Скачать презентацию BASICS OF PLANT LAYOUT Plant layout has
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Скачать презентацию BASICS OF PLANT LAYOUT Plant layout has
Скачать презентацию BASICS OF PLANT LAYOUT Plant layout has
BASICS OF PLANT LAYOUT
Plant layout has been defined as a plan of, or the act of planning an optimum arrangement of industrial facilities, including personnel, operating equipment, storage space, materials handling equipment and all other supporting services along with the design of the best structure to contain these facilities
Introduction • Facility layout means planning: – for the location of all machines, utilities, employee workstations, customer service areas, material storage areas, aisles, restrooms, lunchrooms, internal walls, offices, and computer rooms – for the flow patterns of materials and people around, into, and within buildings – infrastructure services such as the delivery of line communications, energy, and water and the removal of waste water all make up basic utilities.
What Is Layout Planning – Layout planning is determining the best physical arrangement of resources within a facility
Locate All Areas In and Around Buildings – Equipment – Work stations – Material storage – Rest/break areas – Utilities – Eating areas – Aisles – Offices
Characteristics of the Facility Layout Decision – Location of these various areas impacts the flow through the system. – The layout can affect productivity and costs generated by the system. – Layout alternatives are limited by – the amount and type of space required for the various areas – the amount and type of space available – the operations strategy –. . . more
Machine shop process layout Receiving Grinders Mills Raw matl. storage Assembly Large number of low volume products Drills Planers Lathes Automatics Finished Inspec- goods tion storage Part A Part B Facility Layout 13
Problems of layout develop when needed: • to start a new product, • to change the product design, • to reduce the cost; And when • the market demand changes, • the plant, the product, the building become obsolete, • accidents occur frequently, • the working environment is poor.
The resulting problems involve • planning a completely new plant, • re-arranging a presently installed layout, • making adjustments to existing layout.
The objectives of a good study of plant layout are: • ensure effective space utilization, • minimize the cost of material handling (internal transports), • foresee future developments of the plant according to a rational master plan, • improve workers convenience as well as safety and create job satisfaction, and • avoid unnecessary capital investment.
Types of Layout • Product Layout: In this type of layout, only one product or one type of product is produced in a given area. • The product must be standardized and manufactured in large quantities in order to justify the product layout.
Some of the Advantages of Product Layout are: • lower total material handling cost, • lower total production time, • less work in process, • greater incentive for groups of workers to raise level of performance, • less floor area required per unit of production and • greater simplicity of production control, fewer control records needed and lower accounting cost.
Product Layout is Used When: • one or few standard products are to be produced, • large volume of production of each item over a considerable time is needed, • minimum of inspection is required during sequence of operations, • minimum of very heavy equipments or equipments requiring special facilities are needed, • materials and products permit bulk or continuous handling of mechanical means and • one machine is always used for one purpose.
Process Layout: Similar equipment and similar operations are grouped together in the process or functional layout. It is particularly useful where low volume is required.
Some of the Advantages of Process Layout are: • less duplication of equipment, hence lower investment cost, • greater flexibility of production, • better and more efficient supervision, • greater incentive for individual workers to raise level of performance, • better control of complicated or precision processes, • easier to handle breakdowns of equipment by transferring work to anther machine or station.
Process Layout is Used when • many types or styles of products are on special order , • relatively low volume of production on individual items is needed, • many inspections are required during a sequence of operations, • high proportion of very heavy equipment or equipment requiring special treatment exist, • materials or products become too large or too heavy to permit bulk or continuous flow and • one machine is used for different operations.
Fixed-Position Layout • Fixed-Position Layout: In this type of layout, the material or major component remains in a fixed location, and tools, machinery, men as well as other pieces of material are brought to this location. Typical examples are ship building, construction industries, aircraft building and bench work exercises. This type of layout is not frequently used in industrial enterprises. For this reason we are not going to look into its advantage and disadvantages.
STUDY OF PLANT LAYOUT • The solution of any size and type of plant layout problems could be facilitated by using a systematic and logical approach. • An early pioneer in this area was Richard Muther, developer of the Systematic Layout Planning (SLP) methodology.
The SLP procedure leads the planner through • Abstraction (Analysis): Gathering appropriate information and analyzing the flow of materials and the activity relationships to form a relationship diagram. Space considerations when combined with the relationship diagram develop the space relationship diagram.
