Computers ind. En@n~ Vol. 13, Nos I-4, pp.138-143, 1987 0360-8352187 $3.00÷0.00 Printed in Great Britain. All rights reserved Copyright c 1987 Pergamon Journals Lid

Mechanized Material Handling Systems Dem~4n and Routing

A. RavlndzanandB.L. Foote School of Industrial Engineering

University of Oklahoma, Norman, OK 73019

Larry Wil~ OC-ALC-MAE

Tinker AFB, OK 73142

ABSTRACT

Tinker AFB (TAFB) is the prime Air Force rework facility for Jet engine parts that support standard engines. The wear and tear on the engine parts of the various aircraft currently produces about 10 million individual requirements annually for part inspection and subsequent discard or rework. Past practices have resulted in extremely long flow times for rework and a burgeoning requirement for conveyor capacity.

A new concept, called the Modular Repair Center (MRC), is being implemented to correct the problem. The MRC's have most of the processes necessary to inspect and repair components of a given engine assembly. They have the advantage of reducing the number of long moves, giving more accountability for quality and better tracking. A large network model of TAFB facility has been developed to determine the required work-in-process storage, conveyor capacity, shortest routes for parts to flow from one MRC to another and the maximum flow along each conveyor section. The modelwas analyzed using Floyd's shortest route algorithm. It resulted in reducing the "bottlenecks" on certain conveyor sections by rerouting some of the flow along low density traffic links and thus reducing the need for extra conveyor capacity. Simple formulas were designed to estimate the number of pellets generated by disassembly and each MRC to provide the demand requirements for conveyor capacity.

INTRODUCTION

The design of material handling systems in the past has been a combination of art, rule of thumb and basic mathematical and logical analysis. Kwo (1960) and Muth (1975) are examples of approaches to determine conveyor capacity, number of carriers needed, buffer storage capacity and flow incompatibility with required delivery timing. These papers assume input pattern is known and the conveyor system is in place in terms of length and route through the production system. Haines (1985) shows how to route s carrier through a system by taking the shortest path from one point to another when there are only two choices at each possible transfer point. The system is already constructed and the possible paths ere all known. The algorithm is easily implemented on a computer control system.

This paper is concerned with the problem of determining the minimum set of conveyor connections from work area to work area which will deliver the material to all the different processing areas and handle all interdepartment flows. The velocity of the conveyor is preset based on the upper limit of speed that will prevent damage to the pallets and parts they carry. The width of the conveyor is preset to match the size of the standard carrier used in the plant to transfer parts. The work areas where the parts are processed are all at known locations and the destinations outside the work areas are known and the distances from entrances and exits to other entrances and exits are known.

The conveyor design problem is related to the problem of finding the shortest path between all pairs of nodes in a network, where "node" represents e point of exit or entrance to a processing area. The problem is a generalization of the shortest route problem because the flow between two nodes may exceed capacity and either a second link must be added or an alternate route found. Adding a second link is to be avoided due to the fact that the automatic routing system would not handle moving items to a second llnk when one llnk was full. The capability of monitoring whether s link was full and using this information to route pallets to a second link was beyond the control system in use. Such a mechanized material handling systems design problem emerged when the manufacturing system at Tinker Air Force Base was rebuilt after 8 fire.

PROBLEM BACKGROUND

Tinker Air Force Base (TAFB), located in Oklahoma City, Oklahoma, is one of the five overhaul bases in the Air Force Logistic Command. It has the responsibility for overhaul and repair of six types of jet engines, various aircraft and engine accessories, as well as

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Ravindran et a l . : Mechanized material handling 139

worldwide management of selected AF assets. This case study deals with the Propulsion (Engine) Division in the Directorate of Maintenance, and their efforts to recover from a devastating fire in Building 3001, November 11-14, 1984. The division consists of over 2800 employees and produces over 4 million earned hours and over 10 million units to support Department of Defense overhaul requirements each year.

Prior to the fire, the division was organized along functional operational lines with each department responsible for a specific process such as machining, welding, cleaning, inspection, etc. This organization structure was developed in 1974 when engine overhaul functions ware consolidated into one organization. At that time, the functional shop layouts maximized equipment utilization and skill concentrations since a typical long flow part would require 30-50 production operations and change organizations only 7-10 times. Twelve years later, that same part requires over 120 production operations and changes organization as many as 30-50 times. This significant increase was generated by piecemeal introduction of technology and improved repair procedures that offsets wear of critical engine parts and reduces replacement costs. The additional repairs generated a significant increase in routing that overburdened the mechanized conveyor system. The only major change in the last 3 years was an experiment to consolidate or cluster one workload, Combustion Cans, into a semi-self contained work center.

The system of repair was changed from a process specialization type of operation to a family (group) type of operation by TAFB manufacturing system analysts assisted by staff from the University of Oklahoma to solve the problems of long flow times, lack of clear responsibility for quality problems, and eliminate excessive material handling. The plan for reconstruction was based on the concept of a Modular Repair Center (MRC).

