- Email: [email protected]
A systematic procedure for the selection of bulk material handling equipment
233
International Journal ofProduction Economics, 27 ( 1992) 233-240 Elsevier
A systematic procedure for the selection of bulk material handling equipment Jayadev Velury and W.J. Kennedy Department of Industrial Engineering, Clemson University, Clemson, SC 29634, USA (Received 2 1 September
199 1:accepted in revised form 3 February 1992 )
Abstract Many companies use materials shipped in bulk and must solve material handling problems associated with these materials. This paper concentrates on the selection of relevant factors that need to be considered in the design of a bulk material handling system and on the selection of equipment once these factors have been considered. A model is presented which takes into account economics, characteristics of the equipment, environmental characteristics, and compatibilities between equipment types.
1. Introduction The amount of bulk material used in a plant may amount to hundreds of thousands of tons, and its storage and movement can have a significant impact on the productivity of a plant. Movement and transportation of bulk materials have different requirements from other types of materials. Bulk materials can be treated as continuous and are moved in large quantities [ 11. This unique property limits the application of the algorithms developed for other types of materials. A material handling system for such material involves large sums of money and thus justilies a detailed study. The result of such a study is an improved method of choosing the material handling and storage equipment best suited to the purpose and to the material. Factors that need to be explicitly taken into account are: ( 1) The degree to which protection from weather is needed. (2) Compatibility of different materials to be handled and moved with the same equipment. Correspondence to: J. Velury, Department of Industrial Engineering, Clemson University, Clemson, SC 29634, USA.
0925-.5273/92/$05.00
(3) Capacities of handling and moving equipment. (4) Budgetary constraints. The analysis presented here utilizes a mathematical programming decision model and a methodology to assist the decision maker in listing the factors that effect the design of handling system for bulk materials and decide on the specific type of handling or transportation equipment. This methodology can also assist in the evaluation of alternatives based on economic considerations. A specific planning horizon and time value of money are used. 2. Literature overview Most of the literature identifies the material handling equipment selection problem with the plant layout problem [ 2-4 1. Maxwell [ 2 ] modeled two of the typical problems in material handling: inter-plant flow and intra-plant flow. Willougby [ 41 presents a dynamic programming model for material handling equipment selection which minimizes the material handling cost by solving facility location and material handling equipment selection problems simultaneously. Leung et al. [ 31 discuss a mixed integer linear programming model for transportation in a plant
0 1992 Elsevier Science Publishers B.V. All rights reserved.
234
with a given layout, and work load requirements. Davis and Haddock [ 5j discuss the development of simulation generators for automated manufacturing cells that are connected by a material handling system. Tanchoco et al. [ 6 ] model the effects of unit load choices on the performance of a material handling system. Bulk materials have certain characteristics that make them different from other types of materials. Carson [ 7 1, ASME [ 8 1, Broersma [ 9 1, and Frisque [ IO] describe flow problems encountered while handling bulk materials. Carson 17) explains the funneling effect and mass-flow effect on the material while handling powders in ceramic industry. ASME [ 8 ] explains the effect of static and dynamic forces on the bulk material while in transit. Watford [ 1 ] describes the development of software specifically designed to facilitate simulation analysis of bulk material transportation systems. Her dissertation identifies the key decisions that are to be made in order to select transpo~ation equipment. Cooke [ 111 describes the selection of material handling and storage equipment for safer operation and considers the effect the material can have on the containers (or carriers ). The type of equipment to be employed is a function of suitability of the equipment for handling the given type(s) of material with quality, safety and other restrictions being other important characteristics. Tanchoco [ 121, and the Conveyor Equipment Manufacturers Association [ 131 describe the cost factors and decision parameters involved in the selection of belt conveyors. Pitts [ 141 describes the relative advantages and disadvantages of belt conveyors and trucks. Wuertele [ 151 describes the decision paof pneumatic rameters and advantages conveyors. In summary, significant work has been done in areas such as optimization of material layout, transportation, and material flow in a manufacturing environment. However, no attempt has been made to build an economic model which takes the factors that are involved in bulk material handling into consideration. Fu~hermore, in bulk material handling where we deal with material in large quantities, the location of different types of raw material in the storage area, and line
balancing are not the major problems. This restricts the applicability of most of the equipment selection algorithms available in the literature today. The need in such a case is to minimize the number of handling and storage activities and select the equipment that is economical and is capable of handling the requirements of the system such as quantity with acceptable quality. 3. Methodology This paper addresses the development of a decision model and methodology for selecting the material handling equipment for a bulk material handling problem. The objective of the methodology, developed to solve the material handling equipment selection model is to provide solutions to the following problems: ( 1) The type of equipment to select. (2) The number of units of each type of equipment to buy.
The process of material handling starts from the point where the raw material enters the system and ends with the delivery of the finished goods. The intermediate activities can be a nonproductive activity such as storage and delay or a productive activity such as processing. At each of these stages, the decision maker needs to analyze system constraints and make the decisions that are listed above. Also, he/she needs to evaluate the possibilities of eliminating the nonproductive activities. In order to solve this problem, it is necessary to simultaneously optimize the layout of the system and the total cost of equipment. A near optimal solution for a complicated problem of this nature may be achieved by decomposing it into three stages discussed below: Stage I: Reduce the number of storage and handling activities as much as possible, and develop a small number of alternative layouts which incorporate these activities. Stage II: Use the methodology presented below to select the equipment which will minimize the net present worth of all cash flows associated with the equipment, subject to budgetary and
235 compatibility constraints, considering the equipment choices that are available. Stage III Once the optimal equipment combination is found for each of the proposed layouts, select the layout and the corresponding equipment that has the least total discounted cost.
