Logistics
Tactical and Strategic Planning
The work of Rushton, Oxley, and Croucher (2000) entitled: “The Handbook of Logistics and Distribution Management” states that the scheduling problems of vehicle routing are “relatively complicated.” P.422. The reasons for this are stated to be that first of all “the different types of problems that can arise each “needs to be understood and approached in a different way” and secondly “the many detailed aspects that need to be taken into account and the various methods of algorithms that can be used to produce solutions.” (Rushton, Oxley and Croucher, 2000) p.422 Problems may be of the nature of:
(1) Strategic;
(2) Tactical or operational;
(3) Interactive; and (4) Planning. (2000)
Strategic problems are concerned “with the longer-term aspects of vehicle routing and scheduling, in particular where there is a regular delivery of similar products and quantities to fixed or regular customers.” (Rushton, Oxley and Croucher, 2000) Stated as typical examples are “most retail delivery operations (such as grocery multiples), bread delivery and beer delivery to ‘tied’ houses.” (Rushton, Oxley and Croucher, 2000)
Stated as the primary characteristic is that of “a fairly regular demand being delivered to virtually the same locations. Thus it is possible to derive vehicle schedules that can be fixed for a certain period of time (eg three to six months). Tactical or operational problems are stated by Rushton, Oxton and Croucher (2000) to be concerned with routes that have to be scheduled on a weekly or daily basis” and is a type of scheduling that generally is accomplished through parcel delivery companies or by companies that supply parts or contract haul companies working for various clients.
Rushton, Oxley and Croucher state that the primary factor of importance is that “either the demand (quantity) of goods cannot be estimated (random demand) or the location of delivery points varies. Also it is possible that both of these incidents simultaneously occur. Therefore, it is near impossible or at the very least extremely difficult for delivery schedules to be planned on the basis of historical information. Instead the requirement is that each series of orders be viewed on the basis of daily or weekly scheduling and that the routes and schedules be flexible to “this ever changing demand.” (Rushton, Oxley and Croucher, 2000)
Many times scheduling of this nature is accomplished by a manual load planner or computer applications that enable ‘live scheduling’. (Rushton, Oxley and Croucher, 2000, paraphrased) Scheduling is now planned on what is known as an interactive basis and this allows the use of a computer by the scheduler to plan the most effective and efficient routes. This process uses the actual demand data rather than historical demand. This method of scheduling is known to be that which uses ‘real-time’ data therefore the result is formulation of routes that are more accurate.
All routes are not scheduled in this manner due to the cost barriers of these types of routing and scheduling systems. When schedules are formulated with real-time data the routes experience variation each day since the computer has the capacity to “…reappraise demand requirements and come up with a completely original result each time.” (Rushton, Oxley and Croucher, 2000) Stated as a primary benefit of the interactive approach is the scheduler’s ability to make changes to routes if need be. The example stated is that in the case where an urgent order is received after route scheduling the scheduler is able to manually input the order and then to assign the order to an already existing route.
Upon entry of an order into the system it may be rejected and for various reasons include:
(1) Insufficient capacity left on the vehicle;
(2) Insufficient time available; and (3) Other various reasons. (Rushton, Oxley and Croucher, 2000)
Therefore the scheduler is able to ensure that the item is placed on the route of a vehicle that will most assuredly complete the delivery. This cuts out the additional expenses incurred by shipments that never complete delivery and that bring the item back to the beginning point needlessly consuming space on the vehicle. Also noted as a problem relating to routing and scheduling is that of “the planning and measurement of the effect of change.” (Rushton, Oxley and Croucher, 2000)
Computer-based techniques are accredited for touring and scheduling coming into its own as the computer models have the capacity for use in testing or simulations of the change in demand and its effect on vehicle availability and so forth and is known as “what-if planning” (Rushton, Oxley and Croucher, 2000) One such example stated by Rushton, Oxley and Croucher (2000) that third-party contractors generally use routing and scheduling packages to assist them in response to invitations “to tender for business” and the package enable the identification of the fleet and driver requirements and ultimately they cost out the operation accordingly. (Paraphrased)
