Civil defense Community davelopment/admin. Community development/admin. Community development/admin.

Restore departmental budget Administration support M.P.A. intern Employee training

Word processor and printer Vehicle maintenance Radio maintenance

Planning and zoning services Development review services Planning assistance service

Finance/customer service Finance/customer service Finan~/a~ounting Finance/purchasing Finance/customer service Finance/customer service Finance/purchasing Finan~/administration Public Public Public Public Public Public Public Public Public Public Public

Engineering services Unicorn radio

Customer service Service connection Restore clerical and training Purchasing service Replacement vehicles Additional vehicle Word processing and furniture Long range planning

Street lights Labor and materials Labor Building inspector Vehicle maintenance Vehicle Crack seal Street patching Street renovation Code enforcement Traffic engineer

works/street lighting works/street patching works/street sweep and drain works/inspections works/street patching works/traffic works/street construction works/street patching works/street construction works/inspections works/traffi~

Data processing/administration Airport/administration Airport/administration

Software licenses

operations operations operations operations operations

Building Building Building Building Building

Office space lease Service center lease operation Building superintendent Energy conservation modifications Roof replacement

govt/administration govt/administration govt/administration govt/ad~nistration

Gen. Gen. Gen. Gen.

~partment/D;vision

Office supplies Management training Clerical support Office of pr~uctivjty services

Package title

65,000 30,072 26,580 21,653 18,590 8050 25,OoO 175,000 125,000 53,474 21,220

26,435 6950 8934 4300 31,361 8908 5000 8033

259,400 9OtxI 1880

40,147 4400 5585

3500 265 500

9892 1833 9900

27,250

35,187 109,598 19,368 2746 16,000

3000 6400 6699 76,846

Requested amount

z 41

31 32 33 34 35 36 37 38

23 24 25 26 27 28 29 30

20 21 22

14 15 16 17 18 19

10 11 12 13

GP model variable number -

Table 3. Supplemental decision packages funded by ZBB process alone and by model

X X X X

X

X

X X

X

X

X

X

X

X X

X

X

Funded by ZBB process alone

c

X X X

X

X

X

X

X

X X

X

X

Funded by model using priority structure II

10,000 13,659 40,848 73,914 13,137 7481 13,256

Animal control Animal control Animal control Fire Fife Fire Fire Parks/~ks P~ks/parks Parks/recreation Parks/recreation Parks/athletic Parks/parks Parks/parks Parks/administration Parks/parks Parks/parks Parks/parks Parks/athletic Parks/recreation Parks/parks Parks/recreation Parks/recreation ~ibrary/t~h process ~ibrary/adult services ~ibr~y/childr~/youth

Firefighters Motor pool vehicle replacement Motor pool vehicle replacement Fire inspector

~5wing program Mowing equipment repla~ment Summer playground program Youth sports donation Ballfield clay irrigation system, North lakes Chemical and fertilization Comprehensive master plan Irrigation system conversion Truck replacement Playground renovation

Wind Screens Pool improvements Picnic pavilion Basic years course Ceramics program

Ad~tional library clerk Books for adult services Children’s supplies and materials Salary reserve Sycamore street bridge County-wide tax district Contingency reserve Transfers Transfers Transfers Transfers

and and and and

non-departmen~l non-~part~n~l non-departmental non-dep~t~ntal

70,tXlO SO,O(!O 40,000 20,800

10,087 9305 2796

2500 35,000 12,ooo 1600 1423

7585 25,067 25.775 26,100 6mo 12.500 101762 40,000 Noo 61.885 12;aoo

89,340 13,677 6500

Police/patrol Mice/administrative ~oiice/ad~nistrative

operations operations administration prevention

49,735 71,171 37,710 3936 12,322 123,285

Poli~/ad~nistrative Poli~/~ri~nal invest, Police/patrol Police/administrative Police)patrol Police/criminal invest.

Two policeofficerpositions Qne juveniie o&er and six vehicles Sworn personnel overtime (holiday pay) Computer system update (lease/purchase) Pour additional police officers Four additional certified officers Traffic enforcement and Accident investigation unit Crime prevention vehicle Crime prevention program (op. extra-eye) Bird control program Animal control officer Additional patrol unit

Table 3--continued

;: 84

77

74 75 76

!z 71 72 73

2 61 62 63 64 65 66 67 68

58

:: 54 55 56 57

51

48 49 50

42 43 44 45 46 47

z X X

X

X

x

::

X X

X

X X

X X

X

X

X

0.18"

0.48# X

X X

c

B %

D 4 _.

a w

a

2

9

FRANK P. BUFFA

1%

function of the model is: Minimize: x WjP,Dj + 1 WjP,,Dj 551

jdl

where PI through Pi, represent the four priority levels, where Pi $ Pti 9 Piii 9 Pi,. (The symbol 9 implies ‘very much larger’.) The weights within the priority levels are Wj and Ki, where Wj is a function of the ranking sum of the jth decision package and KS is a function of the rank assigned to the ith planning issue. Consider the P,,i level. Here the model focuses on achieving the stated planning issue goals rather than focusing on just the decision packages. At this level, packages are funded such that the underachievement of the planning issue goal is minimized. The other in which specific decision packages are funded at this level depends upon both the rank of the planning issue goal and the contribution that the decision package makes toward achieving the planning issue goal.