4. Model development The model uses mixed integer programming to pick the equipment to be performed at each location. 4.1. Model assumptions
3.2. Inputs to the model Model inputs include: ( 1) Capacity of the equipment: weight, volume, or number of units, per unit time, in dimensions which match the demand. The capacity can be calculated based on the factors listed in Ref. [ 16 1. (2 ) Equipment costs [ 16 ] : First cost (the initial capital investment to acquire the equipment ), fixed operating cost, and variable operating costs, proportional to the work done by the equipment. ( 3 ) Demand: The quantity to be handled and the distance it is to be moved. Both of these factors depend upon the sequence of operations and the layout of the plant. (4) Budget: Budgets impose limits on the funds initially available for purchasing equipment and on those available annually for operating and maintenance. Compatibility, in the following categories: (5) Compatibility of handling and transportation equipment types with one another, compatibility of the type of equipment with the type of material being transported, and capability of the equipment to handle or transport material without affecting the quality of the material. Optimize equipment selection for each selected layout in light of budgetary and compatibility constraints, considering the alternative equipment available. There are assumed to be budgetary constraints on the amount of money the decision maker is allowed to spend on the first cost of purchasing material handling equipment and on the annual fixed and variable costs of operating the material handling equipment. Compatibility constraints include assuring: (a) compatibility of a particular equipment type with the system, (b) compatibility of equipment types at material transfer points, and (c) compatibility of types of material being transported.
The model developed in this paper is based on the following assumptions: ( 1) Only one type of equipment is used in performing a particular job at a particular location. (2) The characteristics of storage bins have no effect on handling and transportation equipment decisions. (3) The expected value of maintenance cost of a unit of equipment is a percentage of its first cost. 4.2. Objectivefunction The total cost is a sum of two factors, handling cost and transportation cost. The handling cost is incurred at every location where there is a transfer of material such as a storage location or a processing location. Hence, the total handling cost is a sum of handling costs at each of the locations:
where TCH,
= FCH, * u, +,$,
TCH,
FCH, u,j
FCH,
(FCH,,+VCH,,X)/
(l+r)k. = Total cost of handling equipment of typej at location i: i= 1, .. .. I; j= 1, . ... J. = First cost of handling equipment of type j at location i. = The number of units of the handling equipment type j employed at location i. = Fixed cost of handling equipment type j located at the location i during the year k, where k= 1, .. .. K (the planning horizon).
236 = Variable cost of equipment j at location i per unit load handled during the year k. = The quantity handled at location i. xi = 1 if equipment typej at ith location PlJ is chosen; 0 otherwise. = The capacity of equipment type j at CH, location i. Y = Interest rate on borrowed capital. Transportation cost is incurred whenever material is transported from one location to another. The sum of all these transportation activities is the total transportation cost for the project: M N VCH,,,
4.3. Constraints Only one type of equipment particular job at any location: for i= 1, 2, 3, . . .
TCT,,
= FCT,,v,,
.
/=I
Only one type of transportation used on a particular route. :
4,,=1,
?I=1
Restrictions i i I=]
where
is chosen to do a
+ !
equipment
is
for m= 1,2, 3, . . . on the first cost are given by
FCH,U, + F
J=l
m=l
d
capital budget,
5 FCT,,V,, n=l
k=l (FCTmnk
+VCT,,kY,)/(
Restrictions
1 +r)“.
= Total cost of transportation equipmenttypenonroutem:m=l;~~, M,n=l;..,N. FCT,, = First cost of transportation mode of type n on route m. = The number of units of the hanV mn dling equipment type n employed on route m. FCTmnk = Fixed cost of handling equipment type n on route m during the year k. VCT,,/, = Variable cost of equipment n on route m per unit load transported during the year k. Y, = The quantity that is moved through route m. = 1 if equipment type n for mth ac4 mn tivity is chosen; 0 otherwise. CT,, = The capacity of equipment type n on route m. Hence the objective function to be minimized may be stated as
on the annual cost are given by
TCT,,
(cost of handling+
i
1~1
i J=l
TCH,p,
[(FCH,+VCH,Xi)
+ (FCT, + VCT, Y, ) ] < annual budget.
The compatibility relationships are based on the actual constraints in individual examples. The binary variables p. and qmn are included in the model to facilitate such constraints. As an example, if transportation of type n on route m requires a jib crane (which is type j) at location i, then this constraint can be introduced into the model as: WPljB4mn,
where W is a large positive number. If the equipment type n on route m is selected, then the right hand side of the equation becomes 1. This forces p,j to be 1 which means that equipment type j is selected at location i. 4.4. Other inputs to the model
cost of transportation) = The quantity that is handled at location i. (2) yt?l = The quantity that is transported on route m. = Int (Xi/CH,) + 1, for all i andj. c3) ulj + 1, for all m and n. (4) V,, = Int ( YJCT,,)
Cl)
= i:
i
i=l/=l
+ f rn=l
f n=l
TCT,,q,,
.
xi
237
(5) Capacity of equipment = (quantity that can be handled in a day) x (availability).