Search (for possible solution): • The overall layout is designed by combining space consideration with the relationship diagram. • The search phase is the phase in which alternative layouts are developed by examining the space relationship diagram under modifying consideration such as materials handling, storage facilities, site conditions and surroundings, building types, personnel convenience, etc. , and practical limitations.
Selection: • The most efficient general method of evaluating layout alternatives is termed factor analysis. It follows the engineering concept of breaking down the problem into its elements and analyzing each one.
Abstraction (Analysis) • There are two basic elements on which every layout problem rests • Product (or material) • Quantity (or volume) • These two elements underline all other features or conditions directly or indirectly in layout work.
This phase will require the assembly of different data. In general, information about the following is needed: • the list of items to produce and store, and the relative quantity; • successive operations needed for every product; • the volume, the weight and the characteristics of materials to transport along the production line;
• the number, type and technical data of machines and plants necessary; • the manpower needed; • the necessary electric energy, steam, water, compressed air, fuel, oil, etc; • the necessary general service (offices, labs, cafeteria etc); • the necessary auxiliary services like maintenance department, tool store, etc; • the possible variation of the product in the future.
• If the study is on an existing plant, it is necessary to have drawings of the plant layout and the building with all the technical data.
Search for Possible Solution • The systematic approach of generating possible alternatives of plant layout is conducted by taking in to consideration: 1. type of layout, 2. the possible internal transport systems and 3. the working condition.
• Type of Layout: It is necessary to determine which type of layout to select, product (line) or process (functional) layout. • In addition to the selection of type of layout it is also important to fix the arrangement of machines
• In region A there are few types of products but in a great quantity. For these products it is advisable to have product layout. • In region C there are very many products in small quantity. Hence, preferred to have process layout. • For products in region B (medium types of products and medium quantity) the case has to be studied closely so as to be able which layout to select.
• There are different types of machine arrangements. The form of an industrial building is mainly dependent on machine arrangements and the advancement of a workpiece. The usual forms are shown
The Possible Internal Transport System: • After considering the type of workpiece advancement, the production capacity and the machineries required, it is necessary to examine the volume and weight of materials that has to be transported from one machine to the other, or from one department to the other
• The type of material handling equipment influences directly the plant layout and also the building. The working position, the form of the layout, the height, width and length of the building, the loading and unloading of materials, the positions and dimensions of accessibility depends in general, on the type of internal transport system adopted.
• A good study of internal transport system may boil down to the following major benefits: Reduce costs by - utilizing space to better advantage, - increasing productivity and - making few number of effective movements. Reduce waste by - eliminating damage to material during the handling process and - maintaining proper control over in-and-out of stock handling process.
Improve working conditions by • providing safer working conditions and • reducing worker fatigue. Improve the efficiency of the plant by • improving location of storage facilities, • improving routing and • increasing productivity.
• In some plants, the cost of repeated handling constitutes a very high proportion of the total cost of the end product, and in some others, the distance, materials have to move is not the sole criterion, and often is not even the primary concern for locating an area or an operation. Hence, more realistic value assessment of the factors that truly affect total cost in different kinds of layout planning situations is needed. • The available computer aided layout algorithms fall into, either improvement, or construction routine categories.
The objective function to be evaluated is: TC = Total internal transport cost Cij = Cost of internal transport, per unit distance per unit weight, for material movement between department i and j Wij =Weight of material transported, per unit time, from department i to j Dij = Distance from department i to j
• The routine accepts input data of Wij and Cij in the form of a FROM - TO chart. It may also accept Dij in the form of a FROM - TO charter, or it may accept the co-ordinates of the work centers. A FROM - TO chart is a square matrix whose elements represent flow or distance between departments. The chart is constructed by listing the departments down the left hand column and then across the top in the same order. The departments on the left are the originating (FROM) departments and the ones at the top are the receiving (TO) ones.
CONSTRUCTION ROUTINE: • This routine constructs layouts without the need for an existing (preliminary) layout. Basically find the starting point or initial activity placement and then add the remaining activity areas in accordance with logical rule. Thus, the routine accepts qualitative information from the relationship chart with closeness value numerically rated.
