Assignment: The Darby Company Manufactures and Distributors

BA561 winter 2006 LP representative Notes 1. This is an individual assignment. As stated in the syllabus you must do your own work or you lead fail the class. 2. You can use any softw be you indirect request to perform the analysis, but the assignment was designed under the assumption that you would be using the LINDO software use for LP in BA555. 3. The project is due at the beginning of class in week four (February 1). The Case The Darby Company manufactures and distributes meters used to measure electric power consumption. The company started with a small production engraft in El Paso, Texas and gradually built a customer base through come start Texas.A dispersal optic (DC) was established in Ft. Worth, Texas and later as business expanded to the North, a second statistical distribution warmness was established in Santa Fe, New Mexico. The El Paso plant was expanded when the company began marketing its meters in Arizona, California, Nevada and Utah. With the ontogenesis of the West Coast business, the Darby Company opened a third distribution center in Las Vegas, Nevada and fair two years ago opened a second manufacturing plant in San Bernardino, California. Manufacturing costs take issue between the companys two production facilities.The cost of each meter produced at the El Paso plant is $10. 50. The San Bernardino plant is more efficient and produces meters at $10. 00 a unit of measurement. Due to the companys rapid growth, non much attention has been paid to the efficiency of the distribution system, but Darbys management has heady that it is time to address this issue. The costs of expatriation a meter from each of the plants to each of the three distribution centers is shown in add-in 1. Yearly production capacity is 30,000 units at the El Paso plant and 20,000 units at the San Bernardino plant.Note that no shipments are allowed from the San Bernardino plant to the Ft. Worth distribution center. The company serves nine customer partitio ns from the three distribution centers. The enter of the number of meters needed in each customer zone for the following year is sacrificen in Table 2. The Unit costs of shipping from each distribution center to each customer zone is given in Table 3. Note that some of the distribution centers can not serve authorized customer zones. In the current distribution strategy demand at the Dallas, San Antonio, Wichita and Kansas City customer zones is fit by shipments from the Ft.Worth DC. In a similar manner the Denver, Salt Lake City and Phoenix customer zones are served by the Santa Fe DC. And the Los Angles and San Diego customer zones are satisfied by the Las Vegas DC. To determine how many units to even off at each plant, the customer demand look forward tos are aggregated at the distribution centers and a transportation work is used to minimize the costs of shipping from the production plants to the distribution centers. Issues the company wants you to address 1. If the comp any does not change its distribution strategy what will its manufacturing and distribution costs be for the following quarter? . muse the company is willing to change its distribution strategy so that customer zones could be served from any distribution center for which costs are available. Would this reduce total costs? If so by how much? Would you make this change? Please be sure to examine all supply chain implications beyond serious direct dollars saved. 3. The company wants to explore the potential of direct shipping from the plants to certain customer zones. Specifically the shipping cost is $. 30 per unit from San Bernardino to Los Angeles and $. 70 from San Bernardino to San Diego.The cost for direct shipments from El Paso to San Antonio is $3. 50 per unit. Should the company do direct shipping? If so on which routes? 4. In 3 years demand is expected to assimilate increased 30% on average across all customers. At that time the company expects to have got saturated the ma rkets they presently serve (in other words additional growth will have to pick out from new markets). It will cost 3 dollars a unit to increase capacity at the El Paso plant and 4 dollars a unit at the San Bernardino plant. How much capacity, if any, would you add to each plant to quit future demand?Instructions 1. When answering the questions it is expected that you address the following a. What is the mathematically optimal government agency to meet all demands and constraints at the minimal cost? You must use LP to answer this question. b. The LP model gives you the nominal cost solution. What assumptions are you making if you implement the optimal solution from the model? At a minimal pleases be sure to consider i. Quality ii. Delivery reliability and speed iii. Managing logistics iv. Optimizing the supply chain v.Customer gratification 2. You must turn in a disk (floppy, cd or dvd) that contains all models you used to bring through the newsprint. The disk should contain the models and the solutions. Assignments that are not accompanied by a disk with the models and solutions will lag 30%. You can not turn your models and solutions in late. 3. You may use any software back up by the COB you wish- but Dr. Pagell will be using LINDO. 4. Your assignment will have an extension where the models are explained, Please use typical LP nomenclature (let statements and the like).If the professor can not figure out what the variables in your models represent you will lose points. 5. You will have a second appendix with a print out of your results. If you run multiple models you will need to print out results from all of the runs. 6. When it comes to formatting you do what you think is best to answer the questions with the following expectations / limitations a. You will turn in a closely written, grammatically correct, logically consistent paper. b. Presentation will be professional. Everything should be typed, easy to read, laid out in a logical manner, a nd so on. . Make sure you signalize the reader where to find randomness. For exemplification if you are using a dual price to answer a question say so. And tell the reader where to find this information in the paper. I am not going to guess where information comes from. d. This is a paper not a 4 questions test. I expect you to write a paper that integrates all four questions. Papers where each question is in its own stand alone partitioning with no linkages to other sections of the paper will get lower grades than papers that integrate the information.Grades Your grade will be based on the proper formulation, solution and interpretation of the models. Formulation and solutions will be charge 70% of your grade and interpretation will be 30% of your grade. The instructor reserves the right to give bonus points to students who come up with very elegant formulations. Table 1 Shipping cost per unit from production facilities to distribution centers Ft. Worth DC Santa Fe DC Las Ve gas DC El Paso Plant $ 3. 0 $ 2. 20 $ 4. 20 San Bernardino Plant - $ 3. 90 $ 1. 20 Table 2 Yearly demand forecast Customer Zone Demand in meters Dallas 6300 San Antonio 4880 Wichita 2130 Kansas City 1210 Denver 6120 Salt Lake City 4830 Phoenix 2750 Los Angles 8580 San Diego 4460 Table 3 Shipping costs from DCs to customer zones in dollars ($) Customer Zone DC Dallas San Antonio Wichita Kansas City Denver Salt Lake City Phoenix Los Angles San Diego Ft. Worth . 3 2. 1 3. 1 4. 4 6. 0 - - - - Santa Fe 5. 2 5. 4 4. 5 6. 0 2. 7 4. 7 3. 4 3. 3 2. 7 Las Vegas - - - - 5. 4 3. 3 2. 4 2. 1 2. 5