(6) Availability = (total work hours -down time-changeover hours ) .
time) / (total work
4.5. Steps in using the model
( 1) Determine alternative layouts. (2 ) Input the down time and changeover time for each equipment type under consideration and calculate their availability and the capacity. ( 3 ) Calculate the compatibility relationships of the equipment types with one another. (4) Minimize the total cost using the integer linear programming model discussed in this section. (5) Repeat steps (2) to (4) for each layout alternative. (6) Compare the projected costs for all the layouts and select the one that has the least total cost. 5. Example A power plant purchases the raw material (coal) from different suppliers across the country. The coal is brought to the storage area in railway cars where the power plant personnel unload, inspect, and store the coal. The coal is then loaded into trucks and dumped into a hopper where a belt conveyor moves the material into a silo. A payloader is used to pick up the coal from the silo and load it onto the conveyor that transports coal into the furnace. 5.1. Exploring the possibilities of alternative
layouts After sen for options and 2, and 2.
study, two alternative layouts were chofurther analysis, with a set of equipment for each. The layouts are given in Figs. 1 with the equipment options in Tables 1
5.2. Optimizing the alternatives
and minimizing alternatives.
the project cost for each of the
5.2.1. Original system At location one, the type of equipment that can be used for handling is a screw conveyor or a pay loader. The data related to this equipment are given in Table 3. The requirement at location one is 22 tons/day. The present worth of all handling costs at location one is 131985 pII+ p21. with the constraint that pi, +pzI = I. The calculations for the coefficients are awkward but feasible. For example, 13 1985 is the present worth of the cost for handling equipment type 1 (the pay loader) at location one, using a 10% interest rate to calculate the present worth, assuming that 22 tons per day are to be moved each of 260 days per year, with the purchase cost given in Table 3, and the fixed and variable costs given in Tables 4 and 5. In this and other calculations, any issues regarding significant figures have been neglected. The data for other handling and transportation activities for the original system is also shown in Table 3. The fixed and variable costs are estimated for every year during the six year period of planning horizon and are given in Tables 4 and 5. The handling and transportation costs for location two can be calculated similarly. With the coefficients thus calculated, the model becomes:
Minimize:
+95744 41, f46535 q21+37991 922. Subject to: (1) PIIt-PZl = 1. (2)
p12+p22=
(3) 4 11= 1
1.
(only available).
one
type
of
equipment
(4) q21+q22=1. (5) Budget: (The only budget constraint is on initial equipment purchase cost. Others could have been included. ) 50000 pr , + 8000 p12 + 30000 p2, + 6000 pz2
Stage two is a process of identifying the requirements of the material handling equipment
+48000 qll + 15000 q2, +20000 q22Il25000.
238 Handling
Handling
Transport
Fig. 1. Original system,
Handling
Handling
Transport
Storage Fig. 2. An alternative system. TABLE 1
TABLE 3
Equipment options for original system
Data for handling and transportation
Handling I: a. Pay loader b. Screw conveyor
equipment
Purchase cost ($I
Capacity (T/day)
Life (yr)
Availability
Transportation I: a. Truck
Location 1 Pay loader Screw conveyor
50000 8000
40 35
3 2
0.80 0.90
Transportation II: Belt conveyor :: Pneumatic conveyor
Location 2 Pay loader Screw conveyor
30000 6000
35 32
3 2
0.80 0.90
Handling II: Pay loader :: Screw conveyor
Route 1 Truck
48000
50
6
0.90
Route 2 Belt conveyor Pneumatic
15000 26000
22 22
6 6
0.70 0.92
TABLE 2 Equipment options for alternative system Handling I: a. Pay loader b. Screw conveyor Transportation I: Belt conveyor :: Pneumatic conveyor Handling II: a. Pay loader b. Screw conveyor
( 6 ) Compatibility. The coal is unloaded from the rail cars on the ground and it is not convenient to use a screw conveyor. This results in
p12=0.
The problem is solved using QSB [ 17 ] and the results are as follows: ( 1) At location one, the payloader is selected. (2) At location two, the screw conveyor is employed. ( 3 ) For movement of material from location one to the silo, a truck is used. (4) For loading coal into the silo, a belt conveyor is used. The total cost of the project is $283911. 5.2.2. Alternative system An alternative
system has been defined in Fig.
239 TABLE 4
Subject to:
Fixed costs for example
(l)P,,+P,z=l. (2)
Year of operation 1 Location 1 Pay loader Screw conveyor
2
3
4
5
6
$1350 8060’
$51300’ 60
$1350 8060’
$1350 60
1. 1.
50000 p1 I + 8000 p21 + 30000 p12 + 6000 pz2 $1300 $1350 60
+ 80000 ql, + 120000 q125 125000
( 5 ) Compatibility:
Location 2 Pay loader Screw conveyor
1000 52
1100 55
1200 6052’
31000’ 55
1100 6052’
1200 55
520
550
550
570
590
600
Route 1 Truck Route 2 Belt conveyor Pneumatic conveyor *Equipment
ih+1)22=
(3) 411+4,2= (4) Budget:
2600 2288
2800
2900 2290
3000
The coal is unloaded from the rail cars on the ground and a screw conveyor cannot be used. This results in assigning a value of 0 to P,~. This problem has no feasible solution as the purchasing cost for belt/pneumatic conveyors for this layout is beyond the budget.
3200
5.3.
Stage III
By comparison of the projects we select the original system as the alternative is not feasible. The total project cost is $2839 11.
is replaced.
