Just, Richard E.

Salkin, Michael S.

English

Research Papers in Economics

SOUTHERN  JOURNAL OF AGRICULTURAL  ECONOMICS  JULY,  1976
A SOLID WASTE PLAN FOR
SOUTHEASTERN  OKLAHOMA
Michael S.  Salkin and Richard E. Just
INTRODUCTION  was  used  to search  for optimal  numbers and location
Several  Southeastern  Oklahoma  towns located in  of landfill sites based on transportation  costs between
the  Kiamichi  Economic  Development  District  origins  and  landfills.  Three  active and  five  potential,
(KEDDO)  are  not  currently  in  compliance  with the  but nonexistent,  landfills  were  selected for considera-
Oklahoma  Solid  Waste Management Act of 1970  [4].  tion.  Sites considered  were  those  indicated  by a  in
The act requires that all incorporated  cities and towns  igure  .
Letting  S1,..., S2 5  5 represent all possible  com- adequately  dispose  of  solid  wastes  generated  within  S,  represent all possible co
incorporated  limits.  Most  areas  of  the  state  were  binations  (nonempty  subsets)  of  the  eight  potential
granted  extensions  until July 1975,  to operate  landfill  site combinations,  255==  1 (),  a cost minimization
facilities  in accordance with state requirements.  Some  problem  was  solved  for  each  landfill  combination.
large  towns  have  collection  and  disposal systems,  but  Each  cost  minimization problem  was subject  to both
many  smaller  towns have  no service  or partial  service.  supply  and  demand  restrictions.  The  problem  was
A few are  not in compliance  with the law.  expressed as:
The  counties  of  Oklahoma  contained  in  the
Kiamichi  Economic  Development  District,  hereafter
referred  to as KEDDO,  have  indicated  the  need for a  min TCk  C+Rk+FCs+  kC
solid  waste  management  plan,  Figure  1.1  In  view  of
the  area's  need,  the  goal  of  this  research  was  to  o
determine  the  least  cost  solid  waste  system  utilizing  +  j  xi  (1)
the  landfill  disposal  method.  The  KEDDO  area  was
divided  into two separate geographical  study areas for
the  purpose  of  examining  waste  systems.  The  firstt 
area,  consisting  of Choctaw and  McCurtain  counties,  n
2  xij =  ai,i=1,...,0  (2) was  considered  here.  Both  single  and  multicounty  j  =1  '
system  alternatives  were studied.  Further, the analysis
included  unincorporated  as  well  as  incorporated  o
E  xij<bj,jeSk  (3) areas.  i=1  -
METHODOLOGY
Linear  programming  was  employed  to  develop  x  0,i=,..,0;  jeSk  (4)
the  optimum  solid  waste  collection  and  disposal
system.2 In  particular,  a  cost-minimization  algorithm  where
The  authors  are  Assistant  Professor  of  Agricultural  Economics  at  Oklahoma  State  University  and  Assistant  Professor  of
Agricultural Economics  at University  of California,  Berkeley.
1The counties included in KEDDO are:  Pittsburg, Pushmataha,  McCurtain,  LeFlore,  Choctaw,  Latimer and Haskell.
The methodology  employed  is similar to that employed  in Clayton [1].
181SEAVER  HARPER  WOODS  ALFALFA  ORANT  KAY  O AGE  CRAIG
M  TAJORAW
FIGURE 1.  COUNTIES  OF  O  KLAHOMA;  KEDDO  COUNTIES  ARE  SHADED
ArDI  BLAINKolE  KI  MHIM  C  —  MK I  —E  \  I——
TCk total  monthly  cost  of  disposal,  collection  AN
oand  transportation  of  solid  waste  with  HK
soi  tIa  OK  CLAHOMA  la  l  a  le  ?.aUO
lOafill  MaILLe cntie  S  ULOHSK  I  •h  s
TCk  = totl monthly  cost of disposal,  collection 
and  transportation  of  solid  waste  with  rans-I  LE  |  <
C o = m  onthly  collection  costs  of  house-to-  /h^  \
house residential  pick-up  t  \m  /o  tu
Rk  - minimum  monthly  cost  of  containerized  MCALISTER  i  PTEAU
rural  collection;  and  transportation  of  HUGO  TOWS  ON  *.oT.\  l/  . \ 
solid waste with landfill alternatives  Sk  / 
FCs  = fixed  costs  of the system  (salaries,  boxes,  \  \
buildings and capital  expenses)  IPITTBU^RG  \  |  ^  LATIX  I  (I-1
xij = monthly  quantity  of  solid  waste  trans-  LEFLORE\
ported  from origin i to landfill j  I  I
bj = maximum  volume  of  waste  per  month  i  (1  FL  S 
crrrm ~  ~  ·~v~n Ici~f~  ~  ......  .:::.:  !  ...
