Ch 3 Manufacturing Models and Metrics Sections: Mathematical Models of Production Performance Manufacturing Costs 1

Why use metrics “A system of related measures that facilitates the quantification of some particular characteristic” To track performance in successive periods, Try out new technologies and systems to determine their merits, identify their problems, To compare alternative methods, and To make good decisions. 2

Production Concepts and Mathematical Models Production performance metrics: Production rate Rp for an individual processing or assembly operation is usually expressed as an hourly rate, that is, number of work units completed per hour (pc/hr). Cycle time Tc is defined as 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

Production Concepts and Mathematical Models Production performance metrics: Production capacity PC Utilization U Availability A Manufacturing lead time MLT Work-in-progress WIP 4

Operation Cycle Time Typical cycle time for a production operation: Tc = To + Th + Tth where Tc = cycle time (min/pc), To = processing time for the operation (min/pc), Th = handling time (min/pc) (e.g., loading and unloading the production machine), and Tth = tool handling time (min/pc) (e.g., time to change tools) 5

Production Rate (batch/job shop/flow) Batch production: Batch time Tb = Tsu + QTc where Tb= batch processing time (min) Tsu= setup time to prepare for the batch (min) Q= batch quantity (pc) Tc = cycle time per work unit (min/cycle) Average production time per work unit Tp Tp = Tb/Q= Tsu/Q + Tc Hourly production rate Rp = 60/Tp 6

Production Rate (batch/job shop/flow) Job shop production: For Q = 1, Tp = Tsu + Tc For Q > 1, Tp is determined as in batch production Mass production: Rp  Rc = 60/Tc since Tsu/Q  0 (Q is very large) where Rc = operation cycle rate of the machine (pc/hr) Tc = operation cycle time (min/pc) 7

Production Rate (batch/job shop/flow) Flow line production: Bottleneck station is the station with the largest operation time (with highest utilization) Tc = Tr + Max To Tc = cycle time of the production line (min/cycle) Tr = time to transfer work units between workstations each cycle (min/cycle) Max To = operation time at the bottleneck station (min/cycle) Rc = 60/Tc Rc = theoretical (ideal) production rate (cycles/hr) 8

Production Capacity “Max rate of output that a production facility is able to produce under a given set of assumed operating conditions” Operating conditions: Number of shifts per day Number of days per week Employment levels A work center is a manufacturing system in the plant typically consisting of one worker and one machine. 9

Production Capacity Plant capacity for facility in which parts are made in one operation (no = 1): PC = n Sw Hsh Rp where PC = weekly plant capacity (units/wk) n = number of work centers working in parallel Sw = number of shifts per week Hsh = hr/shift Rp = hourly production rate of each work center (output units/hr) 10

Production Capacity Plant capacity for facility in which parts require multiple operations (no > 1): PCw = where no = number of operations in the routing 11

Production Capacity This capacity model assumes that all n machines are producing 100% of the time and there are no bottleneck operations due to variations in process routings to inhibit smooth flow of work through the plant. There are some operations that are fully utilized while other operations occasionally stand idle waiting for work. That is, utilization varies. 12

Utilization and Availability Utilization: U = where Q = quantity actually produced, and PC = plant capacity “the amount of output of a production facility relative to its capacity” Utilization can be assessed for an entire plant, a single machine in the plant or any other productive resource. 13

Utilization and Availability Availability: A = where MTBF = mean time between failures, and MTTR = mean time to repair “a common measure for reliability of equipment” 14

Availability - MTBF and MTTR Defined 15

Manufacturing Lead Time where MLTj = manufacturing lead time for part or product j (min) Tsuji = setup time for operation i (min) Qj = quantity of part or product j in the batch being processed (pc) Tcji = operation cycle time for operation i (min/pc) Tnoji = non-operation time (handling, temporary storage, inspections) associated with operation i (min) “the total time required to process a given part/product through the plant including any lost time due to delays, time spent in storage, reliability problems, and so on” 16

Manufacturing Lead Time MLT = no (Tsu + QTc + Tno) where MLT = manufacturing lead time, no = number of operations, Tsu = setup time, Q = batch quantity, Tc = cycle time per part, and Tno = non-operation time (handling, temporary storage, inspections) 17

Manufacturing Lead Time Job shop when Q=1 MLT = no (Tsu + Tc + Tno) Mass production when Q MLT = no QTc Flow line MLT = no (Tr + Max To) = no Tc 18

Work-In-Process WIP = where WIP = work-in-process, pc; A = availability, U = utilization, PC = plant capacity, pc/wk; MLT = manufacturing lead time, wk; Sw = shifts per week, Hsh = hours per shift, hr/shift “quantity of parts or products currently located in the factory that are either being processed or between processing operations” “the inventory in the state of being transformed from raw material to finished product” 19

Costs of Manufacturing Operations Two major categories of manufacturing costs: Fixed costs - remain constant for any output level Variable costs - vary in proportion to production output level Adding fixed and variable costs TC = FC + VC(Q) where TC = total costs, FC = fixed costs (e.g., building, equipment, taxes), VC = variable costs (e.g., labor, materials, utilities), Q = output level. 20

Fixed and Variable Costs 21

Manufacturing Costs Alternative classification of manufacturing costs: Direct labor - wages and benefits paid to workers Materials - costs of raw materials Overhead - all of the other expenses associated with running the manufacturing firm Factory overhead consists of the costs of operating the factory other than direct labor and materials. Corporate overhead is the cost not related to the company’s manufacturing activities. 22

Typical Manufacturing Costs 23

Overhead Rates Factory overhead rate: FOHR = Corporate overhead rate: COHR = where FOHC=annual factory overhead costs ($/yr) COHC= annual corporate overhead costs ($/yr) DLC = annual direct labor costs ($/yr) 24

Example 3.5 Determine The factory overhead rate for each plant Expense category Plant 1 ($) Plant 2 ($) Headquarters ($) Totals ($) Direct labor 800,000 400,000 1,200,000 Materials 2,500,000 1,500,000 4,000,000 Factory expense 2,000,000 1,100,000 3,100,000 Corporate expense 7,200,000 Totals 5,300,000 3,000,000 15,500,000 Determine The factory overhead rate for each plant The corporate overhead rate 25

Cost of Equipment Usage Hourly cost of worker-machine system: Co = CL(1 + FOHRL) + Cm(1 + FOHRm) where Co = hourly rate, $/hr; CL = labor rate, $/hr; FOHRL = labor factory overhead rate, Cm = machine rate, $/hr; FOHRm = machine factory overhead rate 26

Averaging Procedures for Production Models 27

Averaging Procedures for Production Models 28

Averaging Procedures for Production Models 29

Averaging Procedures for Production Models 30

Averaging Procedures for Production Models 31

Averaging Procedures for Production Models 32

Averaging Procedures for Production Models 33

Averaging Procedures for Production Models 34