3.7 Fuzzy Logic Approach to Dispatching in Truckload Trucking
3.7.2 Trucks Dispatching by Fuzzy Logic
3.7.2.2 Proposed Solution to the Problem
The total number of vehicles N available to the dispatcher at the moment he assigns vehicles is
N Nj
j n
=
∑
=1 (3.15)
As already mentioned, the problem considered is the assignment of N available vehicles to m trans-portation requests. This belongs to the category of OR problems known as assignment problems.
Some transportation requests are “more important” than others. In other words, some clients have signed long-term transportation contracts, and others randomly request transportation that will engage transportation capacities for longer or shorter periods of time. In some cases there is no absolutely precise information about the number of individual types of vehicle that will be ready for operation the following day. Bearing in mind the number of operating vehicles and the number of vehicles expected to be opera-tional the following day, the dispatcher subjectively estimates the total number of available vehicles by type. Some vehicle types are more “suitable” for certain types of transportation tasks than others.
Naturally, vehicles with a 5 t capacity are more suitable to deliver goods within a city area than those with a 25 t capacity. On the other hand, 25 t vehicles are considerably more suitable than 5 t or 7 t vehicles for long-distance freighting.
As we can see, the vehicle assignment problem is often characterized by uncertainty regarding input data necessary to make certain decisions. It should be emphasized that the subjective estimation of individual parameters differs from dispatcher to dispatcher, or from decision-maker to decision-maker.
D
FIGuRE 3�15 Depot D and nodes to be served.
The number of available vehicles of a specific type might be “sufficient” for one dispatcher, while another dispatcher might think this number “insufficient” or “approximately sufficient.” Also, one dispatcher might consider a certain type of vehicle “highly suitable” regarding a certain distance, while other dis-patchers might consider this type of vehicle “suitable” or “relatively suitable.” Clearly, a number of parameters that appear in the vehicle assignment problem are characterized by uncertainty, subjectiv-ity, imprecision, and ambiguity. This raises the need in the mathematically modeling phase of the prob-lem to use methods that can satisfactorily treat uncertainty, ambiguity, imprecision, and subjectivity.
The approximate reasoning model presented in the following section is an attempt to formalize the dispatcher’s knowledge, that is, to determine the rules used by dispatchers in assigning vehicles to transportation requests.
Approximate reasoning model for calculating the dispatcher’s preference when only one type of vehicle is used to meet every transportation request
It can be stated that every dispatcher has a pronounced subjective feeling about which type of vehicle corresponds to which transportation request. This subjective feeling concerns both the suitability of the vehicle in terms of the distance to be traveled and vehicle capacity in terms of the amount of freight to be transported.
Dispatchers consider the suitability of different types of vehicles as being “low” (LS), “medium” (MS), and “high” (HS) in terms of the given distance the freight is to be transported. Also, capacity utilization (the relationship between the amount of freight and the vehicle’s declared capacity, expressed as a percentage) is often estimated by the decision-maker as “low” (LCU), “medium” (MCU), or “high”
(HCU).
The suitability of a certain type of vehicle to transport freight different distances, and its capacity utilization can be treated or represented as fuzzy sets (Figs. 3.16 and 3.17).
Vehicle capacity utilization is the ratio of the amount of freight transported by a vehicle to the vehi-cle’s capacity. The membership functions of the fuzzy sets shown in Figures 3.16 and 3.17 must be defined individually for every type of vehicle.
The decision-maker assigns transportation requests to individual types of vehicle bearing in mind above all the distance to be traveled and the capacity utilization of the specific type of vehicle. When dispatching, the decision-maker–dispatcher operates with certain rules. Based on conversations with dispatchers who deal with the vehicle assignment problem every day, it is concluded that the decision-maker has certain preferences:
“Very strong” preference is given to a decision that will meet the request with a vehicle type having
“high” suitability in terms of distance and “high” capacity utilization.
