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Solution Manual for Automation, Production Systems, and Computer-Integrated Manufacturing, 5th Edition

Solution Manual for Automation, Production Systems, and Computer-Integrated Manufacturing, 5th Edition simplifies complex textbook exercises with easy-to-understand solutions and step-by-step guides.

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    Chapter 1 INTRODUCTION REVIEW QUESTIONS 1.1 What is a production system? Answer : As defined in the text, a production system is a collection of people, equipment, and procedures organized to perform the manufacturing operations of a company. 1.2 Production systems consist of two major components. Name and briefly define them. Answer : The two major components given in the text are (1) facilities, which consist of the factory, the equipment in the factory, and the way the equipment is organized; and (2) manufacturing support systems, which are the procedures used by the company to manage production and to solve the technical and logistics problems encountered in ordering materials, moving the work through the factory, and ensuring that products meet quality standards. Product design and certain business functions are included among the manufacturing support systems. 1.3 What are manufacturing systems, and how are they distinguished from production systems? Answer : A manufacturing system is a logical grouping of equipment in the factory and the worker(s) who operate(s) it. Examples include worker-machine systems, production lines, and machine cells. A production system is a larger system that includes a collection of manufacturing systems and the support systems used to manage them. A manufacturing system is a subset of the production system. 1.4 Manufacturing systems are divided into three categories, according to worker participation. Name the three categories. Answer : The three categories are (1) manual work systems, (2) worker-machine systems, and (3) automated systems. 1.5 What are the four functions included within the scope of manufacturing support systems? Answer : As identified in the text, the four functions are (1) business functions, (2) product design, (3) manufacturing planning, and (4) manufacturing control. 1.6 Three basic types of automation are defined in the text. What is fixed automation and what are some of its features? Answer : Fixed automation is a system in which the sequence of processing (or assembly) operations is fixed by the equipment configuration. Each operation in the sequence is usually simple, but the integration and coordination of many such operations in one piece of equipment makes the system complex. Typical features of fixed automation are (1) high initial investment for custom-engineered equipment, (2) high production rates, and (3) relatively inflexible in accommodating product variety. 1.7 What is programmable automation and what are some of its features? Answer : In programmable automation, the production equipment is designed with the capability to change the sequence of operations to accommodate different part or product configurations. The operation sequence is controlled by a program , which is a set of instructions coded so that they can be read and interpreted by the system. Some of the

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    features of programmable automation are (1) high investment in general purpose equipment, (2) lost production time due to changeovers of physical setup and reprogramming, (3) lower production rates than fixed automation, (4) flexibility to deal with variations and changes in product configuration, and (5) most suitable for batch production. 1.8 What is flexible automation and what are some of its features? Answer : Flexible automation is an extension of programmable automation. A flexible automated system is capable of producing a variety of parts (or products) with virtually no time lost for changeovers from one part style to the next. There is no lost production time while reprogramming the system and altering the physical setup. Accordingly, the system can produce various mixes and schedules of parts or products instead of requiring that they be made in batches. Features of flexible automation are (1) high investment for a custom- engineered system, (2) continuous production of variable mixtures of products, (3) medium production rates, and (4) flexibility to deal with product design variations 1.9 What is computer-integrated manufacturing? Answer : As defined in the text, computer-integrated manufacturing (CIM) denotes the pervasive use of computer systems to design the products, plan the production, control the operations, and perform the various information-processing functions needed in a manufacturing firm. True CIM involves integrating all of these functions in one system that operates throughout the enterprise. 1.10 What are some of the reasons why companies automate their operations? Answer : The reasons give in the text are (1) increase labor productivity, (2) reduce labor cost, (3) mitigate the effects of labor shortages, (4) reduce or eliminate routine manual and clerical tasks, (5) improve worker safety, (6) improve product quality, (7) reduce manufacturing lead time, (8) accomplish processes that cannot be done manually, and (9) avoid the high cost of not automating. 1.11 Identify three situations in which manual labor is preferred over automation. Answer : The five situations listed in the text are the following: (1) The task is technologically too difficult to automate. (2) Short product life cycle. (3) Customized product. (4) To cope with ups and downs in demand. (5) To reduce risk of product failure. 1.12 Human workers will be needed in factory operations, even in the most highly automated operations. The text identifies at least four types of work for which humans will be needed. Name them. Answer : The four types of work identified in the text are (1) equipment maintenance, (2) programming and computer operations, (3) engineering project work, and (4) plant management. 1.13 What is the USA Principle? What does each of the letters stand for? Answer : The USA Principle is a common sense approach to automation and process improvement projects. U means “understand the existing process,” S stands for “simplify the process,” and A stands for “automate the process.” 1.14 The text lists ten strategies for automation and process improvement. Identify five of these strategies.