TABLE 5 Variable costs/ton
5.4. Sensitivity analysis
for example Year of operation 1
2
3
4
5
6
Location 1 Pay loader Screw conveyor
$1.50 0.15
$1.70 0.20
$1.90 0.15
$1.50 0.20
$1.70 0.15
$1.90 0.20
Location 2 Pay loader Screw conveyor
1.50 0.14
1.80 0.16
2.10 0.14
1.50 0.16
1.80 0.14
2.10 0.16
1.40
1.60
1.80
2.00
2.20
2.40
0.50 0.10
0.50 0.10
0.70 0.10
0.90 0.15
1.10 0.15
0.15
Route 1 Truck Route 2 Belt conveyor Pneumatic conveyor
1.20
2 and Table 2, using cost and capacity data from Tables 3, 4, and 5. The resulting mathematical formulation for this system is
Minimize: 131985p,,
+23569p12+99621
p2]
+18191p2Z+105665q1,+132992q12.
In order to validate the above solution in light of possible errors in estimating the costs, a sensitivity analysis is conducted to demonstrate the sensitivity of the solution to the variations in each of the equipment costs. In order to test such sensitivity, each variable is analyzed independently and the cost coefticients are varied to determine the limits within which the final solution remains the same. As an example consider transportation activity two. The alternatives on this route are a belt conveyor and a pneumatic conveyor. The model selected the belt conveyor whose total cost is $37991 against the pneumatic conveyor whose total cost is $46535. The objective of the sensitivity analysis is to determine x and y, where x and y are the limits such that any cost in the range ($3799 1 +$x, $3799 1 - $y) still results in selection of the belt conveyor. A series of integer linear programming models are run for various values of x and y to determine that range. In this example, the only alternative to the belt conveyor is the selection of a pneumatic conveyor. Since the total cost of the pneumatic conveyor is higher than that of a belt conveyor, there
240 are no chances of making errors on the lower side of Ihe estimation and hence, as far as the sensitivity of the solution is concerned, the value of y becomes immaterial. On the higher side, the solution is not going to be affected by the errors in the estimation of the total cost of belt conveyor unless it exceeds $46535, which is a an error of about 33%. Any error which is below 33% in the estimation of the total cost of the belt conveyor will not affect the solution. Further, an error of 33% is not expected in the cost estimations and hence, the decision of selecting the belt conveyor on route two can be considered safe.
4
6. Conclusions and recommendations
9
The special characteristics of bulk materials necessitate a careful examination of the factors which influence the material handling equipment selection process. This paper has identified the factors that pertain to the type of material, the type of the system for which the’ material handling sub-system is being designed, and the outside system factors such as geographic location, weather conditions etc. These factors have been analyzed in a systematic way and are built into a mathematical model. Future research in this area could include study of additional factors that have influence on the storage of bulk materials and integration of the factors relevant to both movement and storage into one model. Other factors that could be included in future research are the possibilities of damage induced by some kinds of equipment and the effect such damage might have on processing. References Watford, B.A., 1985. Simulation Software for Bulk Material Transportation System’s Analysis. Unpublished PhD Dissertation. Virginia Polytechnic Institute and State University. Maxwell, L.W., 198 1. Solving Material Handling Design Problems With OR. Ind. Eng.: pp. 58-66. Leung, L.C., Khator, SK. and Kimbler, D.L., 1987. Assignment of AGVs with Different Vehicle Types. Mater. Flow, 4: 65-72.
5
6
7 8
10
II 12
13
14
15 16
17
18
19 20
21
Willou~by, W.D., 1967. A Technique for Integrated Facility Location and Materials Handling Equipment Selection by Dynamic Programming. Unpublished MS Thesis. Purdue University. Davis, R.P. and Haddock, J., 1986. A Simulation Generator for the Selection and Design of Material Handling Devices. Int. J. Model. Simul., 6 (3). Tanchoco, J.M.A., Agee, M.H., Davis, R.P. and Wysk, R.A., 1980. An Analysis of the Interactions Between lJnit Loads, Handling Equipment, Storage, and Shipping. ASME-Century 2. The Material Handling Conference, San Francisco: pp. 185-l 90. Carson, W.J., 1988. Powder Handling in Ceramic Industry. Ceramic Bull., 67(5). ASME, 1979. Mechanics Applied to the Transport of Bulk Materials. American Society of Mechanical Engineers, New York. Broersma, G., 1972. Behavior of Granular Materials. Stam Technical Publications, Culemborg. Frisque, D.E., 197 1. Physical Properties of Bulk Materials. Bulk Materials Handling, 1. In: M. Hawke (Ed. ), pp. 364-380. Cooke, J.A., 1988. Safer Ways to Move Bulk Cargo. Traffic Management. Tanchoco, J.M.A., 1983. Model Formulation. Class Notes, Virginia Polytechnic Institute and State University. Conveyor Equipment Manufacturers Association, 1979. Belt Conveyors for Bulk Materials, Second Edition. CBI Publishing Company, Boston. Pitts, C., 1980. Belt Conveyor Versus Truck for Coal Transportation. Unit and Bulk Materials Handling, presented at the Material Handling Conference, August 1921, 1980: pp. 47-52. Wuertele, F.S., 1988. Pneumatic Conveyors: Moving Material with Air. Plant Eng. 42: pp. 56-58. Velury, J., 1990. An Algorithm for the Selection of Bulk Material Handling Equipment. MS Thesis, Clemson University. Chang, Y.-L. and Sullivan, R.S., 1989. QSBi : Quantitative Systems for Business Plus. Prentice-Hall, Englewood Cliffs, NJ. Apple, J.M., 1976. How to Determine Material Handling Costs. Material Handling and the Industrial Engineer, American Institute of Industrial Engineers. Eastman, R.M., 1987. Materials Handling. Dekker, New York. Material Handling Engineering - Directory & Handbook, 1963-I 964. Industrial Publishing Corporation, Ohio. Reed, R., 1976. Material Handling Cost Factors. Material Handling and the Industrial Engineer. American Institute of Indust~al Engineers.