• A relationship chart is a triangular matrix whose elements represent the relationships among plant layout departments. Letter codes are also used to represent desirable or undesirable levels of closeness between departments. Six standard letter codes are used to show closeness relationships. § "A" indicates an absolutely necessary closeness relationship; § "E" indicates especially important; § "I" important; § "O" ordinary; § "U" unimportant; § "X" indicates a not desirable closeness relationship. • Although the letter codes are standard, the ratings reflect the user's own reasons for assigning the letter codes.
• The relationship chart and the numerically weighted ratings, assigned to the closeness values, are the basis for the order and placement in which departments enter the layout. The ratings assigned for A, E, I, O, U and X are used to calculate the Total Closeness Rating (TCR) for each department.
where TCRj =Total Closeness Rating for department; V(rij) =Numerical value assigned to the closeness value for department i and j. n = Total number of departments.
• The first department to be placed in the layout is assigned by taking the department with the greatest TCR. Next, the relationship chart is scanned to see if there is any department that has an A value with the department already placed. If no A value exists, a check is made for E value, and if no E value appears, a check is made for I value, followed by O value. If ties develop, the department having the greatest TCR is chosen. This process is continually used until finally all departments are placed in the layout.
Working Condition • Proper working conditions are considered important by management because they increase production effectiveness. Employee working conditions are influenced by many factors, over which the employee has very little or no control. • A good layout considers the factors influencing working conditions.
LIGHTING Good lighting facilitates accuracy and ease of seeing. A lighting system that aids these two demands means that the worker is able to see the critical details required in his job without excessive visual strain. The lighting fixtures are described according to the way they distribute light.
• Factors that affect quality illumination include contrast, luminance ratios, uniformity, distribution, shadows and glare. • The following ranges are accepted internationally
TYPE OF WORK ILLUMINATION VALUE IN FLUX • Store and rarely accessible working places 100 - 200 • Rough work (Brewery) 200 - 500 • Medium work (automobile assembly) 500 - 1000 • Precise work (wool work) 500 – 1000 • Fine work (Radio and TV assembly) 1000 - 2000 • Very fine work (controlling wool work) 1000 - 2000 • Working on a very small pieces (watch assembly) 2000 - 7500
AIR CONDITIONING • Air conditioning is used for many plants to control contamination by dust, bacteria and toxic gases in addition to air temperature and humidity. • It is primarily the control of the latter that provides comfortable working conditions. • Air conditioning is a system which provides an atmosphere comfortable to the human being and maintain an atmospheric environment demanded by a manufacturing process or storage of products.
NOISE • A wide variety of sound exists in industry. • Continuous exposure to high noise levels frequently results in temporary or even permanent loss of hearing. • But there is no clear cut line to indicate how much noise results in hearing loss. • The following are standard measurements for different sound sources in decibels:
SOURCE d. B - Hydraulic process at one meter 140 - Automobile hornpush at one meter 120 - Automatic lath at one meter 100 - Conversation at one meter 70 - Workshop (mechanical) 80
The reduction of noise may be brought about by a variety of methods. Some of these methods are: - Control of the noise at the source. - Isolation of the noise. - Use of baffles and sound absorbers. - Acoustical treatment. - Use of ear protection devices.
USE OF COLOR The objective of utilizing scientifically selected colors is to bring about a clear three dimensional vision. Color codes have been developed for particular uses. The red, yellow and green of traffic lights is a well known example of color coding. Red Yellow Green - danger; stop - caution - safety equipment
Different colors have different psychological effects. • Red - Hot and heavy, exciting, stimulating. • Orange - Hot, exciting and stimulating less than red. • Yellow - Hot, exciting lovely. • Green - Fresh and light, pacific. • Blue - Light, pacific. • Violet - Light, loneliness. • White - Cold, brilliant (seems to increase volume). • Black - Hot (seems to decrease volume) depressing.
SPACE REQUIREMENTS • The layout man often finds himself involved in work space arrangement; at any rate, he must determine the floor space that will be required by an operator. The study of floor space needed considers the following points: • While at work, the operator's arms and hands should move as easily as possible and he ought to reduce, to the minimum the movement of his shoulders, his body and his person from one position to another.
• Fixed posts for utensils and materials should be assured. • The disposition of utensils, materials and organs of maneuver near and infront of the operator. • Avoidance of the standing operator wherever possible. The study of the working area should consider a proper and comfortable position for the legs of the operator in an armchair or on a stool. • When the operator is transporting material, or when he is in a position to push, or pull he should do it in such a way that: • he is in an equilibrium position and • he applies the possible minimum force to produce the effect.