We discuss model results based upon two difIerent model priority seethes. The first set of results are based upon the past ZBB priorities set forth by the budget committee with minimal regard for the planning issue goals and their ranks. This structure, described in the previous section, parallels the way the committee used the ZBB system prior to the use of the model. With this structure, it is assumed that the ZBB ranking sum of the decision packages accounts for the planning issues and indirectly reflects the importance of the issues. Model results from using this structure are similar to the funding pattern that would result using just the ZBB ranking sum of the decision packages. Some ~eren~es in funding mix result since the planning issue goals and their ranks are included in the model, but at a relatively low priority level. The ZBB process alone allocated the estimated revenue ($1,871,358) to decision packages with ranking sums of 29 or more, In addition, it allocated $39,695 to decision packages numbered 23 and 35, that each have a ranking sum of 28. The model funded 10 packages that the ZBB process passed over, while the ZBB process funded 11 packages that the model ignored. These differences represent a total of $126,078 or approximately 6.7% of the total revenue allocated to supplemental decision packages, The difference resulted because in the model the priorities placed upon the restoration decision paekages and upon the planning issue goals were both higher than the priority placed upon new decision packages. Thus the model funded restoration decision packages and those packages making a contribution to a planning issue goal before considering new packages. All 10 decision packages funded only by the model are restoration packages and 7 of the 10 are related to a planning issue. Of the 11 decision packages that are funded using only the ZBB process, 9 are new decision packages that had low priority in the model. Considering the fifteen planning issue goals, the model, compared to the ZBB process used alone, yielded results that came closer to goal satisfaction in four cases, was further away in four other cases, and was the same as the ZBB process in seven cases. In addition, only one planning issue goal was fully achieved, and that was when the model determined the funding mix. These model results point out that the committee did not adequately reflect the importance of attaining the planning issue goals when ranking decision packages. The second priority structure discussed here places greater emphasis on the planning issues. In this structure, decision packages relating to legal or contractual commitments are at the first priority level, planning issue goals at the second, restoration decision

A ZBB process with goal programming feedback

107

packages including employee positions at the third, and all other decision packages at the fourth priority level. Table 3 presents the decision packages recommended by the model using this priority structure and those that were selected if only the ZBB process were used. It can be seen from Table 3 that the model using this priority structure recommended a substantially different funding mix. Considering planning goal achievement, the model, as compared to the ZBB system used alone, comes closer to planning issue goal achievement in twelve cases and is further away in three cases. These three cases are planning issues that were not ranked by the committee, but nevertheless were included in the model because they were of minimal significance. These model results are significant for two reasons. They demonstrate that the budget committee can not rely on the ranking of decision packages alone to adequately reflect the significance of the city’s planning issue goals, and that significant underachievement of these can be reduced only by explicitly reflecting the importance of the planning issues in the model priority structure. The model results also pointed out that most planning issues goals were unattainable even if all decision packages relating to the issues were funded. This result had a significant impact on the budget committee forcing it to review the goal levels set for the issues, to review the process of ranking decision packages, and to rethink each relationship between decision packages and planning issue goals. CONCLUSIONS In the Denton ZBB process the goal programming model is most useful at that stage when the budget committee reviews the proposed decision packages submitted by the city department managers. At this point in the ZBB process the decision packages are ranked and planning issues are identified. Using the model at this stage provides a format for the budget committee to be consistent in its rankings; to extend the relationship existing between decision packages and services to include planning issues identified by the city council, the administrative staff, and the citizens; and to appropriately reflect all these factors in the budget decision. The model should be adaptable for use by other cities using ZBB, or some other form of program budgeting. The specific use of the model would vary from one application to the next, but in general it should always be used as a diagnostic tool. The model’s data requirements are similar to those required of the budget process itself. A significant, additional data requirement is that planning objectives and their relationships to budget decision packages must be formalized. In the Denton case, we felt that significant benefits resulted from applying the model because it extended the formal structure of the budget process to explicitly include planning issues and external restrictions on the funding decision. These benefits are: The model (1) formalizes and insures the consistent application of the city’s ranking of the decision packages, (2) provides a format to formally identify and effectively measure how well any funding pattern achieves stated planning goals, (3) measures how external restrictions affect the funding decision, (4) is a very effective diagnostic tool to identify conflicting or invalid budget-related assumptions and incorrect relationships between budget decision packages and either city planning issues or external restrictions on the budget process, (5) is an effective analytical tool to more easily account for the large number of decision packages, planning issues, and external restrictions that one would expect to encounter with a city budget, (6) provides the format to critically evaluate alternative funding proposals with respect to the effects they would have on achieving the planning objectives. Difficulties related to using the model are: (i) The budget committee must quantify each planning issue goal, its priority, and the contribution each decision package makes toward achieving any goal. Quantifying these factors requires the decision maker to collect additional data. In most cases, however, these relationships are known and, in fact, are implicitly included in the ZBB process. (ii) The budget committee should use a

