Research Proposal on "Classification of Time Windows in the Vehicle Routing Problem"

Research Proposal 4 pages (1304 words) Sources: 2 Style: Harvard

[EXCERPT] . . . .

Classification of Time Windows in the Vehicle Routing Problem

The work of Bramel and Simchi-Levi (1992) entitled: "Probabilistic Analyses and Practical Algorithms for the Vehicle Routing Problem with Time Windows" reports that the Vehicle Routing Problem with Time Windows (VRPTW) can be stated as follows: "... A set of customers dispersed in a geographical regions has to be served by a fleet of vehicles initially located at a given depot. Each customer has a load that must be picked up, and the customer specifies a period of time, called a time window, in which this pick up must occur. The customers are served by vehicles of limited capacity, that is, total load carried by each vehicle can be no more than the vehicle capacity. The objective of to find a set of routes for the vehicles, where each route begins and ends at the depot, serves a subset of the customers without violating the capacity and time window constraints, while minimizing the total length of the routes." (Bramel and Simchi-Levi, 1992)

The work of Wolsey (2006) entitled: "Lot-Sizing with Production and Delivery Time Windows" reports a study of two lot-sizing problems with time windows." p.471 in each of these cases it is stated by Wolsey (2006) that the demand data "...consists of a set of orders" and those are stated as follows: "...k = 1, . . ., K consisting of a quantity Dk and a time interval [bk, ek] lying within the time horizon [1, n]." (p.471) Wolsey reports that the production time window "is the interval during which the order must be produced, while delivery of the order takes place in a period 'ek'. P.471 Wolsey goes on to state that this problem involves consideration of two variant: (1) in the first each order is distinct (client-specific) whereas in the second; (2) orders are indistinguishable (non-specific). " (Brahimi, Dauzere-Peres, et al. in: Wolsey, 2006) p.471

It is however held by Lee et al. that the deliver time window for an order "is the time interval in which the order must be delivered to the client." (in Wolsey, 2006) p.471 Wolsey states for the problem that is client-specific with production time windows that the approach taken is one in which polynomial time optimization algorithms and also tight mixed integer programming formulations possibly with additional variables are sought and in some cases "this means that we have a description of the convex hull of feasible solutions." (2006) p.472

Multi-item problems are stated to require the use of: (1) column generation; or (2) Lagrangian relaxation approaches in which one requires the optimization algorithms to solve the subproblems, or one can use a direct mixed integer programming approach and provide an initial MIP formulation including the tight formulations of the subproblems. Stated to be the primary results in the work of Wolsey (2006) are those as follows:

(1) the presentation of several mixed integer programming formulations and the relationship between them, including those of Brahimi et al. And Lee et al.

(2) for the production time window problem with constant capacities and Wagner-Whitin costs, WW ? CC ? TWP, we derive a tight O (n2) x O (n2) extended formulation. For the uncapacitated version WW ? U ? TWP, we obtain a tight formulation in the original production, stock and set-up variables with O (n2) constraints.

(3) We show that the restricted production time window problem with non-inclusive time windows, or equivalently the production time window problem with indistinguishable orders, is also equivalent to the standard lot-sizing problem with upper bounds on stocks. For the problem with general cost structure, we derive an O (n2) DP algorithm and an O (n2) x O (n2) tight extended formulation for the uncapacitated problem LS ? U ? TWP (I) by using the restricted time window structure. On the other hand for the constant capacity version LS ?CC ?TWP (I) we derive an O (n3) DP algorithm… READ MORE

How to Reference "Classification of Time Windows in the Vehicle Routing Problem" Research Proposal in a Bibliography

Related Research Proposals:

Distribution Planning Systems, Vehicle Routing Problems Research Proposal

Distribution Planning Systems, Vehicle Routing Problems

Distribution Planning for Make to Order Manufacturers

The work of Chang and Makatsoris (nd) entitled: "Supply Chain Modeling Using Simulation" published in the International… read more

Research Proposal 20 pages (5118 words) Sources: 10 Style: Harvard Topic: Business / Corporations / E-commerce

---

Windows Migration From XP Capstone Project

Windows XP to Windows 7 Migration

Submittal Cover Sheet

Four Digit Assessment/Project Code: TWA1

Mentor Name: Janet Bringhurst

For Revisions Only Indicate Previous Grader:

Submissions received with an altered, incomplete… read more

Capstone Project 18 pages (6896 words) Sources: 1+ Topic: Computers / IT / Internet

---

Use of Simulation Systems for the Vehicle Routing Problem Research Proposal

Simulation Systems for the Vehicle Routing Problem

The work of Solomon (1987) entitled: "Algorithms for the Vehicle Routing and Scheduling Problems with Time Window Constraints" reports the consideration of the… read more

Research Proposal 4 pages (1244 words) Sources: 3 Style: Harvard Topic: Transportation / Mass Transit

---

Logistics Make-To-Order Manufacturing for Time Windows Research Proposal

Logistics

Make-to-Order Manufacturing for Time Windows in Delivery

Certainty of product definition, accuracy of time window estimates, prerequisite supply inventory availability, and stability of supporting production and supply networks taken… read more

Research Proposal 3 pages (829 words) Sources: 3 Style: Harvard Topic: Business / Corporations / E-commerce

---

Finding Shortest Path Using Antnet Routing Term Paper

Shortest Path Using Antnet Routing

The increasing reliance of mobile IP-enabled and GPS-capable devices is creating a groundswell of support for optimization algorithms that are capable of quickly interpreting and… read more

Term Paper 10 pages (2742 words) Sources: 0 Topic: Computers / IT / Internet

---

View 100+ more related papers  >>