PASSAGE IN AN INDUSTRIAL BUILDING • From the very beginning of the study one has to determine the corridors within the building. Their width is determined according to the internal transport system selected and according to the clearance needed for passages. • Principal corridors which normally start from one end of the building and end at the other end are 3 to 5 meters wide. • Corridors within the department: 1. passage for one person 60 cm, 2. passage for two persons 120 cm, 3. passage for three persons 170 cm.
SAFETY A good plant layout should consider the safety of all personnel. Lack of adequate storage space which is beyond the control of the foreman, can lead to unsafe practices in the storage of materials. Some of the safety hazards to be watched for in plant layout are:
• inadequate passage, • insufficient storage space allowance for safe handling procedures, • insufficient handling equipment capacity, • floor load capacity, • floor obstructions, • slippery finish floors, • inadequate exits, • inadequate stairs, ramps and ladders, • inaccessible fire extinguisher and first aid boxes • unguarded moving parts of equipment , • workers located under the above hazards and • improper ventilation for removal of dangerous or toxic gases.
• The layout man should give due consideration to the problem of safety. Overlooking the problem will lead to lower morale of the workers, lower productivity and heavy accident liability costs.
Selection • Every layout plan has intangible costs which to all intents and purposes cannot be measured in terms of dollars and cents. Moreover, a comparative cost analysis of alternative layouts is sometimes a standoff, no one plan has a clear-cut financial advantage over the other. As a result, perhaps the most effective general method of evaluating layout alternatives is that termed factor analysis
• The overall desires of what is wanted in layout being planned are broken down into so-called factors or considerations. They may also be termed criteria or objectives. • Follows a list of the most commonly involved factors or considerations; not in order of importance.
• ease of future expansion, • adaptability and versatility, • flexibility of layout, • flow of materials effectiveness, • materials handling effectiveness, • storage effectiveness, • space utilization, • effectiveness of supporting service integration, • safety and housekeeping,
• working conditions and employee satisfaction, • ease of supervision and control, • appearance, promotions value, public or community relations, • quality of products, • maintenance problems, • fit with company organization structure, • equipment utilization, • utilization of natural conditions or surroundings , • ability to meet capacity or requirements, • investment or capital required and • savings, payout, returns, profitability.
Plant Design Plant design is a broad function-taking place in the origin of an enterprise. It is the planning of finances, the plant location and all the planning necessary for the physical requirements of an overall design of a plant. The basic decision that must taken for effective plant design include: (i) Acquisition of Capital ØObtaining capital for the initial establishment; ØRaising funds to cover operating costs; ØSecure funds for expansion.
Cont’d The primary sources of capital are: ØPersonal savings; ØLoans and sales of bonds; ØProfit plowback (ii) Sales Planning for Requirement: It is important to know the market demand with the understanding of seasonal variation.
Cont’d (iii) Determination of the Production Process: Process planning is closely allied with plant layout. (iv) Make or Buy: The determination of unit cost is usually the first step in a make-buy analysis. In such analysis management is interested in: ØReducing unit material and processing costs; ØMinimizing cash investment; ØImproving product.
Cont’d (v) Plant Size: The size of a plant dependent upon the volume of output proposed for it. vi) Product Price Range: The choice of competent price range will influence the quality, quantity and the manufacturing process of the product.
Plant design …. . Cont’d (vii) Plant Location: Selecting a location involves large commitments of capital as a result it must be done with utmost care. (viii) Plant Layout: It is the plan of, or the act of planning, a good workable disposition of industrial facilities, like operating equipment, storage space, materials handling equipment and all other supporting services, along with the design of the best structure to contain these facilities.
Plant design …. . Cont’d (ix) Building Type Selection: Selection of the type of building will take place before, or during the plant layout phase. (x) Diversification: To diversify doesn't mean widening the scope of the presently manufactured line, but rather mean entering a completely new field.
Cont’d (xi) Organization Development: The manner in which the overall objectives of an enterprise are clearly defined, the objectives of various subdivisions are determined and clearly specified influences the arrangement of plant facilities.
Plant design …. . Cont’d (xii) Product Design: The design of the product is the foundation upon which a plant layout is built. § Design for function: in order to create a satisfied customer or to attract customers, a product must perform the function for which its customer intends to.