International Journal ofProduction Economics, 27 ( 1992) 233-240 Elsevier
A systematic procedure for the selection of bulk material handling equipment Jayadev Velury and W.J. Kennedy Department of Industrial Engineering, Clemson University, Clemson, SC 29634, USA (Received 2 1 September
199 1:accepted in revised form 3 February 1992 )
Abstract Many companies use materials shipped in bulk and must solve material handling problems associated with these materials. This paper concentrates on the selection of relevant factors that need to be considered in the design of a bulk material handling system and on the selection of equipment once these factors have been considered. A model is presented which takes into account economics, characteristics of the equipment, environmental characteristics, and compatibilities between equipment types.
1. Introduction The amount of bulk material used in a plant may amount to hundreds of thousands of tons, and its storage and movement can have a significant impact on the productivity of a plant. Movement and transportation of bulk materials have different requirements from other types of materials. Bulk materials can be treated as continuous and are moved in large quantities [ 11. This unique property limits the application of the algorithms developed for other types of materials. A material handling system for such material involves large sums of money and thus justilies a detailed study. The result of such a study is an improved method of choosing the material handling and storage equipment best suited to the purpose and to the material. Factors that need to be explicitly taken into account are: ( 1) The degree to which protection from weather is needed. (2) Compatibility of different materials to be handled and moved with the same equipment. Correspondence to: J. Velury, Department of Industrial Engineering, Clemson University, Clemson, SC 29634, USA.
0925-.5273/92/$05.00
(3) Capacities of handling and moving equipment. (4) Budgetary constraints. The analysis presented here utilizes a mathematical programming decision model and a methodology to assist the decision maker in listing the factors that effect the design of handling system for bulk materials and decide on the specific type of handling or transportation equipment. This methodology can also assist in the evaluation of alternatives based on economic considerations. A specific planning horizon and time value of money are used. 2. Literature overview Most of the literature identifies the material handling equipment selection problem with the plant layout problem [ 2-4 1. Maxwell [ 2 ] modeled two of the typical problems in material handling: inter-plant flow and intra-plant flow. Willougby [ 41 presents a dynamic programming model for material handling equipment selection which minimizes the material handling cost by solving facility location and material handling equipment selection problems simultaneously. Leung et al. [ 31 discuss a mixed integer linear programming model for transportation in a plant
0 1992 Elsevier Science Publishers B.V. All rights reserved.
234
with a given layout, and work load requirements. Davis and Haddock [ 5j discuss the development of simulation generators for automated manufacturing cells that are connected by a material handling system. Tanchoco et al. [ 6 ] model the effects of unit load choices on the performance of a material handling system. Bulk materials have certain characteristics that make them different from other types of materials. Carson [ 7 1, ASME [ 8 1, Broersma [ 9 1, and Frisque [ IO] describe flow problems encountered while handling bulk materials. Carson 17) explains the funneling effect and mass-flow effect on the material while handling powders in ceramic industry. ASME [ 8 ] explains the effect of static and dynamic forces on the bulk material while in transit. Watford [ 1 ] describes the development of software specifically designed to facilitate simulation analysis of bulk material transportation systems. Her dissertation identifies the key decisions that are to be made in order to select transpo~ation equipment. Cooke [ 111 describes the selection of material handling and storage equipment for safer operation and considers the effect the material can have on the containers (or carriers ). The type of equipment to be employed is a function of suitability of the equipment for handling the given type(s) of material with quality, safety and other restrictions being other important characteristics. Tanchoco [ 121, and the Conveyor Equipment Manufacturers Association [ 131 describe the cost factors and decision parameters involved in the selection of belt conveyors. Pitts [ 141 describes the relative advantages and disadvantages of belt conveyors and trucks. Wuertele [ 151 describes the decision paof pneumatic rameters and advantages conveyors. In summary, significant work has been done in areas such as optimization of material layout, transportation, and material flow in a manufacturing environment. However, no attempt has been made to build an economic model which takes the factors that are involved in bulk material handling into consideration. Fu~hermore, in bulk material handling where we deal with material in large quantities, the location of different types of raw material in the storage area, and line
balancing are not the major problems. This restricts the applicability of most of the equipment selection algorithms available in the literature today. The need in such a case is to minimize the number of handling and storage activities and select the equipment that is economical and is capable of handling the requirements of the system such as quantity with acceptable quality. 3. Methodology This paper addresses the development of a decision model and methodology for selecting the material handling equipment for a bulk material handling problem. The objective of the methodology, developed to solve the material handling equipment selection model is to provide solutions to the following problems: ( 1) The type of equipment to select. (2) The number of units of each type of equipment to buy.
The process of material handling starts from the point where the raw material enters the system and ends with the delivery of the finished goods. The intermediate activities can be a nonproductive activity such as storage and delay or a productive activity such as processing. At each of these stages, the decision maker needs to analyze system constraints and make the decisions that are listed above. Also, he/she needs to evaluate the possibilities of eliminating the nonproductive activities. In order to solve this problem, it is necessary to simultaneously optimize the layout of the system and the total cost of equipment. A near optimal solution for a complicated problem of this nature may be achieved by decomposing it into three stages discussed below: Stage I: Reduce the number of storage and handling activities as much as possible, and develop a small number of alternative layouts which incorporate these activities. Stage II: Use the methodology presented below to select the equipment which will minimize the net present worth of all cash flows associated with the equipment, subject to budgetary and
235 compatibility constraints, considering the equipment choices that are available. Stage III Once the optimal equipment combination is found for each of the proposed layouts, select the layout and the corresponding equipment that has the least total discounted cost.