In addition to the basic demand data and the routing and scheduling are the following primary areas:
(1) Demand data;
(2) distance factors;
(3) Customer and service constraints;
(4) Vehicle restrictions;
(5) Driver constraints;
6) Route factors; and (7) product/unit load constraints. (Rushton, Oxley and Croucher, 2000)
The demand data is however, stated to be the most important of all data and in fact “can often be the most difficult data item to collect, will certainly be the most time consuming and will also require the most manipulation and clarification prior to use within the manual method or computer package.” (Rushton, Oxley and Croucher, 2000) Additional analyses may well be necessary “to take account of peak demand periods because they are likely to require different schedules.” (Rushton, Oxley and Croucher, 2000) Demand data can be represented in several ways and this is stated to be fortunate since “the most appropriate choice of data is not available, so second or even third choice has to be sufficient.” (Rushton, Oxley and Croucher, 2000)
Stated as the ‘key’ requirement for the collection of data is that it is “collected to be representative of the main measure of the vehicle capacity constraint. This might be weight-, volume- or unit-related.” (Rushton, Oxley and Croucher, 2000) Examples stated include the following:
(1) weight (per product type delivered or as a total delivered tonnage figure in kilograms or tonnes);
(2) Cube or volume (in cubic metres or cubic feet);
(3) Carton/Case/parcel (numbers to be delivered — common in retail distribution); (4) Unit load (eg numbers of pallets or roll cages-again common in retail distribution);
(5) Value in revenue or sales (rarely appropriate because of the problem of interpreting value as a physical measure); (6) Product item (generally too detailed); and (7) Product group. (Rushton, Oxley and Croucher, 2000)
Demand data also can be classified by location in various ways. It is clear that the “level of detail and accuracy is very important in order to ensure good results from the scheduling process.” (Rushton, Oxley and Croucher, 2000) it is related that some computer packages are “more amenable to some classifications than others” and that the best choice is generally the “classification that is in general use within the company.” (Rushton, Oxley and Croucher, 2000) Primary alternatives include the following:
(1) post- or zip codes;
(2) Ordnance Survey codes or any other type of map referencing system;
(3) 10-kilometre grid squares — useful simplification of map referencing system;
(4) Gazetter (main town or city) rather impressive but easily recognizable;
(5) Latitude and longitude — again, may not be sufficiently precise;
(6) Population-based — can be a good approximation if there is no other data available; and (7) Plumbly management bricks (a marketing, sales-based system of identifying sales areas). (Rushton, Oxley and Croucher, 2000)
Various methods are used in the estimations of distance traveling in conducting marketing and scheduling analysis. Stated as the three primary methods of measurement are the following:
(1) True distance method — all actual distances are physically measured on a road map. This is a time-consuming task and one that could not be performed for large applications; (2) Coordinate method — customer and delivery points are located on a map and the mapped; and (3) Digitized road network — computer modeling system application.
Stated as customer and service constraints are the following factors:
(1) specified times for delivery;
(2) specified delivery windows;
(3) early closing days;
(4) lunch breaks;
(5) access restrictions;
(6) unloading restrictions;
(7) drop size limitation; and (8) parking problems. (Rushton, Oxley and Croucher, 2000)
The work of Vural (2003) entitled: “A GA-Based Meta-Heuristic for Capacitated Vehicle Routing Problem with Simultaneous Pick-up and Deliveries” states that the vehicle routing problem is represented as the following graph theoretic problem:
“Let G = (V, a) be a complete graph where V = {0, 1, & #8230;, n} is the vertex set and a is the arc set. Vertices j = 1, & #8230;, n correspond to the customers, each with a known non-negative demand, dj, to be delivered whereas vertex 0 correspond to the depot. A non-negative cost, cij, is associated with each arc (i, j) ? A and represents the travel cost to go from vertex I to vertex j. If the cost values satisfy the symmetry, such that for any I and j ? V, cij = cji, then the problem is said to be symmetric VRP, else, it is called an asymmetric VRP. In several practical cases the cost matrix satisfies the triangle inequality, such that cik + ckj ? cij for any i, j, k ? V.” (Toth and Vigo, 1998, cited in Vural (2003).