disposed  in landfill  j  (in  terms  o  f  truck  h  1i
~l~o~~ad~s~~)  ^  TLERS~~~~~~~~~~~HSE · STIiLlHLL
ai = monthly  volume  of  waste  generated  in  \..  U^I^^
orig  in  i (in term s  of  truck  loads)  1j  EONT  \  e  d  f  o
eac~h  landfill  alternative.Theoptimalwa  .-.. "..'.'ste~......  s..  ......
cij =  wca  ost  p  er  ton  transported  from  origin i  to  .
landfill j
o = number of ori gins............  ...... 
(i)  Potential  La.ndfill Sites  \^ 
.......  .. ::''"-....'  ... :............
In  solving  the  above  transportation  problem  Co,  '""
FCs,  and  Cj  were  ignored  because  they  represented
fixed  values  for  each  landfill  alternative.  Hence,  for  FIGURE  2.  SOLID  WASTE  ORIGINS  AND  LAND.
urban  problems,  where  Rk=0,  the  function  in  (1)  FL  SITES  IN  CHOCTAW  AND
could  be  replaced  by  minTCk=jesk  zi= 1 XijCij  McCURTAIN  COUNTIES,  KEDDO,
subject  to  constraints  in  (2),  (3)  and  (4).  To  1  9  7  6 
determine  the  best  landfill  combination,  the  third
right  hand  term  in  (1),  jeSk Cj,  was  estimated  for
each  landfill  alternative.  The  optimal  waste  system
(landfill  alternative)  was  then  found  by  determining  TC = mn TC+S  C  (5)
k  jSk
182where  TCk  are  the  respective  minimums  for  TCk  in  routing  problem  consisted  of  devising  routes  to
the above  transportation  problems.  Since  Co and  FCS  minimize total mileage.
were  fixed  over  all  landfill  alternatives,  they  needed  Routes  were  established  on  the  basis  of  truck
to be estimated  only to establish user fees.  capacity.  Each  was  designed  so that  a  20 cubic  yard
For rural  problems,  the  SjeSkij=iXijCij  term  of  truck  could collect a week's solid waste production  in
equation  (1)  remained  equal  to  TCk  since  collection  one  trip. Thus,  each  route  was  contrained  to include
costs in the  rural system were  based entirely  on route  no  more  than  182  homes  or  business  equivalents;
mileage  traveled  by  collection  vehicles  (reflected  in  once-a-week  collection  was  assumed  and  resulted  in
Rk).  The  objective  function  for unincorporated  areas  40 routes.3
was:  The  major  difference  between  the  incorporated
areas  system  and  the  rural  one  was  inclusion  of
min TCk =Co+FCs+Rk+  I  Cj+TCk  (6)  collection  time.  In  the  urban  system,  number  of
6Je~Sk ~turcks  required  for  use  was  determined  on  basis  of
volume.  In  the  rural  system, calculation  of monthly
THE COMPONENTS  OF COST driving  time  to collect  solid  waste on  all  routes was
To  evaluate  the  objective  functions  in  (1),  (5)  necessary  because  a  significant  amount  of  time  was
and  (6)  it  was  necessary  to identify  costs associated  required  in  driving.4 A  practical  method  of  route
with  their  components.  Four  cost  categories  were  selection,  called  the lockset  method,  was  used in this
identified:  collection,  transportation,  landfill  costs  study  [2].
and shared  costs.  Transportation  costs  consisted  of  vehicle
Collection  costs were  directly associated  with the  operating  costs  between  origins  and  landfills.  Given
physical  collection  of  solid  waste.  These  included  the  twelve  origins  and  eight destinations,  transporta-
truck operating costs  (fuel,  depreciation,  maintenance  tion  costs  were  determined  between  each  landfill
and  repairs),  driver  salaries  and interest payments  on  combination  and  all  origins.  Although  255  landfill
collection  vehicles.  Collection  costs  were  a function  combinations  were possible, many combinations  were
of number of vehicles  required and distances  traveled  ruled  out on  the  basis of unnecessary  costs. With  few
per  month.  Vehicle  requirements  were  estimated  on  exceptions,  least  cost  combinations  resulted  when
the  basis  of  volume  and  miles  driven  in  making  existing  landfills  (Hugo,  Idabel,  Broken  Bow),
collections.  Assuming  a $.50  per mile  operating  cost  opposed to potential  ones were  included.