Cont’d § Design for manufacturing: a product that solves the functional problem nicely, but is impossible to manufacture, is worthless. § Design for selling: a product that functions well and easy to make, but wanted by no one is useless.
Plant Location • A facility is something built or established to serve a purpose and facilities location is the determination of the site for that facility. It is part of a larger study area called faculty’s management, which involves both the location of the facility and the composition, or internal layout of the facility once located. • There analytical procedures to aid in the process but the decision must also included factors that are difficult if not impossible to quantify.
Cont’d The decision usually is made in two stages but there is substantial overlap, as shown. 1. The selection of general territory 2. The selection of a specific community and site
Selection of a General Territory i. Cost of construction may very form one territory to the other. ii. Market may be concentrated or distributed iii. Wages and Labor are lower in one area than in the other, depending upon the living cost. iv. Availability of Raw material may determine the location of the plant.
Cont’d v. Transport: Refers to the external transportation of the raw material and the finished product. vi. Energy: Other than electric power, in most plants it may be necessary to use gas, coal fuel oil, etc.
Selection of a Specific Site i. Community Attitude: The plant has to be located according to the master plan of the city or the region; ii. Transport: It is important to consider the transportation infrastructure of the area. iii. Water: There are certain industrial processes, which require large quantities of water.
Cont’d iv. Communication: The new plant has to be located in proximity to one or more of communication systems v. Wind Direction: If the industry produces smoke, gas, odor, etc, it will be necessary to place the pant with respect to the dominating wind direction. vi. Condition of the Site: The ground has to have a good resistance to the load induced by the foundation of the building.
Cont’d vii. Future Development: The plant has to be in a position to develop or change product quantity, type and size. Space has to be at its disposal for its future development. viii. Complementary pant: an industry, to produce as intended, may need material; service and assistance form other plants.
Cont’d Wind Direction: If the industry produces smoke, gas, odor, etc, it will be necessary to place the pant with respect to the dominating wind direction. x. Condition of the Site: The ground has to have a good resistance to the load induced by the foundation of the building. ix
Cont’d xi. Future Development: The plant has to be in a position to develop or change product quantity, type and size. Space has to be at its disposal for its future development. xii. Complementary plant: an industry, to produce as intended, may need material; service and assistance form other plants.
Territory Selection Location Factor 1. Market 2. Raw Materials 3. Transportation 4. Power 5. Climate and Fuel 6. Labor and Wages 7. Laws and Taxation 8. Comm. ty Services and Attitude 9. Water and Waste * * * * Selection of Site and Community * * * A typical team studying location possibilities might include accountants, lawyers, marketing experts, various consultants, executives, and industrial engineers.
Principle of plant layout • Principle of overall integration – Integrates the man, materials, machinery supporting activiteis…. • • Principle of flow Principle of cubic space Principle of satisfaction and saftey Principle of flexibility – Can be adopted and rearranged at minimum cost with least inconvinence
• Principle of expansion • Principle of versality – Layout should be adaptable to changes in product design , sales requirement and process improvement • Principle of orderliness – Clean work areas with suitable equipment for removing scrap waste, etc…
Procedures for plant layout • Procure the basic data • Analyse the product and production process • Make or buy parts decision • Plan the material flow pattern • Consider general material handling plan • Calculate equipment requirement • Plan individual workstation
• Select specific material handling equipment • Coordinate group of related opertation • Construct flow diagram for production centers • Plan service and auxiliaries activities • Determine space requirements • Allocate activity area and plot plan • Consider building type
• • Construct master layout Seek opinions and suggestions Evaluate adjust and select the best layout Check final layout Obtain official approvals Install layout Follow up on implementation of the layout.
Analytical Techniques Usually, the criterion or objective is to minimize some cost function. Often, the distance traveled is chosen as the cost function. Thus, the objective becomes one of minimizing total distance traveled. Another possible stratification is in the distance measure used. Sometimes the straight-line or Euclidean distance may be more appropriate.
Cont’d If two facilities are located at points represented by (X 1, Y 1) and ((X 2, Y 2), then the Euclidean distance between the two is While the rectilinear distance is
Transportation Method of Linear Programming It is simple to formulate a location problem as a transportation linear programming problem involving minimization of total cost to distribute the product. Then total cost can be calculated, various locations tried, and the location with the least total cost chosen.