Vural (2003) states that the primary attributes within the configuration of the majority of VRP problems are those as follows:
(1) Number of vehicles;
(2) Vehicles homogeneity/heterogeneity;
(3) Time windows;
(4) Backhauls;
(5) Splitting/Unsplitting of Load;
(6) Single Depot/Multi Depot;
(7) Static/Dynamic Service Needs; (8) Precedence/Coupling Constraints. (Vural, 2003)
Heuristic and Meta-heuristic Models
The work of Badr (nd) Solving Dynamic Vehicle Routing: An Alternative Metaheuristic Approach” states that Dynamic Vehicle Routing Problem (DVRP) can be considered a good example of a distribution context, because of the fact that intelligent manipulation of real-time information can distinguish between one company and another by superior on-time service. Problems of both generic and vehicle routing (VRP) and dynamic vehicle routing (DVRP) are identical. But in VRP all routing and demand information are certain known prior to the day of operation, whereas in DVRP part of or all of the necessary information is available only at the day of operation.” (Badr, nd) the DVRP significance is stated to be “crystallized by the variety of environments it can model.” (Badr, nd)
The work of Gambardella, Taillard and Agazzi (1999) entitled: “MACS-VRPTW: A Multiple Ant Colony System for Vehicle Routing Problems with Time Windows” states that one of the most successful and exact methods for the CVRP is the method known as the: “…k-tree method of (Fisher, 1994) that succeeded in solving a problem with 71 customers. However, there are smaller instances that have not been exactly solved yet. To treat larger instances, or to compute solutions faster, heuristic methods must be used.” (Gambardella, Taillard and Agazzi, 1999)
Tabu and Genetic Search
Among the best heuristic methods are tabu searches (Taillard, 1993, Rochat and Taillard, 1995, Rego and Roucairol, 1996, Xu and Kelly, 1996, Toth and Vigo, 1998) and large neighborhood search (Shaw, 1998). The CVRP can be extended in many ways.” (Gambardella, Taillard and Agazzi, 1999) the service time si for each customer (with so = 0) and a time limit over the duration of each tour can be considered. The goal is again to search for a set of tours that minimizes the sum of the travel times.” (Gambardella, Taillard and Agazzi, 1999)
Gambardella, Taillard and Agazzi (1999) states that in addition to the CVRP features, included in this problem is
“…for the depot and for each customer ci (i = 0,…, n) a time window [bi, ei] during which the customer has to be served (with b0 the earliest start time and e0 the latest return time of each vehicle to the depot) the tours are performed by a fleet of v identical vehicles. The additional constraints are that the service beginning time at each node ci (i = 1,…, n) must be greater than or equal to bi, the beginning of the time window, and the arrival time at each node ci must be lower than or equal to ei, the end of the time window. In case the arrival time is less than bi, the vehicle has to wait till the beginning of the time window before starting servicing the customer.” (Gambardella, Taillard and Agazzi, 1999)
Planning under Certainty and Uncertainty
The work of Kelywegt and Shapiro (2000) entitled: “Stochastic Optimization” states that decisions are often made by decision makers “in the presence of uncertainty. Decision problems are often formulated “as optimization problems and thus in many situations decision makers wish to solve optimization problems which depend on parameters which are unknown.” (Kleywegt and Shapiro, 2000) Formulation and solution of such type problems are generally very difficult “both conceptually and numerically.’ (Kleywegt and Shapiro, 2000)
The conceptual stage of modeling contains difficulty since there are various ways that formalization of the uncertainty can be modeled formally. The attempt in formulating optimization problems is to identify a suitable trade-off between “the realism of the optimization model, which usually affects the usefulness and quality of the obtained decisions, and the tractability of the problem, so that it could be solved analytically or numerically.” (Kleywegt and Shapiro, 2000) Kleywegt and Shapiro state a static optimization problem as follows in relation to operation under uncertainty:
“Suppose we want to maximize an objective function G (x, ?), where x denotes the decision to be made, X denotes the set of all feasible decisions, ? denotes an outcome that is unknown at the time the decision has to be made, and ? denotes the set of all possible outcomes.” (Kleywegt and Shapiro, 2000)
Kelywegt and Shapiro state that there are
“…several approaches for dealing with optimization under uncertainty” for example in the case of the company that sells products that are seasonal in nature and which are characterized by a selling season that is short and the value of the products experience a substantial decrease following this brief selling season, it is necessary that a decision be made without the surety of how much of the product must be manufactured or purchased before the brief selling period begins. Upon the selling period beginning there is not enough remaining time to change the purchase or manufacture decision so the product quantity is a ‘given’ and the decision made prior to the selling period remains regardless of whether much more of the product could have been sold. Therefore, the situation is such that the decision has to have been made prior to the knowledge of the eventual outcome is known to the decision maker. (Kleywegt and Shapiro, 2000)
Stochastic & Dynamic Simulation-based Planning in DPS
The work of Ganesh, Dhanlakshmi, Thangavelu, Parthiban (2009) entitled: ‘Hybrid Artificial Intelligence Heuristics and Clustering Algorithm for Combinatorial asymmetric Traveling Salesman Problem” states that stochastic and/or dynamic information in most real life applications “occurs parallel to the routes being carried out.” (Ganesh, Dhanlakshmi, Thangavelu, and Parthiban 2009)
Real-life examples of stochastic and/or dynamic routing problems include the distribution of oil to private households, the pick-up of courier mail/packages and the dispatching of buses for the transportation of elderly and handicapped people.” (Ganesh, Dhanlakshmi, Thangavelu, and Parthiban, 2009)
It is related by Ganesh, Dhanlakshmi, Thangavelu, and Parthiban, 2009) that in these specific examples unknown may include:
(1) customer profiles;
(2) time to begin service;
(3) geographic location; and
4) actual demand and these factors may not be known when planning begins or even at the time service has begun for the customers with advance requests.