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    Answer : The ten strategies listed in the text are (1) specialization of operations, (2) combined operations, (3) simultaneous operations, (4) integration of operations, (5) increased flexibility, (6) improved material handling and storage, (7) on-line inspection, (8) process control and optimization, (9) plant operations control, and (10) computer- integrated manufacturing (CIM). 1.15 What is an automation migration strategy? Answer : As defined in the text, an automation migration strategy is a formalized plan for evolving the manufacturing systems used to produce new products as demand grows. 1.16 What are the three phases of a typical automation migration strategy? Answer : As defined in the text, the three typical phases are the following: Phase 1: Manual production using single-station manned cells operating independently. Phase 2: Automated production using single-station automated cells operating independently. Phase 3: Automated integrated production using a multi-station automated system with serial operations and automated transfer of work units between stations.

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    Chapter 2 MANUFACTURING OPERATIONS REVIEW QUESTIONS 2.1 What is manufacturing? Answer : Two definitions are given in the text. The technological definition is the following: Manufacturing is the application of physical and chemical processes to alter the geometry, properties, and/or appearance of a given starting material to make parts or products. Manufacturing also includes the joining of multiple parts to make assembled products. The economic definition is the following: Manufacturing is the transformation of materials into items of greater value by means of one or more processing and/or assembly operations. 2.2 What are the three basic industry categories? Answer : The three basic industry categories are (1) primary industries, which are those that cultivate and exploit natural resources, such as agriculture and mining; (2) secondary industries, which convert the outputs of the primary industries into products; they include manufacturing, construction, and power generation; and (3) tertiary industries, which constitute the service sector of the economy; examples include banking, retail, transportation, education, government. 2.3 What is the difference between consumer goods and capital goods? Answer : Consumer goods are products that are purchased directly by consumers, such as cars, personal computers, TVs, tires, toys, and tennis rackets. Capital goods are products purchased by other companies to produce goods and supply services. Examples include commercial aircraft, mainframe computers, machine tools, railroad equipment, and construction machinery. 2.4 What is the difference between a processing operation and an assembly operation? Answer : A processing operation transforms a work material from one state of completion to a more advanced state that is closer to the final desired part or product. It adds value by changing the geometry, properties, or appearance of the starting material. An assembly operation joins two or more components to create a new entity, called an assembly, subassembly, or some other term that refers to the joining process. 2.5 Name the four categories of part-shaping operations, based on the state of the starting work material. Answer : The four categories are (1) solidification processes, (2) particulate processing, (3) deformation processes, and (4) material removal processes. 2.6 Into which of the four basic categories of part-shaping operations does each of the following belong: (a) powder metallurgy, (b) plastic molding, (c) drilling, (d) forging, and (e) grinding? Answer : (a) Particulate processing, (b) solidification, (c) material removal, (d) deformation, and (e) material removal. 2.7 Assembly operations can be classified as permanent joining methods and mechanical assembly. What are the four types of permanent joining methods?

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    Answer : The joining processes are (1) welding, (2) brazing, (3) soldering, and (4) adhesive bonding. 2.8 What is the difference between hard product variety and soft product variety? Answer : Hard product variety is when the products differ substantially. In an assembled product, hard variety is characterized by a low proportion of common parts among the products; in many cases, there are no common parts. Soft product variety is when there are only small differences between products. There is a high proportion of common parts among assembled products whose variety is soft. 2.9 With what type of production is a job shop usually associated? Answer : Low production of specialized and customized products. The products are typically complex, such as experimental aircraft and special machinery. 2.10 Flow line production is associated with which one of the following layout types: (a) cellular layout, (b) fixed-position layout, (c) process layout, or (d) product layout? Answer : (d) Product layout. 2.11 What is the difference between a single-model production line and a mixed-model production line? Answer : A single-model production line makes products that are all identical. A mixed- model production line makes products that have model variations characterized as soft product variety. 2.12 What is meant by the term technological processing capability ? Answer : Technological processing capability of a plant (or company) is its available set of manufacturing processes. It includes not only the physical processes, but also the expertise possessed by plant personnel in these processing technologies. 2.13 Define the term production capacity . Answer : Production capacity is defined as the maximum rate of production that a plant can achieve during a given period (such as a week, month, or year) under assumed operating conditions (e.g., direct labor manning levels, number of shifts per week, hours per shift, etc.). PROBLEMS Answers to problems labeled (A) are listed in the Appendix at the back of the book. 2.1 (A) A manufacturing plant produces three product lines in one of its plants: A, B, and C. Each product line has multiple models: 5 models within product line A, 3 models within B, and 4 within C. Total annual production quantity of all models of product A is 2000 units, 1500 units for product B, and 800 units for product C. Determine the number of (a) different product models and (b) total quantity of products produced annually in this plant. Solution : (a) The total number of different product models produced is P = 5 + 3 + 4 = 12 different models (b) The total production quantity of all products made in the factory is Q f = 5(2000) + 3(1500) + 4(800) = 10,000 + 4500 + 3200 = 17,700 units annually