Example Production and distribution costs per unit L M N O P Weekly Capacity Producti on. Costs A 5. 00 3. 00 2. 00 7. 000 $75. 00 B 6. 50 5. 00 3. 50 1. 50 . 20 5, 500 $70. 00 C 1. 50 1. 80 6. 50 500 12, 500 $70. 00 D 3. 80 5. 00 8. 00 7. 50 8. 00 12, 500 $67. 00 Dem. /Week 5, 000 6, 000 4, 000 7, 000 3, 000 From To
The cost in the transportation matrix TO L M N O P From Plant Capacity A 80. 00 78. 00 77. 00 7, 000 B 76. 50 75. 00 73. 50 71. 50 70. 20 5, 500 C 71. 50 70. 50 71. 80 76. 50 75. 00 12, 500 Dem. /Week 5, 000 6, 000 4, 000 7, 000 3, 000 25, 000
Cont’d There are several ways of solving this problem. Some give optimal solutions with a relatively high cost of time and effort and others yield very fast, good but not necessarily optimal solutions with a relatively low cost. The latter procedures are called heuristic; the former procedures are called optimal seeking
Least cost assignment From L A M 80. 0 0 TO 78. 0 0 N 2, 500 O 77. 0 0 P 78. 0 0 77. 00 Plant Capacity 7, 000 4, 500 B 76. 5 0 75. 0 0 73. 5 0 71. 5 0 70. 20 2500 C 71. 5 0 70. 5 0 5, 000 Demand (Weekly) 6, 000 5, 000 6, 000 71. 8 0 3000 5, 500 76. 5 0 75. 00 12, 5000 1, 500 4, 000 7, 000 3, 000 25, 000
Cont’d • The total cost for location C is 2, 500(77) + 4, 500(78) + 2, 500(71. 50) + 3, 000(70. 20) + 5, 000(71. 50) + 6, 000(70. 50) + 1, 500(71. 80) = $1, 821, 050 • Similarly for location D the total cost is • 4, 000(77) + 3, 000(78) + 2, 500(71. 50) + 3, 000(70. 2) + 5, 000(70. 80) + 6, 000(72) + 1, 500(74. 50) = $1, 829, 100 • The total weekly cost of C town is $1, 821, 050, which $8, 050 per week more economical than the total cost D.
Public Sector Location Problems • In the location of public sectors ( fire stations, hospitals, emergency centers, equipment yards, and landfills) the objective is to minimize some maximum response time. Example Location of Blood Bank
Hospital or Research Center Map Location Weekly Trips 1. Hillcrest (22. 5, 5. 5) 10 1. South community (26. 5, 9. 5) 10 1. Capitol Hill (29. 5, 14. 0) 5 1. St. Anthony (28. 5, 24. 0) 3 1. Bone and Joint (28. 5, 24. 5) 1 1. Mercy (29. 0, 25. 0) 3 1. Polyclinic (30. 0, 25. 0) 1 1. Wesley (29. 5. 24. 5) 1 1. University (32. 0, 24. 5) 3 1. School of medicine (32. 0, 25. 0) 1 1. Research Institute (32. 5, 25. 0) 1 1. Admin. Hospital (33. 0, 25. 0) 1 1. Crippled Children’s (32. 5, 24. 5) 1 1. Deaconess (16. 0, 36. 5) 5 1. Baptist Memorial (18. 0, 37. 5) 4
Solution Procedure Location of a new facility with respect to several existing facilities (rectilinear distances assumed): 1. Arrange all facilities in increasing order of the X coordinates. Add up the number of trips for that same order. The optimum X location is such tat no more than half the trips are to the left and no more than half to the right. 2. Repeat for the Y coordinate such that no more than half the trips are above and no more than half below.
Cont’d 3. The X and Y coordinates just chosen are the optimum locations. The price of land, neighborhood, and other parameters must now be considered.
Cont’d • In the example problem the calculations for the X coordinate are The total number of trips is 50. The optimum X location than is that location where no more than 25 trips are to the left and no more than 25 are to the right. This occurs exactly at For the Y coordinate, the same procedure is required
Cont’d • There are 50 total trips. At 25 trips are to the left and exactly 25 trips are to the right of the blood bank. This implies that the optimum location is at 14, 0.
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