Stated as two distinct features result in the planning of routes that are of high quality in this environment more complex are those of:
(1) constant change; and (2) time horizon. (Ganesh, Dhanlakshmi, Thangavelu, and Parthiban, 2009)
Simulated Annealing
Simulated annealing (SA) is stated in the work of Ganesh, Dhanlakshmi, Thangavelu, and Parthiban (2009) to be a “generalization of a Monte Carlo method for examining the equation of state and frozen states of n-body systems. The concept is based on the manner in which liquids freeze or metal recrystalize in the process of annealing.” (Ganesh, Dhanlakshmi, Thangavelu, and Parthiban, 2009)
The annealing process involves a melt generally at a high temperature “and disordered, is slowly cooled so that the system at any time is approximately in thermodynamic equilibrium.” (Ganesh, Dhanlakshmi, Thangavelu, and Parthiban,, 2009) the procession of cooling results in the system becoming more ordered and approaching a ground state that is termed as ‘frozen’…at T=0. Therefore this process can be viewed as “an adiabatic approach to the lowest energy state.” (Ganesh, Dhanlakshmi, Thangavelu, and Parthiban,, 2009)
Ganesh, Dhanlakshmi, Thangavelu, and Parthiban (2009) state that in order to use this specific analogy when referring to thermo dynamic systems in attempting mathematical optimization solutions the following elements are required:
(1) a description of possible system configurations, i.e. some way of representing a solution to the minimization (maximization) problem, usually this involves some configuration of parameters that represent a solution;
(2) a generator of random changes in a configuration; these changes are typically solutions in the neighborhood of the current configuration, for example, a change in one of the parameters.”
Capacitated Vehicle Routing
The work of Ormerod and Slavin (nd) entitled: “Human Solutions to the Capacitated Vehicle Routing Problem” states that the Vehicle Routing Problem (VRP) “arises naturally in transportation, distribution and logistics.” The focus of the Vehicle
Routing Problem (VRH) is a given set of customers with needs (loads) and vehicles (capacity limited) and finding the shortest set of tours from the depot(s) that collect/deliver specified loads. Other concerns are stated as the Intersection of TSP and bin packing problems. The work of Matson, Miller and Matson (1999) entitled: “A Capacitated Vehicle Routing Problem for Just-in-time delivery” reports a work that has its focus on the “formulation and solution of the problem of planning vehicle routes for material delivery within the premises of a plant working under a just-in-time production system. The unique characteristic of this problem is that the quantity to be delivered at each of the demand nodes is a function of the route taken by the vehicle assigned to serve that node.” ( ) Matson, Miller and Matson (1999) state as follows concerning the just-in-time system:
“The JITCVRP can be defined as follows. There is a central location (single depot) where all required parts are stocked. Demand points (customers) for the parts occur at specified locations in the production system. A fleet of identical vehicles with fixed capacities is available to deliver the parts to the demand points. All vehicles start from the depot and return to the depot at the end of the trip. Any vehicle can be assigned to any customer and is capable of carrying any part. The problem is to determine the route for each vehicle that will permit just-in-time delivery of parts to the demand locations in the production system, while minimizing the requirements for material handling equipment. The quantity delivered per trip should be just enough to meet the demand for the duration of the trip so that a vehicle will have no idle time between trips and inventories at the demand points are minimized.” (Matson, Miller, and Matson, 1999)
It is reported that there are various types of VRPs and that each of these has unique features differentiating it from the others. The Inventory “Routing Problem, or IRP is stated to be the most closely related to the JITCVRP.” (Matson, Miller and Matson, 1999) the IRP is stated to be that which “deals with determining the quantity to be delivered to different locations such that the delivery costs and inventory costs are minimized.
PPS — the Hybrid Approach
Classifications and Summary
Bibliography
Rushton, Alan, Oxley, John, and Croucher, Phil (2000) the Handbook of Logistics and Distribution Management: Creating Success. Kogan Page Publishers 2000.
Vural, Arif Volkan (2003) a GA-Based Meta-Heuristic for Capacitated Vehicle Routing Problem with Simultaneous Pick-up and Deliveries. August 2003. Online available at: http://digital.sabanciuniv.edu/tezler/etezfulltext/vuralarifvolkan.pdf
Badr, Amr (nd) Solving Dynamic Vehicle Routing: An Alternative Metaheuristic Approach. Cairo University. Online available at: http://www.ici.ro/ici/revista/sic2009_2/art07.html
Kleywegt, Anton J. And Shapiuro, Alexander (2003) Stochastic Optimization.10 Feb 2000. Online available at: http://www2.isye.gatech.edu/people/faculty/Alexander_Shapiro/publications/StochOptIEBook.pdf
Ganesh, K. Dhanlakshmi, R., Thangavelu, . And Parthiban, P. (2009) ‘Hybrid Artificial Intelligence Heuristics and Clustering Algorithm for Combinatorial asymmetric Traveling Salesman Problem. Igi Global 2009. Online available at: http://www.igi-global.com/downloads/excerpts/33341.pdf
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