4. Model development The model uses mixed integer programming to pick the equipment to be performed at each location. 4.1. Model assumptions
3.2. Inputs to the model Model inputs include: ( 1) Capacity of the equipment: weight, volume, or number of units, per unit time, in dimensions which match the demand. The capacity can be calculated based on the factors listed in Ref. [ 16 1. (2 ) Equipment costs [ 16 ] : First cost (the initial capital investment to acquire the equipment ), fixed operating cost, and variable operating costs, proportional to the work done by the equipment. ( 3 ) Demand: The quantity to be handled and the distance it is to be moved. Both of these factors depend upon the sequence of operations and the layout of the plant. (4) Budget: Budgets impose limits on the funds initially available for purchasing equipment and on those available annually for operating and maintenance. Compatibility, in the following categories: (5) Compatibility of handling and transportation equipment types with one another, compatibility of the type of equipment with the type of material being transported, and capability of the equipment to handle or transport material without affecting the quality of the material. Optimize equipment selection for each selected layout in light of budgetary and compatibility constraints, considering the alternative equipment available. There are assumed to be budgetary constraints on the amount of money the decision maker is allowed to spend on the first cost of purchasing material handling equipment and on the annual fixed and variable costs of operating the material handling equipment. Compatibility constraints include assuring: (a) compatibility of a particular equipment type with the system, (b) compatibility of equipment types at material transfer points, and (c) compatibility of types of material being transported.
The model developed in this paper is based on the following assumptions: ( 1) Only one type of equipment is used in performing a particular job at a particular location. (2) The characteristics of storage bins have no effect on handling and transportation equipment decisions. (3) The expected value of maintenance cost of a unit of equipment is a percentage of its first cost. 4.2. Objectivefunction The total cost is a sum of two factors, handling cost and transportation cost. The handling cost is incurred at every location where there is a transfer of material such as a storage location or a processing location. Hence, the total handling cost is a sum of handling costs at each of the locations:
where TCH,
= FCH, * u, +,$,
TCH,
FCH, u,j
FCH,
(FCH,,+VCH,,X)/
(l+r)k. = Total cost of handling equipment of typej at location i: i= 1, .. .. I; j= 1, . ... J. = First cost of handling equipment of type j at location i. = The number of units of the handling equipment type j employed at location i. = Fixed cost of handling equipment type j located at the location i during the year k, where k= 1, .. .. K (the planning horizon).
236 = Variable cost of equipment j at location i per unit load handled during the year k. = The quantity handled at location i. xi = 1 if equipment typej at ith location PlJ is chosen; 0 otherwise. = The capacity of equipment type j at CH, location i. Y = Interest rate on borrowed capital. Transportation cost is incurred whenever material is transported from one location to another. The sum of all these transportation activities is the total transportation cost for the project: M N VCH,,,
4.3. Constraints Only one type of equipment particular job at any location: for i= 1, 2, 3, . . .
TCT,,
= FCT,,v,,
.
/=I
Only one type of transportation used on a particular route. :
4,,=1,
?I=1
Restrictions i i I=]
where
is chosen to do a
+ !
equipment
is
for m= 1,2, 3, . . . on the first cost are given by
FCH,U, + F
J=l
m=l
d
capital budget,
5 FCT,,V,, n=l
k=l (FCTmnk
+VCT,,kY,)/(
Restrictions
1 +r)“.
= Total cost of transportation equipmenttypenonroutem:m=l;~~, M,n=l;..,N. FCT,, = First cost of transportation mode of type n on route m. = The number of units of the hanV mn dling equipment type n employed on route m. FCTmnk = Fixed cost of handling equipment type n on route m during the year k. VCT,,/, = Variable cost of equipment n on route m per unit load transported during the year k. Y, = The quantity that is moved through route m. = 1 if equipment type n for mth ac4 mn tivity is chosen; 0 otherwise. CT,, = The capacity of equipment type n on route m. Hence the objective function to be minimized may be stated as
on the annual cost are given by
TCT,,
(cost of handling+
i
1~1
i J=l
TCH,p,
[(FCH,+VCH,Xi)
+ (FCT, + VCT, Y, ) ] < annual budget.
The compatibility relationships are based on the actual constraints in individual examples. The binary variables p. and qmn are included in the model to facilitate such constraints. As an example, if transportation of type n on route m requires a jib crane (which is type j) at location i, then this constraint can be introduced into the model as: WPljB4mn,
where W is a large positive number. If the equipment type n on route m is selected, then the right hand side of the equation becomes 1. This forces p,j to be 1 which means that equipment type j is selected at location i. 4.4. Other inputs to the model
cost of transportation) = The quantity that is handled at location i. (2) yt?l = The quantity that is transported on route m. = Int (Xi/CH,) + 1, for all i andj. c3) ulj + 1, for all m and n. (4) V,, = Int ( YJCT,,)
Cl)
= i:
i
i=l/=l
+ f rn=l
f n=l
TCT,,q,,
.
xi
237
(5) Capacity of equipment = (quantity that can be handled in a day) x (availability).
