Making. MRP work. Vendors must address long-standing problems with capacity planning, lot sizes and lead-times

Size: px
Start display at page:

Download "Making. MRP work. Vendors must address long-standing problems with capacity planning, lot sizes and lead-times"

Transcription

1 Making MRP work Vendors must address long-standing problems with capacity planning, lot sizes and lead-times By Gregory W. Diehl & Aaron J. Armstrong November

2 making mrp work Materials requirements planning (MRP 1), developed in the 1960s and 1970s, offered an important breakthrough for shop floor managers by linking production plans for finished goods with the supply of the component parts required to achieve those plans. The idea was to ensure that enough of the correct components were on hand to build assemblies, such as cars, before the parts were needed. Recognizing that labor and machines were key requirements, manufacturing resource planning (MRP 2) extended the idea of production requirements to include the number of labor-hours and machine-hours needed at each work center in a plant. However, as is so often the case, providing insight and structure to address one set of issues often reveals deeper and more complex challenges that managers must address. Initial stopping point Such is the case with MRP 2 and the fundamental questions of capacity planning, lot sizing and their implications for lead-times, often assumed to be static in MRP 2 systems regardless of scheduled labor or machine utilization. These systems had no mathematical foundation to describe the numerical relationship between capacity, lot sizes and lead-times. Thus, MRP 2 and enterprise resource planning (ERP) systems cannot account for how these three measures interact. MRP 2 systems cannot estimate waiting times or provide a coherent and satisfactory method for dynamically generating lot sizes. Contrast this with MRP 1, which has a mathematical foundation that calculates the number of components an assembly needs. Even scrap in production and in assembly is included as a more complex calculation. MRP 2 systems turned the responsibility of estimating waiting times over to the user as an input rather than managing or 36 Industrial Engineer even calculating this critically important output. MRP 2 provided many different ways to set lot sizes, the most sophisticated one being economic order quantity. EOQ is used in retail situations to trade off order costs with stock carrying costs. In manufacturing, however, one is trading off the setup costs with the work-inprocess (WIP) carrying cost. Several problems are inherent in using EOQ in manufacturing because it ignores some fundamental issues, such as finite capacity. As a result, the lot sizes it generates can have a negative impact on waiting times. Furthermore, other common lot sizing methods have even more failings. Critical information ignored The internal portion of the manufacturing critical-path time (MCT) is the amount of time needed to get a part from raw materials to finished goods. MCT determines how far in advance customers must call to get reorders. Even if you have a warehouse and are making to stock, the problem remains. It s just buried within your internal operations, and this delay emerges when your warehouse calls for a reorder. If the quoted MCT is too short, you have late starts and late deliveries. If it is too long, you have too much WIP on the floor, too much capital tied up in WIP, and too much material and money in finished goods. If your company decides via MRP/ERP when to start production to meet demands, it most likely is ignoring the true MCT that determines when production should start. The lot size is the number of pieces made in one run before a machine is changed over or set up to run a different part. In all production situations, someone or something will have to make this decision. If the lot size is set too small, the number of setups required will be so large that eventually all of the machine s available time will be used up, over-utilizing the machine. Once this happens, the machine will become a bottleneck and build up a backlog. This will require overtime or transferring some work to other machines. If lot sizes are too large, MCT will grow longer needlessly, and too much inventory will build up in all the parts produced by the machine as everything will have to wait for the expanded lot size to be completed. Lot size is one of the most powerful tools you can use to reduce MCT and become leaner and more responsive to customer demand. The lot size also affects MCTs indirectly by changing machine utilization and the coordination of work between different work centers. It is an easy operational parameter to change, far easier than changing setup and run times or capacity. However, it is an extremely difficult number to optimize using MRP/ ERP or other traditional manufacturing practices. The fact that no current MRP/ ERP system in use today can manage lot sizes in a dynamic and coordinated way is a significant deficit in their functionality, which hampers the profitability of their customers. Why this must be fixed Scrapping the MRP system still leaves the basic problems of deciding lot sizes and lead-times. If you manufacture, you decide the amount (the lot size) and the time to start (due date minus the MCT). If you eat, you decide the amount and the time to start. No matter what you decide to manufacture (or eat), decisions must and will be made. After doing lean, theory of constraints, Six Sigma, just in time, or any other buzzword-based methodology, and after any kaizen events, consultants, setup reductions and engineering tuneups, you ultimately return to MRP and are hamstrung by its inability to manage lot sizes and MCTs effectively. Although some methodologies can provide rough

3 directions, none can provide actual numbers to use for these parameters as inputs for MRP. Take the short question, To get a 25 percent cut in MCTs, how much overtime must I add, and how much should I change my lot sizes? No current MRP system or add-on will provide an accurate answer. Advanced production scheduling (APS) won t provide an accurate answer either, as will be detailed later. It is precisely after using lean, theory of constraints and whatever else that you are most in need of a change in lot sizes and MCT estimates. You have done the hard work of improving the manufactur- ing system, but you need new lot sizes and MCTs to realize the value of these changes. MRP woes A simple Internet search of problems with MRP reveals that the second most common issue is MCT, just behind datarelated issues. A reasonably experienced MRP user usually can deal with the first problem sufficiently, but even then there remains the underlying issue that a user cannot hope to address directly. One Wikipedia writer sees the issue with as much clarity as possible: Another major problem with MRP systems is the requirement that the user specify how long it will take a factory to make a product from its component parts (assuming they are all available). Additionally, the system design also assumes that this lead-time in manufacturing will be the same each time the item is made, without regard to quantity being made, or other items being made simultaneously in the factory. This is not merely operator error; it is a systemic and structural problem with the current MRP framework. Setting MCTs is what defines MRP 2. If the MRP system does not suggest MCTs, it is simply MRP 1 with holes or places where a user enters November