Or
0.0 0.2 0.4 0.6 0.8 1.0
0 200 400 600 800 1000
Distance (km)
LS MS HS
FIGuRE 3�16 Membership functions of fuzzy sets: LS is low, MS is medium, and HS is high suitability in terms of distance.
“Very weak” preference is given to a decision that will meet the request with a vehicle that has “low”
suitability regarding distance and “low” capacity utilization.
The strength of the dispatcher’s preference can be “very strong,” “strong,” “medium,” “weak,” and
“very weak.” Dispatchers most often use five terms to express the strength of their preference regarding the meeting of a specific transportation request with a specific type of vehicle. These five preference categories can be presented as corresponding fuzzy sets P1, P2, P3, P4, and P5. The membership functions of the fuzzy sets used to describe preference strength are shown in Figure 3.18. Preference strength will be indicated by a preference index, PI, which lies between 0 and 1, where a decrease in the preference index means a decrease in the “strength” of the dispatcher’s decision to assign a certain trans-portation request to a certain type of vehicle.
For every type of vehicle, a corresponding approximate reasoning algorithm is developed to deter-mine the dispatcher’s preference strength in terms of meeting a specific transportation request with the type of vehicle in question. The approximate reasoning algorithms for each type of vehicle differ from each other in terms of the number of rules they contain and the shapes of the membership functions of individual fuzzy sets. For example, for a vehicle with a capacity of 14 t, the approximate reasoning algorithm reads as shown in Table 3.4.
Using the approximate reasoning by max–min composition, every preference index value is assigned a corresponding grade of membership. Let us denote this value by Pij. This value expresses the “strength”
of the dispatcher’s preference that the i-th transportation request be met by vehicle type j. Similar approximate reasoning algorithms were developed for the other types of vehicle.
Calculating the dispatcher’s preference when several types of vehicle
are involved in meeting requests
Up until now, we have only considered the vehicle assignment problem when one type of vehicle is used to meet every transporta-tion request. Some transportatransporta-tion compa-nies often use several different types of vehicle to meet a specific transportation request. When meeting requests with sev-eral different types of vehicle, every request can be met in one or several different ways.
For example, if the amount of freight in the i-th request equals Qi = 18 t and if we have
0.0 0.2 0.4 0.6 0.8 1.0
0 20 40 60 80 100
Capacity utilization (%)
LCU MCU HCU
FIGuRE 3�17 Membership functions of fuzzy sets: LCU is low, MCU is medium, HCU is high vehicle capacity utilization.
FIGuRE 3�18 Membership functions of fuzzy sets: P1 is very strong, P2 is strong, P3 is medium, P4 is weak, P5 is very weak preference.
0.0 0.2 0.4 0.6 0.8 1.0
0.0 0.2 0.4 0.6 0.8 1.0
Preference
P5 P4 P3 P2 P1
two types of vehicle whose capacities are 5 t and 7 t, respectively, there are four possible alternatives to meeting the i-th request, shown in Table 3.5.
The first of the possible alternatives to meet any transportation request is the one in which only one type of vehicle is used, the vehicle with the greatest capacity. Every other alternative differs from the previous to the effect that there is a smaller share of vehicles with a higher capacity and a greater share of vehicles with a smaller capacity. The last possible alternative uses vehicles with the smallest capacity.
Let us denote the following:
Qijk is the amount of freight from the i-th request transported by vehicle type j when request Ti is met using alternative k.
Nijk is the number of type j vehicles that participate in meeting request Ti when request Ti uses alternative k.