(6) Availability = (total work hours -down time-changeover hours ) .
time) / (total work
4.5. Steps in using the model
( 1) Determine alternative layouts. (2 ) Input the down time and changeover time for each equipment type under consideration and calculate their availability and the capacity. ( 3 ) Calculate the compatibility relationships of the equipment types with one another. (4) Minimize the total cost using the integer linear programming model discussed in this section. (5) Repeat steps (2) to (4) for each layout alternative. (6) Compare the projected costs for all the layouts and select the one that has the least total cost. 5. Example A power plant purchases the raw material (coal) from different suppliers across the country. The coal is brought to the storage area in railway cars where the power plant personnel unload, inspect, and store the coal. The coal is then loaded into trucks and dumped into a hopper where a belt conveyor moves the material into a silo. A payloader is used to pick up the coal from the silo and load it onto the conveyor that transports coal into the furnace. 5.1. Exploring the possibilities of alternative
layouts After sen for options and 2, and 2.
study, two alternative layouts were chofurther analysis, with a set of equipment for each. The layouts are given in Figs. 1 with the equipment options in Tables 1
5.2. Optimizing the alternatives
and minimizing alternatives.
the project cost for each of the
5.2.1. Original system At location one, the type of equipment that can be used for handling is a screw conveyor or a pay loader. The data related to this equipment are given in Table 3. The requirement at location one is 22 tons/day. The present worth of all handling costs at location one is 131985 pII+ p21. with the constraint that pi, +pzI = I. The calculations for the coefficients are awkward but feasible. For example, 13 1985 is the present worth of the cost for handling equipment type 1 (the pay loader) at location one, using a 10% interest rate to calculate the present worth, assuming that 22 tons per day are to be moved each of 260 days per year, with the purchase cost given in Table 3, and the fixed and variable costs given in Tables 4 and 5. In this and other calculations, any issues regarding significant figures have been neglected. The data for other handling and transportation activities for the original system is also shown in Table 3. The fixed and variable costs are estimated for every year during the six year period of planning horizon and are given in Tables 4 and 5. The handling and transportation costs for location two can be calculated similarly. With the coefficients thus calculated, the model becomes:
Minimize:
+95744 41, f46535 q21+37991 922. Subject to: (1) PIIt-PZl = 1. (2)
p12+p22=
(3) 4 11= 1
1.
(only available).
one
type
of
equipment
(4) q21+q22=1. (5) Budget: (The only budget constraint is on initial equipment purchase cost. Others could have been included. ) 50000 pr , + 8000 p12 + 30000 p2, + 6000 pz2
Stage two is a process of identifying the requirements of the material handling equipment
+48000 qll + 15000 q2, +20000 q22Il25000.
238 Handling
Handling
Transport
Fig. 1. Original system,
Handling
Handling
Transport
Storage Fig. 2. An alternative system. TABLE 1
TABLE 3
Equipment options for original system
Data for handling and transportation
Handling I: a. Pay loader b. Screw conveyor
equipment
Purchase cost ($I
Capacity (T/day)
Life (yr)
Availability
Transportation I: a. Truck
Location 1 Pay loader Screw conveyor
50000 8000
40 35
3 2
0.80 0.90
Transportation II: Belt conveyor :: Pneumatic conveyor
Location 2 Pay loader Screw conveyor
30000 6000
35 32
3 2
0.80 0.90
Handling II: Pay loader :: Screw conveyor
Route 1 Truck
48000
50
6
0.90
Route 2 Belt conveyor Pneumatic
15000 26000
22 22
6 6
0.70 0.92
TABLE 2 Equipment options for alternative system Handling I: a. Pay loader b. Screw conveyor Transportation I: Belt conveyor :: Pneumatic conveyor Handling II: a. Pay loader b. Screw conveyor
( 6 ) Compatibility. The coal is unloaded from the rail cars on the ground and it is not convenient to use a screw conveyor. This results in
p12=0.
The problem is solved using QSB [ 17 ] and the results are as follows: ( 1) At location one, the payloader is selected. (2) At location two, the screw conveyor is employed. ( 3 ) For movement of material from location one to the silo, a truck is used. (4) For loading coal into the silo, a belt conveyor is used. The total cost of the project is $283911. 5.2.2. Alternative system An alternative
system has been defined in Fig.
239 TABLE 4
Subject to:
Fixed costs for example
(l)P,,+P,z=l. (2)
Year of operation 1 Location 1 Pay loader Screw conveyor
2
3
4
5
6
$1350 8060’
$51300’ 60
$1350 8060’
$1350 60
1. 1.
50000 p1 I + 8000 p21 + 30000 p12 + 6000 pz2 $1300 $1350 60
+ 80000 ql, + 120000 q125 125000
( 5 ) Compatibility:
Location 2 Pay loader Screw conveyor
1000 52
1100 55
1200 6052’
31000’ 55
1100 6052’
1200 55
520
550
550
570
590
600
Route 1 Truck Route 2 Belt conveyor Pneumatic conveyor *Equipment
ih+1)22=
(3) 411+4,2= (4) Budget:
2600 2288
2800
2900 2290
3000
The coal is unloaded from the rail cars on the ground and a screw conveyor cannot be used. This results in assigning a value of 0 to P,~. This problem has no feasible solution as the purchasing cost for belt/pneumatic conveyors for this layout is beyond the budget.
3200
5.3.
Stage III
By comparison of the projects we select the original system as the alternative is not feasible. The total project cost is $2839 11.
is replaced.
TABLE 5 Variable costs/ton
5.4. Sensitivity analysis
for example Year of operation 1
2
3
4
5
6
Location 1 Pay loader Screw conveyor
$1.50 0.15
$1.70 0.20
$1.90 0.15
$1.50 0.20
$1.70 0.15
$1.90 0.20
Location 2 Pay loader Screw conveyor
1.50 0.14
1.80 0.16
2.10 0.14
1.50 0.16
1.80 0.14
2.10 0.16
1.40
1.60
1.80
2.00
2.20
2.40
0.50 0.10
0.50 0.10
0.70 0.10
0.90 0.15
1.10 0.15
0.15
Route 1 Truck Route 2 Belt conveyor Pneumatic conveyor
1.20
2 and Table 2, using cost and capacity data from Tables 3, 4, and 5. The resulting mathematical formulation for this system is
Minimize: 131985p,,
+23569p12+99621
p2]
+18191p2Z+105665q1,+132992q12.