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    2.2 Consider product line A in preceding Problem 2.1. Its five models have an average of 27 components each, and the average number of operations needed to produce each component is 4.5. All components are made in the same plant. Determine the total number of (a) components produced and (b) operations performed in the plant annually for product line A. Solution : (a) Total number of components produced is given by Equation (2.7). PQ = 2000 products n pf = PQn p = 2000(27) = 54,000 components (b) Total number of operations performed annually in the plant is given by Equation (2.9). n of = PQn p n o = 2000(27)(4.5) = 243,000 operations 2.3 A company produces two products in one of its plants: A and B. Annual production of Product A is 3000 units and of Product B is 2000 units. Product A has 25 components and Product B has 36 components. For Product A, 40% of the components are made in the plant, while 60% are purchased parts. For Product B, 30% of the components are made in the plant, while 70% are purchased. For these two products taken together, what is the total number of (a) components made in the plant and (b) components purchased? Solution : (a) The total number of components produced in the plant can be determined using Equation (2.3), adjusting it for the proportions of each part made in the factory: n pf = 3000(25)(0.40) + 2000(36)(0.30) = 30,000 + 21,600 = 51,600 parts made in plant (b) Let n pp = the total number of parts purchased: n pp = 3000(25)(0.60) + 2000(36)(0.70) = 45,000 + 50,400 = 95,400 purchased parts 2.4 (A) A product line has two models: X and Y. Model X consists of 4 components: a, b, c, and d. The number of processing operations required to produce these four components are 2, 3, 4, and 5, respectively. Model Y consists of 3 components: e, f, and g. The number of processing operations required to produce these three components are, 6, 7, and 8 respectively. The annual quantity of Model X is 1000 units and of Model Y is 1500 units. Determine the total number of (a) components and (b) processing operations associated with these two models. Solution : (a) The total number of components can be determined using Equation (2.3): n pf = 1000(4) + 1500(3) = 4000 + 4500 = 8500 components Alternatively, Equation (2.7) can be used, first computing the average values for Q and n p using Eqs. (2.6) and (2.8). Q = (1000 + 1500)/2 = 1250 units n p = (1000(4) + 1500(3))/(2 × 1250) = 3.4 components per unit product n pf = 2(1250)(3.4) = 8500 components (b) The total number of processing operations can be determined using Equation (2.4): n of = 1000(2 + 3 + 4 + 5) + 1500(6 + 7 + 8) = 1000(14) + 1500(21) = 45,500 operations Alternatively, Equation (2.9) can be used, first computing the average values for n p and n o using Eqs. (2.8) and (2.10). The value of n p was calculated above: n p = 3.4 components per unit product n o = (1000(2 + 3 + 4 + 5) + 1500(6 + 7 + 8))/3.4 = 5.353 operations per component n of = 2(1250)(3.4)(5.353) = 45,500 operations