[3,  5]  and  a  monthly  tonnage  of  1500  tons,  collec-  Disposal  costs  included  fixed  and variable  costs.
tion  cost  in  incorporated  areas  was  approximately  Fixed  costs  included  land,  bulldozer  and  dozer
$4,500 per month.  operator,  utilities  and  set-up  expenses.  Variable  costs
Unincorporated  areas  were  characterized  by  a  included  the  hourly  operating costs of the equipment
wide  dispersion  of residences,  making house-to-house  plus maintenance.  Based on surveys of two Oklahoma
collection  prohibitively  expensive;  hence,  the  Rk  landfill  sites,  these  costs  were  approximately  $400
component  of equation  (6)  had to be estimated.  The  per site.5 Landfill  costs  were  estimated at $3,006  per
type  of collection  system planned  in rural areas  made  month.
use  of  steel  containers  placed  at  strategic  locations,  The  fourth  cost  component  estimated  was  the
enabling  rural  residents  to travel  short  distances  to a  shared  system  cost(s).  These  costs  were  spread  over
container.  all  system  components.  Major  items  of  shared  costs
Container  locations  were  at major highway  inter-  included  acquisition  and  operations  of a  truckbarn,
sections,  in  unincorporated  towns,  and  along  paved  hiring  of  employees  and  maintenance  of  collection
roads.  The  number  of  containers  employed  at  each  equipment.  Other costs  were  salaries  for a  supervisor
collection  point  was  determined  by  number  of  and  secretary,  insurance,  utilities  and  office  supplies.
residences  served,  where  each  container  served  13  For  the  two-county  system,  shared  costs  were
residences.  Given  a  set  of  landfill  alternatives,  the  $17,645  [5].
3 Each household produced  about 56 pounds of solid waste for disposal per week.  Given this estimate,  182 households would
produce about five tons of waste, which is 20 cubic yards,  or one truck load.
4Each  route  contained  14 containers  spaced  an average  of  2.85 miles apart.  Assuming  average  speeds  of 30  miles per hour
along the  routes and  45  miles  per hour  driving  to the  landfills,  the total  driving  time  per week  was approximately  45  hours. In
addition, almost 36 hours per week of truck time were required for loading, unloading and  overhaul.
5The variable  costs of operating a bulldozer were estimated at $2.50 per hour.  The machine consumes five gallons of fuel per
hour at a cost of $.40 per gallon. The cost of oil and maintenance  was approximately  $.50 per hour.
183EMPIRICAL  RESULTS  Combined  Analysis
Incorporated Area Analysis  Since  the  average  cost  of waste  collection  and Incorporated Area Analysis
disposal  fell  as  tonnage  handled  increased, costs  were
Table  1  contains  the  results  of the multicounty  estimated  when  incorporated  and  unincorporated
urban  analysis.  The  least  costly  option  was  that  in  areas  were combined  (Table 3). In the unincorporated
which  landfills  were  located  in  Hugo,  Idabel  and  areas,  house-to-house  collection  was  not  feasible
Broken  Bow.  Total  costs  were  $33,905  per  month,  because  residences  were  scattered.  Hence,  a  con-
with  a  fee  of  $2.58  per  residence.6 Other locations  tainerized collection  system was utilized in rural areas
with differing  numbers  of landfills and  other options  and  house-to-house  collection  in  incorporated  areas.
resulted in higher monthly costs.  As shown,  the least-cost  solution  required landfills at
As  a basis  of comparing  costs and corresponding  Hugo  and  Idabel  with  a  cost of $44,941  per month.
user  charges,  a  similar analysis  was  performed  on  an  User  fees  were  estimated  at  $2.18  per  month  per
individual  county  basis  to  determine  if  the  multi-  residence, resulting in a $.40 per month savings.