In order to validate the above solution in light of possible errors in estimating the costs, a sensitivity analysis is conducted to demonstrate the sensitivity of the solution to the variations in each of the equipment costs. In order to test such sensitivity, each variable is analyzed independently and the cost coefticients are varied to determine the limits within which the final solution remains the same. As an example consider transportation activity two. The alternatives on this route are a belt conveyor and a pneumatic conveyor. The model selected the belt conveyor whose total cost is $37991 against the pneumatic conveyor whose total cost is $46535. The objective of the sensitivity analysis is to determine x and y, where x and y are the limits such that any cost in the range ($3799 1 +$x, $3799 1 - $y) still results in selection of the belt conveyor. A series of integer linear programming models are run for various values of x and y to determine that range. In this example, the only alternative to the belt conveyor is the selection of a pneumatic conveyor. Since the total cost of the pneumatic conveyor is higher than that of a belt conveyor, there
240 are no chances of making errors on the lower side of Ihe estimation and hence, as far as the sensitivity of the solution is concerned, the value of y becomes immaterial. On the higher side, the solution is not going to be affected by the errors in the estimation of the total cost of belt conveyor unless it exceeds $46535, which is a an error of about 33%. Any error which is below 33% in the estimation of the total cost of the belt conveyor will not affect the solution. Further, an error of 33% is not expected in the cost estimations and hence, the decision of selecting the belt conveyor on route two can be considered safe.
4
6. Conclusions and recommendations
9
The special characteristics of bulk materials necessitate a careful examination of the factors which influence the material handling equipment selection process. This paper has identified the factors that pertain to the type of material, the type of the system for which the’ material handling sub-system is being designed, and the outside system factors such as geographic location, weather conditions etc. These factors have been analyzed in a systematic way and are built into a mathematical model. Future research in this area could include study of additional factors that have influence on the storage of bulk materials and integration of the factors relevant to both movement and storage into one model. Other factors that could be included in future research are the possibilities of damage induced by some kinds of equipment and the effect such damage might have on processing. References Watford, B.A., 1985. Simulation Software for Bulk Material Transportation System’s Analysis. Unpublished PhD Dissertation. Virginia Polytechnic Institute and State University. Maxwell, L.W., 198 1. Solving Material Handling Design Problems With OR. Ind. Eng.: pp. 58-66. Leung, L.C., Khator, SK. and Kimbler, D.L., 1987. Assignment of AGVs with Different Vehicle Types. Mater. Flow, 4: 65-72.
5
6
7 8
10
II 12
13
14
15 16
17
18
19 20
21
Willou~by, W.D., 1967. A Technique for Integrated Facility Location and Materials Handling Equipment Selection by Dynamic Programming. Unpublished MS Thesis. Purdue University. Davis, R.P. and Haddock, J., 1986. A Simulation Generator for the Selection and Design of Material Handling Devices. Int. J. Model. Simul., 6 (3). Tanchoco, J.M.A., Agee, M.H., Davis, R.P. and Wysk, R.A., 1980. An Analysis of the Interactions Between lJnit Loads, Handling Equipment, Storage, and Shipping. ASME-Century 2. The Material Handling Conference, San Francisco: pp. 185-l 90. Carson, W.J., 1988. Powder Handling in Ceramic Industry. Ceramic Bull., 67(5). ASME, 1979. Mechanics Applied to the Transport of Bulk Materials. American Society of Mechanical Engineers, New York. Broersma, G., 1972. Behavior of Granular Materials. Stam Technical Publications, Culemborg. Frisque, D.E., 197 1. Physical Properties of Bulk Materials. Bulk Materials Handling, 1. In: M. Hawke (Ed. ), pp. 364-380. Cooke, J.A., 1988. Safer Ways to Move Bulk Cargo. Traffic Management. Tanchoco, J.M.A., 1983. Model Formulation. Class Notes, Virginia Polytechnic Institute and State University. Conveyor Equipment Manufacturers Association, 1979. Belt Conveyors for Bulk Materials, Second Edition. CBI Publishing Company, Boston. Pitts, C., 1980. Belt Conveyor Versus Truck for Coal Transportation. Unit and Bulk Materials Handling, presented at the Material Handling Conference, August 1921, 1980: pp. 47-52. Wuertele, F.S., 1988. Pneumatic Conveyors: Moving Material with Air. Plant Eng. 42: pp. 56-58. Velury, J., 1990. An Algorithm for the Selection of Bulk Material Handling Equipment. MS Thesis, Clemson University. Chang, Y.-L. and Sullivan, R.S., 1989. QSBi : Quantitative Systems for Business Plus. Prentice-Hall, Englewood Cliffs, NJ. Apple, J.M., 1976. How to Determine Material Handling Costs. Material Handling and the Industrial Engineer, American Institute of Industrial Engineers. Eastman, R.M., 1987. Materials Handling. Dekker, New York. Material Handling Engineering - Directory & Handbook, 1963-I 964. Industrial Publishing Corporation, Ohio. Reed, R., 1976. Material Handling Cost Factors. Material Handling and the Industrial Engineer. American Institute of Indust~al Engineers.