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    2.5 The ABC Company is planning a new product line and a new plant to produce the parts for the line. The product line will include 8 different models. Annual production of each model is expected to be 900 units. Each product will be assembled of 180 components. All processing of parts will be accomplished in the new plant. On average, 6 processing operations are required to produce each component, and each operation takes an average of 1.0 min (including an allowance for setup time and part handling). All processing operations are performed at workstations, each of which includes a production machine and a human worker. The plant operates one shift. Determine the number of (a) components, (b) processing operations, and (c) workers that will be needed to accomplish the processing operations if each worker works 2000 hr/yr. Solution : (a) Number of components produced in the plant: n pf = PQn p = 8(900)(180) = 1,296,000 components (b) Number of operations performed in the plant: n of = PQn p n o = 8(900)(180)(6) = 7,776,000 operations in the plant per year (c) Total operation time TT = n of T p , where T p = time for one processing operation. TT = 7,776,000(1.0) = 7,776,000 min = 129,600 hr of processing time At 2000 hours/yr per worker, number of workers w = 129,600/2000 = 64.8 workers This should be rounded up to 65 workers . 2.6 The XYZ Company is planning a new product line and a new factory to produce the parts and assembly the final products. The product line will include 10 different models. Annual production of each model is expected to be 1000 units. Each product will be assembled of 300 components, but 65% of these will be purchased parts (not made in the new factory). There are an average of 8 processing operations required to produce each component, and each processing step takes 30 sec (including an allowance for setup time and part handling). Each final unit of product takes 48 min to assemble. All processing operations are performed at work cells that include a production machine and a human worker. Products are assembled at single workstations consisting of one worker each plus assembly fixtures and tooling. Each work cell and each workstation require 25 m 2 of floor space and an additional allowance of 45% must be added to the total production area for aisles, work-in-process storage, shipping and receiving, rest rooms, and other utility space. The factory will operate one shift (the day shift, 2000 hr/yr). Determine (a) how many processing and assembly operations, (b) how many workers (direct labor only), and (c) how much total floor space will be required in the plant. Solution : (a) The number of products is Q f = PQ = 10(1000) = 10,000 products/yr Therefore, the number of final assembly operations = 10,000 asby ops/yr Total number of parts n pf = 10(1000)(300) = 3,000,000 components, but 65% of these are purchased, so the number made in the plant will be 0.35(3,000,000) = 1,050,000 Number of processing operations n of = 1,050,000(8) = 8,400,000 proc ops/yr (b) Total processing time TT p = n of T p , where T p = time for one processing operation. TT p = 8,400,000(0.50) = 4,200,000 min = 70,000 hr/yr Total assembly time TT a = QT a , where T a = assembly time for each product. TT a = 10,000(48) = 480,000 min/yr = 8000 hr/yr Number of workers w = (70,000 + 8000)/2000 = 39 workers

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    (c) With 1 worker per workstation for processing operations and 1 worker per assembly workstation, n = w = 39 workstations. Total floor space TA = nA w (1 + AL ), where A w = area of each work cell or workstation, and AL = allowance for aisles, storage, etc. TA = 39(25)(1 + 0.45) = 1413.75 m 2 (~15,217 ft 2 ) 2.7 Suppose the company in Problem 2.6 were to operate two shifts (a day shift and an evening shift, a total of 4000 hr/yr) instead of one shift to accomplish the processing operations. The assembly of the product would still be accomplished on the day shift. Determine (a) how many processing and assembly operations, (b) how many workers on each shift (direct labor only), and (c) how much total floor space will be required in the plant. Solution : (a) Number of final assembly operations PQ = 10(1000) = 10,000 asby ops/yr Total number of parts n pf = 10(1000)(300) = 3,000,000 components, but 65% of these are purchased, so the number made in the plant will be 0.35(3,000,000) = 1,050,000 Number of processing operations n of = 1,050,000(8) = 8,400,000 proc ops/yr (b) Total processing time TT p = n of T p , where T p = time for one processing operation. TT p = 8,400,000(0.50 min) = 4,200,000 min = 70,000 hr/yr total for two shifts TT p = 70,000/2 = 35,000 hr/yr total for each shift Number of processing operation workers per shift w p = 35,000/2000 = 17.5 rounded up to 18 parts production workers per shift Total assembly time TT a = QT a , where T a = assembly time for each product. TT a = 10,000(48) = 480,000 min/yr = 8000 hr/yr Number of assembly workers w a = 8000/2000 = 4 assembly workers Number of workers on day shift w = 18 + 4 = 22 workers Number of workers on evening shift w = 18 workers (c) The floor space must be based on the number of day shift operations, which includes processing and assembly operations. Total floor space TA = nA w (1 + AL ), where A w = area of each work cell or workstation, and AL = allowance for aisles, etc. TA = 22(25)(1 + 0.45) = 797.5 m 2 (~8584 ft 2 ) Comment : This is a savings in floor space of ~44% compared to the one-shift operation in the previous problem.

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    Chapter 3 MANUFACTURING METRICS REVIEW QUESTIONS 3.1 What is the cycle time in a manufacturing operation? Answer : As defined in the text, the cycle time T c is the time that one work unit spends being processed or assembled. It is the time between when one work unit begins processing (or assembly) and when the next unit begins. 3.2 What is the difference between sequential batch production and simultaneous batch production? Answer : In sequential batch production the parts in the batch are processed one after the other, resulting in a batch time = T su + Q b T c , where T c = cycle time per part. In simultaneous batch production, the parts in the batch are all processed at once, resulting in a batch time = T su + T c , where T c = cycle time to process all of the parts in the batch. 3.3 What is a bottleneck station in a production line? Answer : The bottleneck station is the slowest workstation in a production line, and therefore it limits the pace of the entire line. 3.4 What is availability and how is it defined? Answer : Availability is a reliability metric that indicates the proportion of time that a piece of equipment is up and working properly. It is defined as follows: A = ( MTBF – MTTR )/ MTBF where A = availability, MTBF = mean time between failures, and MTTR = mean time to repair. 3.5 What is workload? Answer : Workload is defined as the total amount of time required to complete a given amount of work. In production it refers to the total amount of time to produce a given quantity of work units, for example in sequential batch production, WL = QT p , where T p = T su + QT c . 3.6 What is production capacity? Answer : Production capacity is the maximum rate of output that a production facility (or production line, work center, or group of work centers) is able to produce under a given set of assumed operating conditions. 3.7 How can plant capacity be increased or decreased in the short term? Answer : As listed in the text, the two ways that plant capacity can be increased or decreased in the short term are (1) add workers, (2) change the number of work shifts per week, and (3) change the number of hours worked per shift. 3.8 How can plant capacity be increased or decreased in the intermediate or long term?