county  system  resulted  in  economies  of scale.  Costs  To  obtain  a  comparison  with  the  single  county
for  single  county  systems  and  corresponding  user  result,  presented  in  Table 2,  single  county  analyses
charges are presented in Table  2.  were  again  made,  including  unincorporated  area
The  lowest  cost  Choctaw  county  system  was  collection.  The  least-cost  system  serving  Choctaw
$21,902,  with  a  landfill  located  in  Hugo.  The  county  was  $27,783  per  month,  with  user  fees  of
least-cost  solution  in  McCurtain  County  also resulted  $3.02  per residence.  For McCurtain  county, the least
in a single landfill, located in Idabel.  cost  was  $29,621  per month  with  a $2.54  residence
Both  single  county  systems resulted  in  user  fees  charge.  Both  counties  incurred  user  costs lower than
larger  than  multicounty  systems.  Cost  reductions  those  reported  in  Table  2  but  larger  than  those  in
obtained  through  sharing  of equipment and  manage-  Table  3,  emphasizing  advantages  of  including  all
ment resulted  in economies  to users. In fact, the total  potential  customers.  Both the single county least-cost
cost of  operating  the Choctaw and McCurtain  county  system  and  single  county  combined  system  were
systems  separately  ($21,901  plus  $22,658)  was  obtained  with  single  landfills  in  Hugo  for  the
$44,560  which  was  $10,655  per  month  higher than  Choctaw  analysis  and  Idabel  for  the  McCurtain
the  least-cost  multicounty  plan.  An  excess  annual  system
cost of $127,860  resulted if the single county systems
were  operated independently.  The corresponding user
fees  for  a  single  county  system  were  lower  in
CONCLUSIONS  AND LIMITATIONS McCurtain County  (with a greater population) than in 
Choctaw  County,  further  supporting the economy of  The  hypothesis  that  economies  of  scale  can  be
size hypothesis.  achieved  through  the  operation  of  large  solid  waste
TABLE  1.  ESTIMATED  MONTHLY  SYSTEM  COSTS  FOR  A  MULTICOUNTY  URBAN  SYSTEM,  VARIOUS
LANDFILL COMBINATIONS,  KEDDO,  1975
(1)  (2)  (3)  (4)  (5)  (6)  (7)
LANDFILL  COLLECTION  TRANSPORTATION  DISPOSAL  SHARED  TOTAL  RESIDENCE
LOCATIONS  COSTS ($)  COSTS  ($)  COSTS ($)  COSTS ($)  COSTS ($)  CHARGE ($)
Hugo, Idabel,
Broken Bow  4,500  2,742  9,018  17,645  33,905  2.58
Idabel, Broken Bow  4,500  10,669  6,012  17,645  38,826  2.95
Hugo, Antlers, Idabel,
Broken Bow  4,500  1,973  12,024  17,645  36,142  2.75
Hugo, Antlers, Valliant,
Idabel, Broken Bow  4,500  1,408  15,036  17,645  35,583  2.71
Hugo  4,500  9,778  3,006  17,645  34,929  2.66
6Residence  fees  were  estimated  by  dividing total  system  costs by the  number of residences  being  served.  No attempt  was
made  to  calculate business  fees because  fees are traditionally  based on the frequency  of service  provided and volume of waste per
collection.
184TABLE  2.  ESTIMATED  MONTHLY  SYSTEM  COSTS  FOR  TWO  URBAN  SYSTEMS  IN  CHOCTAW  AND
McCURTAIN  COUNTIES,  KEDDO, 1975
(1)  (2)  (3)  (4)  (5)  (6)  (7)
LANDFILL  COLLECTION  TRANSPORTATION  DISPOSAL  SHARED  TOTAL  RESIDENCE
LOCATIONS  COSTS (  COSTS ($)  COSTS  ($)  COSTS  ($)  CHARGE ($)
Choctaw  County
Kent,  Hugo  2,354  1,276  6,012  14,922  24,564  4.92
Kent  2,354  2,511  3,006  14,922  22,793  4.56
Hugo  2,354  1,620  3,006  14,922  21,902  4.39
McCurtain  County
Rroken  Bow,  Valliant,
Golden  2,156  1,662  9,018  15,871  28,707  4.26
Broken  Bow,  Idabel  2,156  1,019  6,012  15,871  25,058  3.72
Idabel  2,156  1,628  3,003  15,871  22,658  3.36
systems  was  supported.  Counties  with  large  other  areas.  Our  conclusions  were  presented  for  a
populations  could  operate  a  system  at  a  lower  specific  geographical  area.  We  assumed  house-to-
per-resident  cost  than  a  small  county.  Multicounty  house  collection  in urban locations and containerized
systems  result  in  less  cost  per  residence  than  the  collection  in  rural  areas  would  take  place.  Certain
lowest  cost single-county  system.  Also, the operation  specifications  were  made  regarding  size  of  trucks,
of a multicounty  system resulted in $127,000  less per  containers,  wages,  size  of  facilities,  etc.  Changes  in
year than separate county-wide  systems.  the  method  of  collection  or specifications  of equip-
First,  Choctaw  and  McCurtain  counties  should  ment would alter results.
