Consumption Problem Selection of a

¶ … Consumption Problem Selection of a planning horizon: time period Selection of a geographical focus: location Motivation Reasons others are interested in the project Formulation of the Problem Discussion of the Variables used in the Project Controllable Decision Variables Uncontrollable Non-Decision Variables Discussion of all Restriction on Variables Constraints Structure of the Model: Formulation of the Problem into an Engineering Systems Model Identify Input Requirements: Data sets Representation of mathematical relationships among variables in the: Objective function Constraints Clarifications of outputs and potential values of the projects Analysis of this Engineering System Suggested Methods for the Optimal Solution Solution Techniques to obtain Optimal Solution Sensitivity Analysis Conclusion Works Cited Notation Appendices Analysis of the Engineering System The optimal solutions from the linear-programming model will be used to address the intrinsically complex and interrelated problems facing Amtrak.

The optimal solutions to the company problem are train planning, crew planning, and locomotive planning. The solutions to each problem are provided using cost-effective techniques. Train Planning This paper suggests that Amtrak Rail should integrate training planning in its operations to solve sequential problem such as train scheduling, railroad blocking and train dispatching. Train planning involves a myriad of decisions to plan arrival and departure of railcars, arrival of customer orders, intermediate attaching and detaching of train routes.

This paper suggests that Amtrak should use train-planning technique to solve blocking problem. Amtrak should group several shipments into one block to address the blocking problem. Typically, railroad blocking aims to reduce the operation costs by minimizing the intermediate handling of railcars. It is essential to realize that normal train operation renders individual handling infeasible because each railroad receives thousands of shipments daily and each shipment is being handled individually. This system is not cost effective because the company does not have available resources to render individual shipment feasible.

This paper suggests that Amtrak Company should group several shipments into one block and transport the block into a single unit. For example, if two shipments originate from New York yard and have destinations to San Diego (SD) and Los Angeles (LA). These two shipments could be grouped into one block solving the problem of classification process. It should be noted that once these shipments have been grouped, it would no longer be classified until it reaches the destination.

Typically, the cost of the classification process is a potential bottleneck for the company leading to the substantial regrouping costs and delay costs. The classification costs for 50,000 shipments per month will be $1 billion of the yearly classification process. This paper also addresses the schedule or planning problem and routing that Amtrak is facing. The two problems are among the major problems that the company is facing which are escalating company's costs of operations. A train schedule is a detailed description of the train frequencies, routes, and timetables along railroad's network.

A company using manual method to run 400 trains will incur average annual costs of $320 million to run all the 400 trains. Amtrak should replace the current manual approach of scheduling planning into the operation research (or) tools to improve the service level in order to save tens of millions of dollars. This paper suggests that Amtrak rail should use decomposition approach to solve scheduling problem. The decomposition technique divides the large-scale problem facing Amtrak Rail into several parts. This paper decomposes the Amtrak scheduling problem in two phases.

In the first phase, the paper determines the route of each train and optimizing the number of train starts. The second phase uses the solution of the first phase to assist in determining the train route frequency and train times. The solutions will be able to address the fueling problem, servicing and locomotive routing problem. This paper uses the locomotive scheduling model for the recommendation of the planning problem facing Amtrak Rail.

The model minimizes the accumulated total costs, which is the sum of deadheading costs, active locomotive costs, consist-busting costs, light travel costs, and locomotive usage costs. The solution will be able to make the company to save $100 million annually. Major problem facing the Amtrak Company is that the company ignores to integrate the operational locomotive scheduling model into its planning operation. The operational locomotive scheduling model will assist the company to address the fueling and maintenance problems which are the major problems facing the company.

The integration of the model will assist management to run the company efficiently which will make the company to address the optimization problem. Crew Planning Crew comprises set of engineers, conductors, and service personnel working with the company. Analysis of the company operations reveals that Amtrak is incurring several millions of dollars yearly with mismanagement of its crew.

With inability to implement crew planning effectively, the company is incurring the costs such as detention costs, which is the detention time that crew needs to wait for long duration before starting the work. Additionally, the company incurs delay costs from crew mismanagement, which is approximately $1,000 per hour. All these costs make Amtrak to incur high costs of operations making the company to run at a loss. The objective of crew planning is to ensure that Amtrak operates the training with minimum of crew-related costs.

This paper suggests crew pairing is the solution to the detention time and wait costs that are making the company to incur the delay and detention costs. The crew pairing has been widely implemented in different countries such as New Zealand and Hong Kong, and this paper suggests that Amtrak Rail should assign individual crewmembers to these pairing using a localized optimization model. The crew-planning model using crew pairing will be able to solve the problem such as crew-caused train delays, crew detentions, and crew deadheading.

Using this technique, the company will be able to solve highly complex problem to reduce the crew-related operating costs making the company to run effectively and efficiently. "The importance of these optimization tools has been shown by a computational study on real-world data, which indicates a total savings of billions of dollars each year." (Nemani, & Ahuja, 2010, P 18).

Locomotive Planning A typical locomotive, which is a power unit that pulls trains, represents one of the biggest problems of Amtrak Rail making the company to incur the costs reaching million of dollars yearly. The costs of each locomotive unit include maintenance costs and periodic fueling. While Amtrak is currently implementing locomotive planning, however, the plan does not satisfy the operational constraints such as fueling and servicing requirements.

The suggested locomotive planning provided by this paper satisfies all the operational constraints, which include servicing and fueling constraints thereby assisting Amtrak Company to achieve operational efficiency. "The locomotive planning (or scheduling) problem (LPP) is to assign locomotive types to trains in a cyclic train schedule while honoring several operational constraints and minimizing the overall cost of assignment." (Vaidyanathan, Ahuja, & Orlin, 2008 P. 2). This paper uses the LLP model and locomotive routing problem (LRP) model to address the problem facing Amtrak train.

The LPP assigns locomotive types to train on a weekly basis thereby repeating the train schedule and making every train to get sufficient pulling power, balancing locomotive flows as well as satisfying other constraints. On the other hand, the LRP models route each locomotive unit on cyclic sequence basis thereby satisfying all other business and operational constraints cited in the LPP. The study provides sensitivity analysis to enhance greater understanding on the validity of the recommendations for solving Amtrak problems.

Sensitivity Analysis Sensitivity analysis is used to gain insight on the effect of the inputs value to the.