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    Answer : As listed in the text, the two ways that plant capacity can be increased or decreased in the intermediate or long term are (1) increase or decrease the number of work centers in the plant or (2) increase the production rate of the work centers by making methods improvements or using more productive processing technologies. 3.9 What is meant by the term part mix ? Answer : The term part mix refers to the relative proportions of different part styles made in a production facility. The symbol p j = the proportion of part style j out of a total of P different part styles, p j = 1, 2, . . P . 3.10 What is utilization in a manufacturing plant? Provide a definition. Answer : Utilization is defined as the proportion of time that a productive resource, such as a manufacturing plant, is used relative to the time available under the definition of plant capacity. 3.11 What is manufacturing lead time? Answer : Manufacturing lead time is the total time required to process a given part or product through the plant, including any lost time due to delays, time spent in storage, reliability problems, and so on. 3.12 What is work-in-process? Answer : Work-in-process (WIP) is the quantity of parts or products currently located in the factory that are either being processed or are between processing operations. WIP is inventory that is in the state of being transformed from raw material to finished product. 3.13 How are fixed costs distinguished from variable costs in manufacturing? Answer : Fixed costs remain constant for any level of production output. Examples include the cost of the factory building and production equipment, insurance, and property taxes. Variable costs vary in proportion to the level of production output. As output increases, variable costs increase. Examples include direct labor, raw materials, and electric power to operate the production equipment. 3.14 Name five typical factory overhead expenses? Answer : Table 3.2 in the text lists the following examples of factory overhead expenses: plant supervision, applicable taxes, factory depreciation, line foremen, insurance, equipment depreciation, maintenance, heat and air conditioning, fringe benefits, custodial services, light, material handling, security personnel, power for machinery, shipping and receiving, tool crib attendant, payroll services, and clerical support. 3.15 Name five typical corporate overhead expenses? Answer : Table 3.3 in the text lists the following examples of corporate overhead expenses: corporate executives, engineering, applicable taxes, sales and marketing, research and development, cost of office space, accounting department, support personnel, security personnel, finance department, insurance, heat and air conditioning, legal counsel, fringe benefits, and lighting. 3.16 Why should factory overhead expenses be separated from corporate overhead expenses?

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    Answer : A manufacturing company may operate more than one factory, and each factory has its own overhead expenses that are different from the expenses at other factories. On the other hand corporate overhead expenses are applied to all factories operated by the company. Also, in matters of analyzing costs, corporate overhead would simply inflate the operating costs so they should not be included in the cost analyses, but at least some of the factory overhead costs should be included. In pricing decisions, both factory and corporate expenses must be included. PROBLEMS Answers to problems labeled (A) are listed in the Appendix at the back of the book. Cycle Time and Production Rate 3.1 (A) A batch of parts is produced on a semi-automated production machine in a sequential batch production operation. Batch quantity is 300 units. Setup takes 55 min. A worker loads and unloads the machine each cycle, which takes 0.75 min. Machine processing time is 3.46 min/cycle, and tool handling time is negligible. One part is produced each cycle. Determine (a) average cycle time, (b) time to complete the batch, and (c) average production rate. Solution : (a) T h = 0.75 min, T o = 3.46 min, and T t = 0 Cycle time T c = 0.75 + 3.46 = 4.21 min (b) Batch time T b = 55 + 300(4.21) = 55 + 1263 min = 21.05 hr (c) Average production time T p = 1263/300 = 4.21 min/pc Production rate R p = 60/4.21 = 14.25 pc/hr 3.2 In a sequential batch machining operation, setup time is 1.5 hours and batch size is 120 units. The cycle time consists of part handling time of 30 sec and processing time of 2.85 min. One part is produced each cycle. Tool changes must be performed every 10 parts and this takes 2.0 min. Determine (a) average cycle time, (b) time to complete the batch, and (c) average production rate. Solution : (a) T h = 30/60 = 0.50 min, T o = 2.85 min, and T t = 2.0/10 = 0.20 min Cycle time T c = 0.50 + 2.85 + 0.20 = 3.55 min (b) Batch time T b = 1.5(60) + 120(3.55) = 90 + 426 = 516 min = 8.6 hr (c) Average production time T p = 516/120 = 4.3 min/pc Production rate R p = 60/4.3 = 13.95 pc/hr 3.3 The setup time in a sequential batch production operation is 2.0 hours, and the actual processing time of 1.60 min per cycle. Three parts are produced each cycle. No tool handling time is included in the cycle. Part handling time each cycle is 45 sec. It consists of the worker obtaining two starting work units from a parts tray, loading them into the machine, and then after processing, unloading the completed parts and placing them into the same tray. Each tray holds 24 parts. When all of the starting work units have been replaced with completed parts, the tray of completed parts is moved aside and a new tray of starting units is moved into position at the machine. This irregular work element takes 4.0 min. Batch quantity is 2400 units. Determine (a) average cycle time, (b) time to complete the batch, and (c) average production rate.