plan  to  operate  a  multicounty  system  designed  to  Likewise,  purchase  of  used  machinery  would
serve  both  rural residents  and  those living in  incorpo-  alter  not  only  initial  outlays  but also  variable  costs.
rated  areas.  If  rural  service  were  not  possible,  the  These  assumptions,  to  some  extent,  dictate  the
second  best  solution  was  a  multicounty  system  magnitude  of  system  cost.  Planners  in  any  state,
serving the  12 incorporated  areas.  If cooperation was  however,  can adopt  the  methodology  developed here
not feasible,  individual  counties  could minimize costs  to  determine  location  and  number(s)  of landfill sites
by  operating  a  single landfill each, and offering urban  and  the  costs  of  single  or multicommunity  systems.
as  well  as rural  service.  It  was  shown  that  incorpora-  Identification  of  prospective  landfill  sites,  distances
tion of rural areas lowered user  fees.  between  origins  and  these  sites,  and cost estimates  of
Assumptions  in this  analysis  must be  recognized  needed  equipment and personnel  are required data to
and kept in proper  perspective  by  system planners in  develop system  alternatives for any  area.
TABLE 3.  ESTIMATED  MONTHLY  COSTS  OF A MULTICOUNTY  RURAL-URBAN  SYSTEM IN CHOCTAW
AND McCURTAIN  COUNTIES,  KEDDO,  1975
(1)  (2)  (3)  (4)  (5)  (6)
LANDFILL  TRANSPORTATION  AND  DISPOSAL  SHARED  TOTAL  RESIDENCE
LOCATIONS  COLLECTION  COSTS  ($)  COSTS  ($)  COSTS  ($)  COSTS  ($)  CHARGE  ($)
Hugo,  Idabel,
Broken  Bow  11,546  9,018  26,763  47,327  2.30
Hugo,  Idabel  12,166  6,012  26,763  44,941  2.18
Hugo,  Idabel,
Broken  Bow,  Kent  8,690  12,024  26,763  47,477  2.31
Hugo,  Idabel,  Broken
Bow,  Valliant,  Golden,
Kent  10,009  18,038  26,763  54,810  2.67
185REFERENCES
[1]  Clayton,  Kenneth  C. and  John  M.  Huie.  Solid  Wastes  Management:  The  Regional Approach, Ballinger
Publishing Co.,  1973.
[2]  Hallberg,  M.  C.  and  W.  R.  Kriebel.  "Designing  Efficient Pickup  and  Delivery Route Systems by Computer,"
Penn State Bulletin  782, Penn  State University,  1972.
[3]  Kincannon,  D.  F.  and  T. A.  Haliburton.  "Solid  Waste  Collection  and  Disposal  for Rural  Areas,"  Oklahoma
State University,  August 1972.
[4]  Oklahoma State  Department of Health.  The Oklahoma Solid Waste Management Act of 1970, House Bill No.
1499,  Oklahoma Sessions  Law  1970  with  Rules and Regulations, O.D.H.  Engineering  Bulletin  No.
0525,  Oklahoma  City: Solid Waste Management,  Sanitation Division,  Environmental Health  Service.
[5]  Salkin,  M.  S.  "Solid  Waste  Planning:  Components  and  Costs  for  a Rural  System  in Southeast  Oklahoma,"
Agricultural  Experiment  Station, Oklahoma  State University,  Research  Report P-717, May  1975.
186

A SOLID WASTE PLAN FOR SOUTHEASTERN OKLAHOMA

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