The Modular Repair Center concept was created and defined as a singe organization to inspect and repair a:

"Collection of parts with similar geometries a n d industrial processes that provides the most economical assignment of equipment and personnel to provide single point organizational responsibility and control."

With the exception of initial chemical cleaning, plating, paint, and high temperature heat treat, all industrial equipment and processes ware available for assignment to an MRC.

Since an entire overhead conveyor system was lost in the fire, implementing the MRC concept requires a new conveyor design in terms of routing, size, and location of up and down elevators. The need for a conveyor in the new system was driven by movement of parts to the respective (MRC's) from the disassembly area, movement to special areas for heat treat, painting, etc., and back to engine reessembly. Thus, when any type engine arrived for repair, the turbine blades in the engine will he removed and routed via the overhead conveyor to the blade MRC, out to plating and heat treat, back to the blade MRC and then returned to be assembled back into an engine.

GENERAL MODEL FOR CONVEYOR DESIGN

To establish a basks for construction of a minimum size conveyor system to handle the load, a network model of the material handling system was constructed. In the network representation, nodes are used to represent (i) different MRC's and their associated loading/tmloading points, (ii) the assembly areas and (iii) the transfer points in the conveyor, (iv) general purpose shops such as painting, plating, heat treat, blast and clean. Arcs or links An the conveyor network represent the different sections of the conveyor. The arrows of the arcs are used to specify the direction of item flow (one way/2-way).

Figure I represents the network for the present conveyor design and routing configuration. It has 56 nodes representing various MRC's, assembly areas and transfer points. Using the conveyor system drawings, the distance between all pairs of nodes representing the linear feet of conveyor ware calculated.

Floyd's Al~orithm

The algorithm developed by Floyd (1962) was used to determine the shortest path between all pairs of nodes. Dreyfus (1969) shows that Floyd's algorithm is one of the most efficient methods requiring only N(N-1)(N-2) additions and comparisons where N is the number of nodes in the network. Floyd's algorithm builds optimal paths progressively by inserting nodes, when appropriate, into a more direct path. The basic steps of the algorithm are as followa:

Step 0 D (0) = [dij(O)] where (NxN)

dlj = direct distance from node i to node J. (If there exists no direct arc, set dij = +~)

Step I: Determine D(1) = [dij(1)] where dij(1) = mln [dij(O) , (dil O + d|jO)]

for all i,J = 1,2,...,N

140 Proceedings of the 9th Annual Conference on Computers & Industrial Engineering

In other words, at Step I, we construct a matrix D (1) whose elements give the shortest distance between all pairs of nodes considering only node 1 as the intermediate node.

Step k+1

- (k), di,k+1(k) (k)] dij(k+1) = min [dij + dk+1, j

The k th matrix D (k) can be interpreted as giving the shortest distance between all pairs of nodes (i,j), where only paths with intermediate nodes belonging to nodes I through k are allowed.

The algorithm terminates when the matrix D (N) is calcuated.

Once the shortest path between all pairs of nodes are determined, the volume of flow in each conveyor section is estimated by summing up the appropriate flows through that section. For example, in Figure I, the shortest path from node 17 to 2 is 17-23-15-40-24,2 and the shortest path from node 22 to 2 is 22-21-23-15-40-24-2. Thus, the load flow on arc 23-15 is the sum of the two flows from 22 and 17. Using the network representation allowed the flow from 23 to 15 to be calculated based on the flow from all nodes to node 2 or any other nodes which had a path that included arc 23-15.

BASIC DATA

The basic information for analysis came from standard sources at Tinker Air Force Base (TAFB). The first source was the Work Control Document (WCD) which gave the operation sequence for a given part. From this it is known which MRC a part will go to and what special processes will be utilized. From this data the nodes where the part will travel to are known.

The second data source was the engine repair plan, which told how many engines of each type were expected to be repaired each year. This information was used to determine how many units of each family type would enter the system.

The third source of data was TAFB standard Material Handling (MH) coding of each part. The MH coding was based on the size and weight of each part. Parts move on pallets at Tinker Air Force Base. The MH coding was then used to estimate the number of parts per pallet.

Computer Generated Data

From the processing sequence on the work control document and the numbers of engines required to he maintained, a calculation of the flow from each MRC to another MRC was developed. A computer program called FROMTO was written to scan the processing sequence and determine when a move out of the MRC would be made. For example, when process code A appeared, the item would move from its MRC to A (heat treat) and then would move back to the MRC. The number of items of each type moving was the number of engines times the number of parts of this type/engine. The movements from each MRC to A were then summed over all part types and movement between other locations were found in the same way. The movement in terms of parts was then converted to pallets moved per half hour.

Once the flow in pallets was known, the standard deviation of flow was estimated by assuming that the number of pallets sent/half hour had a Poisson distribution, thus giving the standard deviation as the square root of the average flow. The route of the flow from point to point is known from the solution of the shortest route problem, and consequently the load on each segment of the conveyor is known.