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    Solution : (a) T h = 45/60 sec = 0.75 min/cycle, T o = 1.60 min, and T t = 0. The irregular work element of replacing the parts trays is an additional component of work handling time that must be done every 24 parts or 24/3 = 8 cycles: T h 2 = 4.0/8 = 0.5 min Cycle time T c = 0.75 + 1.60 + 0.5 = 2.85 min (b) Batch time T b = 2.0(60) + (2400/3)(2.85) = 120 + 2280 = 2400 min = 40 hr (c) Average production time T p = 2400/800 = 3.00 min/cycle = 1.0 min/pc Production rate R p = 60/1.0 = 60 pc/hr 3.4 An automated production line consists of eight workstations. Work units are moved between stations with a transfer time of 12 sec. The automated operations performed at the eight stations take 40 sec, 52 sec, 43 sec, 48 sec, 30 sec, 54 sec, 53 sec, and 49 sec, respectively. Determine (a) cycle time for the line, (b) time to process one work unit through the eight workstations, (c) average production rate, and (d) time to produce 25,000 units. Solution : (a) The longest processing operation time, Max T o = 57 sec at station 6. It sets the pace for the rest of the line. T c = 12 + 54 = 66 sec = 1.1 min (b) Time to process one work unit through the eight workstations = 8(1.1) = 8.8 min (c) Production rate R p = 60/1.1 = 54.55 pc/hr (d) Time to produce 25,000 units = 25,000/54.55 = 458.33 hr 3.5 Simultaneous batch production is used in a heat treating operation. The batch size that fits in the furnace at one time is 12 parts of a certain type. A total of 500 of these parts are to be heat treated. Loading of 12 parts into the furnace takes 3.0 min. Unloading time at the end of heat treatment is 1.5 min. The cycle time to heat treat each batch is 25 min. How many hours are required to process the 500 parts? Solution : Assuming the furnace has been heated to the proper temperature in advance of production, the time to process each batch of 12 parts = 3.0 + 25 + 1.5 = 29.5 min. The number of batches = 500/12 = 41.67. This would have to be rounded up to 42 batches. Accordingly, total time for 500 parts = 42(29.5) = 1239 min = 20.65 hr 3.6 (A) The proportion uptime of a certain piece of production equipment is 97.5%. When a breakdown occurs, the mean time to repair is 45 min. Determine the mean time between failures of this equipment. Solution : From Equation (3.9), A ( MTBF ) = MTBF – MTTR 0.975( MTBF ) = MTBF – 45/60 = MTBF – 0.75 0.75 = MTBF – 0.975( MTBF ) = 0.025( MTBF ), MTBF = 0.75/0.025 = 30 hr 3.7 Setup time on a certain production machine is 3.0 hours. Batch size is 36 parts, and operation cycle time is 2.5 min. Parts are processed sequentially. The reliability of this machine is characterized by a mean time between failures of 47 hours and a mean time to repair of 48 min. (a) If availability is ignored, what is the average hourly production rate of the machine. (b) Taking into account the availability of the machine, determine its average hourly production rate. (c) Suppose that availability only applied during the actual run time of the machine and not during the setup time. Determine the average hourly production rate of the machine under this scenario. Solution : (a) Batch time T b = 3.0(60) + 36(2.5) = 180 + 90 = 270 min