108

FRANKP.

BUFFA

computer to solve the model of a large ZBB process that is typically found in most city or state budgeting cases. With the recent technical advances in minicomputer systems and with the increased availability of these systems to small users, this is not a major difficulty to overcome. The model described here ran on an AMDAHL 47OV/6 computer, requiring 312 kbytes of memory, taking from 20 to 30 set to reach a solution using a goal programming simplex code similar to the one in Lee’s text L-63. Acknowledgemenfs-This research was supported by the Texas Innovation Group-Urban Program Group of the Center for Strategic Technology of the Texas Engineering Experiment Station of the Texas A&M University System. Support originated from the National Science Foundation’s Grant No. ISP7911986 to the Texas A&M University System. REFERENCES 1. Cowen S. and Dean B. V. The use of zero-base budgeting in local government: some observations. Interfaces 9(4), 61-66 (August, 1979). 2. Cowen S. Zero-base budgeting in municipalities. Cornput. Environ. Urb. Syst. 4(l), 65-77 (1979). of Linear Proaramming. 3. Charnes A. and Cooner W. W. Manaaement Models and Industrial Applications .. Wiley, New York (1961). 4. Ijiri Y. Management Goals and Accounting for Control. Rand-McNally, Chicago (1965). 5. Lee S. M. Decision analysis through goal programming. Decision Sci. Z(2), 172-180 (April, 1971). 6. Lee S. M. Goal Programming For Decision Analysis. Auerback, Philadelphia (1972). 7. Ruefli T. W. A Generalized Goal Decomposition Model. Mgmt Sci. 17(8), B505-B518 (April, 1971). 8. Ruefli T. W. PPBS-an analytical approach. In Studies in Budgeting (Edited by Byrne R. F., Charnes A., Cooper W. W., Davis 0. A. and Gilford, Dorothy), Vol. II, pp. 167-209. North-Holland, Amsterdam (1971). 9. Chaudhuri A. K. Analytical Modeling For Planning and Budgeting: Application of Mathematical Programming in a Zero Base Approach. University Microfilms International, Ann Arbor, Michigan (1980). 10. Pyhrr P. A. Zero-base budgeting. Haru. Bus. Rev. 48(6), 11 l-121 (November-December, 1970). 11. Pyhrr P. A. Zero-Base Budgeting: A Practical Tool For Evaluating Expenses. Wiley, New York (1973). 12. Pyhrr P. A. The zero-base approach to government budgeting. Public Admin. Rev. 37(l), l-8 (JanuaryFebruary, 1977). 13. Rehfuss J. Zero-base budgeting: the experience to date. Public Personnel Mgmt. 6(3), 181-197 (May-June, 19771 -.. .,. 14. Haider D. F. Zero base; federal style. Public Admin. Rev. 37(4), 40&407 (July-August, 1977). 15. LaFaver J. D. Zero-base budgeting in New Mexico. State Gout 47(2), 108112 (Spring, 1974). 16. Minmier G. S. and Hermanson R. H. A look at zero-base budgeting-the Georgia experience. Atlanta Econ. Rev. 26(4), >12 (July-August, 1976). 17. Scheiring M. J. Zero-base budgeting in New Jersey. State Gout 49(3), 174179 (Summer, 1976). 18. Singleton D. W., Smith B. A. and Cleaveland J. R. Zero-based budgeting in Wilmington, Deleware. Goutal Fin. 5(3), 20-29 (August, 1976). 19. Vanderbilt D. H. Budgeting in local government: where are we now? Public Admin. Rev. 37(S), 538542 (September-October, 1977). 20. Ignizio J. P. and Perlis J. H. Sequential linear goal programming: implementation via MPSX. Comput. Ops Res. 6(3), 141-145 (1979).

21. Arthur J. L. and Ravindran A. An efficient goal programming algorithm using constraint partitioning and variable elimination. Mgmt Sci. 24(R), 867-868 (April, 1978).