CONVEYOR DESIGN ANALYSIS

The capacity of a conveyor link was developed from the following computations:

Max Flow/half hour = (v)(t)/cell length

v = velocity of conveyor/min. t = 50 minutes = time of flow cell length = 12 ft.

A pellet is 2' x 4' and 8 ft. is the normal spacing. Using v = 45 ft/min gives max flow/half hour = (45)(30)/12 = 112 pallets.

This max flow calculation assumes no Jam ups or stoppages in the conveyor. An estimate of O for specific flow rate is /'~'~ow using the Poisson distribution. This o is an under estimate due to the possibility of pallets being allowed to queue before being placed on the conveyor. If flow is large (i.e. > .5 max flow), the approximation is much better (within 10% of the simulated value). Thus, if ~ = flow rate, X + 3~" would give a good upper bound on flow.

Ravindran et a l . : Mechanized material handling 141

The cycle time of the up or down only elevators is 30 seconds and that of the two-way elevators is 50 seconds. Thus, at an up-only station, 60 pallets/helf hour can be loaded. This is an upper bound on entry at any one point on the conveyor.

The analysis of the system was done by first reducing the current description of the proposed conveyor system to a directed network of nodes and arcs. All possible nodes and arcs were included. Figure 1 illustrates the representation. The u and d subscript denotes an up or down elevator. Floyd's algorithm was used to find the shortest path from each node to any other node. Using this information, the material was routed along the shortest path and then the flow on each arc was summed up. Figure 1 also shows a sample output which graphically displays the flow on each arc. Flows greater than 80 have a potential f_for overflow due to random variation since a flow of approximately 107 or less (ref. ~ + 3/~ upper bound) can occur with probability one. Thus, alternative routes could then be chosen to avoid bottleneck arcs and unused arcs can be dropped resulting in construction savings or, if necessary, new arcs can be added. Figure I shows arc (15,40) with a flow much greater than SO. Consequently, some items were routed through an alternative path that was not the shortest but did have under utilized arcs.

The resulting set of programs called COPT (Conveyor Optimization) was used to study the effects of:

1) different routing rules on the conveyor 2) adding or deleting sections of the conveyor 3) changes in workload 4) changes in location of ioading/u~loading elevators 5) changes in the process sequence of the different WCD'a.

RESULTS AND CONCLUSIONS

The conveyor section loading reports provided an effective tool for variable routing or non minimum distance routing of pallets to reduce the load on critical sections of the system. This process has reduced the impact of temporary mechanical/electrical outages on overall material flow, improved the utilization of the conveyor system through load distribution and reduced the manual effort required to keep parts moving from one point to another.

The use of the shortest route model resulted in an efficient and cost effective mechanized material handling system. Prior to the fire, all routes were single path; the system could be impacted by variations in work loads or temporary mechanical/electrical outages within minutes and when major problems occurred, the entire system would experience a total lock-up. With the detailed knowledge of routes, and associated point to point cumulative volumes the use of the shortest path model resulted in net travel time improving by 10-15%. Loading of the conveyor system was reduced by 30-40%. The availability of alternative routes has reduced the impact of mechanical failures and maintained production needs.

For future operations, we now have an accurate tool to judge the impact of various workload mixes, identify bottlenecks and plan corrective actions before our production processes are affected.

The application of the model has also provided a means to assign human resources to critical conveyor sections and predict time variable manpower needs at each of the 40 input and output stations associated with the system.

REFERENCES

Haines, C.L., "An Algorithm for Carrier Routing in a Flexible Material Handling System", IBM Journal of Research and Development, Vol. 2, No. 4, July 1985, pp. 356-362.

Kwo, T. T., "A Method for Designing Irreversible Overhead Loop Conveyors", Journal of Industrial En~ineerin$, Nov.-Dec. 1960, Vol. 11, No. 6, pp. 459-466.

Muth, Egunhard, "Modeling and System Analysis of Multistatlon Closed-Loop Conveyor", International Journal of Production Research, Vol. 13, No. 6, 1975, pp. 559-566.

Floyd, R. W., "Algorithm 97: Shortest Path", Comm. of the ACM, Vol. 5, No. 6, p. 345 (1962).

Dreyfus, S.E., "An Appraisal of Some Shortest-Path Algorithms", Operations Research, Vol. 17, No. 3 (1969).

142 Proceedings of the 9th Annual Conference on Computers & Industrial Engineering

Legend for Figure 1

Figure I. Volume Flow in Pallets/Half Hour on Conveyor Sections (Northeast area)

d subscripts down elevator only u subscript: up elevator only

Q : t r a n s f e r po in t a t node n

(coda)

O,

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ZWs General PUrpose Shop

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• s Combustion Can

Ct Case

S t Sea l s

Ps P l a t l n 6

Ds Chemical Cleanln E

both up 'and down e l eva to r to (code) shop a t node I

Ravindran et a l . : Mechanized mater ial handling 143

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