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    T p = 270/36 = 7.5 min and production rate R p = 60/7.5 = 8.0 pc/hr (b) Availability A = (47 – 48/60)/47 = 0.983 = 98.3% Production rate including effect of availability = AR p = 0.983(8.0) = 7.86 pc/hr (c) If availability only applies during run time, then T b = 3(60) + 36(2.5/0.983) = 180 + 91.56 = 271.56 min T p = 271.56/36 = 7.54 min and production rate R p = 60/7.54 = 7.95 pc/hr Workload and Production Capacity 3.8 In a certain week, a production schedule for a certain department shows the following parts being produced: 540 parts of type A, 1200 parts of type B, 490 parts of type C, and 780 parts of type D. The respective production times for these parts are the following: T p A = 5.28 min, T p B = 2.86 min, T p C = 4.65 min, and T p D = 3.22 min. Determine the workload for this department in hours per week. Solution : WL = 540(5.28) + 1200(2.86) + 490(4.65) + 780(3.22) WL = 2851.2 + 3432 + 2278.5 + 2511.6 = 11,073.3 min = 184.56 hr/wk 3.9 (A) A mass-production plant has eight machines and currently operates one 8-hour shift per day, 5 days per week, 50 weeks per year. Each machine produces the same part at a rate of 24 parts per hour. (a) Determine the annual production capacity of this plant. (b) If the plant were to operate three 8-hour shifts per day, 7 days per week, 52 weeks per year, determine the annual percentage increase in plant capacity? Solution : (a) From Table 3.1, H pc = 2000 hr Annual plant capacity using 50 weeks/yr PC y = 2000(8)(24) = 384,000 pc/yr (b) From Table 3.1, H pc = 8736 hr. Annual plant capacity PC y = 8736(8)(24) = 1,677,312 pc/wk This is an increase of 1,677,312/384,000 – 1 = 3.368 = 336.8% Comment: This problem illustrates the significant effect that hours of operation can have on plant capacity. 3.10 One/half million parts of a certain type are to be manufactured annually on dedicated production machines that run 16 hours per day, five days per week, 50 weeks per year. (a) The cycle time to produce one part is 1.8 min. If availability and utilization are each 100%, and setup time is neglected, how many of the machines will be required to satisfy demand? (b) Solve part (a) except that availability = 95%. Solution : (a) Total workload WL = 500,000(1.8 min/60) = 15,000 hr/yr From Table 3.1, hours available/machine = 4000 hr Number of machines n = (15,000 hr)/(4000 hr/machine) = 3.75 rounded up to 4 machines (b) At A = 90%, n = (15,000 hr)/(4000 × 0.95) = 3.95 rounded up to 4 machines 3.11 A factory produces cardboard boxes. The production sequence consists of three operations: (1) cutting, (2) indenting, and (3) printing. There are three machines in the factory, one for each operation. The machines are 100% reliable and operate as follows when operating at 100% utilization: (1) In cutting, large rolls of cardboard are fed into the cutting machine and cut into blanks. Each large roll contains enough material for 4,000 blanks. Production cycle time = 0.03 minute per blank during a production run, but it takes 35 minutes to change rolls