It is clear that the total freight Qi from transportation request Ti that is met using transportation alternative k equals the sum of the amount of freight of request Ti transported by individual types of vehicles, that is,
Qijk Qi
j n
=
∑
= 1(3.16)
The capacity utilization (expressed as a percentage) λijk of vehicle type j that takes part in meeting transportation request Ti using alternative k can be defined as,
λijk ijk
j ijk i
Q C N n
= 100[%]
(3.17)
Let us denote by Pk the dispatcher’s preference to use service alternative k to meet transportation request Ti. It is clear that,
TABLE 3�4 Approximate Reasoning Algorithm for a Vehicle with a Capacity of 14 t
Capacity Utilization
LCU MCU HCU
Suitability LS P5 P4 P3
MS P3 P2 P2
HS P2 P1 P1
TABLE 3�5 Comparison of the Total Number of Ton-Kilometers Realized for the Four Different Ways of Assigning Vehicles to Transportation Requests
Possible Ways of Assigning Vehicles to Transportation Requests
Amount of Time Needed to Assign Vehicles to Planned
Transportation Requests Total Number of Realized
Ton-kilometers Percentage of Realized Ton-kilometers
I 2 hr 30 min 163,821 92.26%
II 2 hr 15 min 154,866 87.15%
III 40 152,727 86.01%
IV 40 170,157 95.83%
P
N C n P N C n
k
ijk j i ij j
n
ijk j i j
= =n
=
∑
∑
1
1
(3.18)
The corresponding dispatcher’s preference Pij must be calculated for every type of vehicle j taking part in meeting transportation request Ti. Preference values Pij are calculated based on approximate reasoning algorithms.
Based on relation 3.18, the dispatcher preference to meet transportation request Ti with any of the possible service alternatives k can be calculated.
Heuristic algorithm to assign vehicles to transportation requests
The basic characteristics of every transportation request are the amount of freight that is to be trans-ported and the distance to be traveled. Therefore, requests differ in terms of the volume of transporta-tion work (expressed in ton-kilometers) to be executed, and in terms of the revenues and profits that every transportation request brings to the transportation company. It was also emphasized in our previ-ous remarks that a company might have long-term cooperation with some clients, while other clients request the transportation company’s services from time to time. Therefore, some transportation requests can be treated as being “more important,” or “especially important requests,” having “absolute priority in being carried out,” and so on. All of this indicates that before assigning vehicles to transpor-tation requests, the requests must first be sorted. The requests can be sorted in descending order by number of ton-kilometers that would be realized if the request were carried out, in descending order of the amount of freight in each request, in descending order of the requests’ “importance” or in some other way. The manner in which the requests are sorted depends on the company’s overall transporta-tion policy. It is assumed that sorting of the transportatransporta-tion requests is made before vehicles are assigned to transportation requests.
The heuristic algorithm of assigning vehicles to transportation requests consists of the following steps:
Step 1: Denote by i the index of transportation requests. Let i = 1.
Step 2: Generate all possible alternatives to meet transportation request Ti.
Step 3: Denote by k(i) the index of possible alternatives to meet transportation request Ti. Let k(i) = 1.
Step 4: Analyze alternative k(i). If available resources (number of available vehicles of a specific type) allow for alternative k(i), go to Step 5. Otherwise go to Step 7.
Step 5: Determine the preference for every type of vehicle that takes part in implementing alter-native k(i) using an approximate reasoning by max–min composition.
Step 6: Calculate the dispatcher’s preference to use alternative k(i) to meet transportation request Ti. Use relation 3.18 to calculate this preference.
Step 7: Should there be any uninvestigated alternatives, increase the index alternative value by 1 (k(i) = k(i) + 1) and go to Step 4. Otherwise, go to Step 8.
Step 8: Should none of the potential alternatives be possible owing to a lack of resources, trans-portation request Ti cannot be met. The final value of the dispatcher’s preference (when there is at least one alternative possible) equals the maximum value of the calculated pref-erences of the considered alternatives. In this case, transportation request Ti is met by the alternative that corresponds to the maximum preference value.
Step 9: Decrease the number of available vehicles for the types of vehicle that took part in meet-ing transportation request Ti by the number of vehicles engaged in meeting the request.
Step 10: If any transportation requests have not been considered, increase the index by i (i = i + 1) and return to Step 2.