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    between runs. (2) In indenting, indentation lines are pressed into the blanks to allow the blanks to later be bent into boxes. The blanks from the previous cutting operation are divided and consolidated into batches whose starting quantity = 2,000 blanks. Indenting is performed at 4.5 minutes per 100 blanks. Time to change dies on the indentation machine = 30 min. (3) In printing, the indented blanks are printed with labels for a particular customer. The blanks from the previous indenting operation are divided and consolidated into batches whose starting quantity = 1,000 blanks. Printing cycle rate = 30 blanks per min. Between batches, changeover of the printing plates is required, which takes 20 minutes. In-process inventory is allowed to build up between machines 1 and 2, and between machines 2 and 3, so that the machines can operate independently as much as possible. Determine the maximum possible output of this factory during a 40-hour week, in completed blanks per week (completed blanks have been cut, indented, and printed)? Assume steady state operation, not startup. Solution : Determine maximum production rate R p for each of the three operations: Operation (1) - cutting: T b = 35 min. + 4000 pc × 0.03 min/pc = 35 + 120 = 155 min/batch R p = 4000 pc/batch/(155 min/batch) =25.806 pc/min = 1548.4 pc/hr Operation (2) - indenting: T b = 30 min. + 2000 pc(4.5/100 min./pc) = 30 + 90 = 120 min/batch R p = 2000 pc/batch/(120 min/batch) = 16.667 pc/min = 1000 pc/hr Operation (3) - printing: T b = 20 min. + 1000 pc/(30 pc/min) = 20 + 33.33 = 53.33 min/batch R p = 1000 pc/(53.33 min/batch) = 18.751 = 1125 pc/hr Bottleneck process is operation (2). Weekly output = (40 hr/wk)(1000 pc/hr) = 40,000 blanks/wk 3.12 A machine shop has ten machines in its automatic lathe section. Setup time on an automatic lathe is 5 hours. Batch size is 100 for parts processed through the section. Cycle time per part is 9.0 minutes. Under shop rules, an operator can be assigned to run one or two machines. Accordingly, there are five operators in the section for the ten lathes. In addition to the lathe operators, there are two setup workers who only perform machine setups. These setup workers are busy the full shift. The section runs one 8-hour shift per day, 5 days per week. Scrap losses are negligible and availability = 100%. The production control manager claims that the capacity of the section should be 2000 parts per week. However, the actual output is only 1600 units per week. What is the problem? Recommend a solution. Solution : Hours/week = 40 hr T p = (5 + 100 × 9/60)/100 = 20 hr/100 pc = 0.20 hr/pc, R p = 5 pc/hr Production capacity of automatic lathe section: PC = (40 hr/wk)(5 pc/hr)(10 machines) = 2000 pc/wk But the actual output = 1600 pc/wk. Why? Consider the workload of the setup workers. Number of setups per week = (2 setup workers)(40 hr/wk)/(5 hr/setup) = 16 setups/wk = 16 batches/wk. At 100 pc/batch, total pc/week = 16 × 100 = 1600 pc/week The problem is that the setup workers represent a bottleneck. To solve the problem, hire one more setup worker. With three setup workers, number of batches per week = 3(40)/5 = 24 batches/wk. At 100 pc/batch, total output could be 24 × 100 = 2400 pc/week Comments : (1) There are 10 machines but with 2 setup workers each setting up during the 40-hr week, this means that only 8 machines are producing parts at any given moment. Thus two of the five machine operators only have one machine to tend at any given moment. To

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    maximize worker utilization, each machine operator should be tending two machines at all times. An ideal situation would be to have 12 machines, in which two machines are being set up at any given time, and 10 machines are producing, so that there are two machines for each of the five machine operators. (2) In order to increase output and balance the workloads between the machine operators and setup workers, the shop should consider purchasing two additional automatic lathes. Three setup workers would be capable of (3)(40 hr/wk)/(5 hr/setup) = 24 setups/wk. Each batch takes 20 hr, so each machine can complete 2 batches/wk. Total batches with 12 machines is 24/wk or 24 setups/wk. Bottleneck Model 3.13 (A) A job shop has three workstations, each with multiple servers. It operates 80 hours per week and produces four different product styles: A, B, C, and D. Part-mix ratios, batch quantities, part routings, machines, servers, and production times are given in the table below for the four product styles made in the shop. Operation sequence for product style is in the order of station number. Determine (a) which station is the bottleneck, (b) total weekly output of all four products, (c) weekly output of each of the four product styles, (d) utilization of each server at each station, (e) average utilization of the machine shop. Setup times are accounted for in the T p values. Part style ( j ) A B C D Part mix p j 0.24 0.18 0.31 0.27 Batch quantities Q b 15 20 10 12 Stations ( i ) Servers s i T p A (hr) T p B (hr) T p C (hr) T p D (hr) 1 3 0.55 0.40 0.38 0.42 2 4 0.62 0.75 0.52 0.38 3 2 0.38 0.28 0.45 0.24 Solution : (a) Computations were performed on a spreadsheet calculator with the results shown in the table below. Workloads are calculated by Equation (3.20). For example, WL 1 = 0.24(0.55) + 0.18(0.40) + 0.31(0.38) + 0.27(0.42) = 0.435 hr/pc. The bottleneck station is identified in bold characters: station 3 with two servers. Part style ( j ) A B C D Part mix p j 0.24 0.18 0.31 0.27 Batch quantity Q b 15 20 10 12 Stations ( i ) Servers s i T pi A (hr) T pi B (hr) T pi C (hr) T pi D (hr) WL i (hr) WL i /s (hr) R p * (pc/hr) U server 1 3 0.55 0.40 0.38 0.42 0.435 0.145 0.839 2 4 0.62 0.75 0.52 0.38 0.548 0.137 0.792 3 2 0.38 0.28 0.45 0.24 0.346 0.173 5.78 1.0 (b) Total production rate of all five parts = 5.78 pc/hr Weekly output = 5.78(80) = 462 pc/wk (c) Production rates of each part style: R p A = 1.39 pc/hr, R p B = 1.04 pc/hr, R p C = 1.79 pc/hr, and R p D = 1.56 pc/hr Weekly outputs for A = 1.39(80) = 111 pc , B = 82 pc , C = 143 pc , and D = 125 pc

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