4 making mrp work the MCT estimates. MRP problems include a number of distinct issues that must be addressed if MRP is going to work the way it needs to. For example, users cannot presume that capacity is infinite. For shipping via UPS or FedEx, you can assume infinite shipping capacity. Their shipping capacity is their problem, not yours. Your problem is managing shop capacity. You can assume that your shop has infinite capacity if pigs can fly and mules can foal. It is better to work in the real world. The second issue is that any decent foreperson with simple observation skills knows the following three observations to be true. First, the use of the bottleneck affects the estimated waiting times. In addition, using the bottleneck should affect the choice of lot sizes. Finally, the lot size of one part affects the waiting times of other parts. None of these facts of life are considered adequately within current MRP systems. They all assume that utilization, lot sizes and waiting times are independent of each other, and you can change one without affecting the others. This is exactly where MRP needs to start working and not go AWOL. It needs to tell the user what a change in utilization or lot sizes does to lead-times. The third issue is a set of systemwide concerns. Do the lot size recommendations even guarantee a feasible schedule? For example, is utilization less than 100 percent? How do you calculate waiting times? Asking the user for an estimated waiting time at a workstation is no different than a consultant asking for your watch and telling you that in two hours it will be 3 o clock. In Principles of Operations Research, published in 1975, Harvey Wagner states that EOQ should not be used for production lot sizing because there is no finite capacity constraint within EOQ and that, within EOQ, the lot size choice for one part does not affect the waiting time of any part, not even for the part we are choosing the lot size for. Mean time to repair Do you know what the mean time to repair (MTTR) is for your machines? Does your MRP ask for this information? Unless repair times are tiny, they will have a big impact on lead-times since the repair time determines the size of the backlog that develops during an equipment failure. We now turn aside for a moment to see the effects of MTTR and the backlog. We also will see how the equipment failure and repair can be used as an analogy for other phenomena within manufacturing systems. Down time will affect the utilization of an equipment group. The mean time to repair also is a critical number for computing MCT and WIP. The MTTR determines the size of the backlog that builds at the machine, which directly affects the WIP and MCT. Estimating these numbers is quite easy. Now suppose a user specifies any two of three values: mean time to failure (MTTF), mean time to repair and percentage down time. Any two of these numbers determines the third, but they do not affect setup and run time utilization. The effect on lead-time depends on MTTR and the utilization. A machine with low utilization will not generate much backlog, whereas a machine with high utilization will have a bigger backlog. The length of the breakdown or MTTR determines the size of the backlog that will develop. Utilization obviously determines how long it will take to clear the backlog. This illustrates why MTTR is so important. Consider an office with 10 percent down time. Losing six minutes on the hour every hour isn t too hard to handle. Missing a day every other week is a bit trickier, but losing a whole week every two and a half months puts a wrench in the works. Scheduling the lost week would make the problem simpler, but you can t schedule when equipment will fail. In a busy office a lot of work will not get done, creating backups during down time. Resolving the backlog requires a lot of rescheduling, which can be difficult, particularly if the length of the down time is highly variable. Calculating these efforts Down time percentage alone does not tell us how much backlog will develop, how long it will take to dissipate and how much this adds to the average WIP and lead-time. MTTR and the utilization determine these numbers. A simple approach can calculate these effects. If U equals utilization, then U multiplied by MTTR is the amount of backlog generated by a failure, which determines the number of hours of extra work at the end of the equipment repair. For example, 80 percent utilization (U) multiplied by a 10-hour MTTR creates an eight-hour backlog during 10 hours of down time (0.8 x 10 = 8). In addition, 1-U tells us the rate at which the backlog is removed. So a machine with 75 percent utilization removed one-fourth of an hour of backlog per one hour of clock time ( = 0.25). Inverting 1-U calculates the time needed to clear the backlog. A machine with a 75 percent utilization clears onefourth of an hour of backlog per hour (1/ (1-0.75) = 1/(0.25) = 4). This machine, once repaired, will take four hours of clock time to clear one hour of backlog. Putting it all together, MTTR x U/ (1-U) equals the number of hours needed to clear the backlog from the equipment failure. Reasonable assumptions in this analysis include that work arrives at the same rate whether the equipment is running or not and that the level of backlog at a 38 Industrial Engineer

5 wip with equipment failures Figure 1. This chart shows WIP backlog caused by equipment failures for different mean time to repair (MTTR) values. The percentage down time is 10 percent in all cases. WIP + backlog machine does not affect repair time. The third assumption is that the machine runs at the same speed regardless of the backlog s size. The analysis looks only at the average arrival of work and the average rate at which the backlog is cleared. The equation above and Figure 1 show how critical MTTR is. Figure 1 presents results from three situations where the only difference is MTTR. The MTTR values are one, three and 10 hours, with the same equipment utilization (80 percent) and down time percentage (10 percent). The average extra WIP or backlog is 12, three and one respectively. There is a matching lead-time effect as well. The MTTR determines the size of the initial backlog, and the slack or idle time determines the rate at which the backlog is worked off. In Figure 1, the green peaks stacked on top of each other create a yellow peak, while the yellow peaks stacked on top of each other equal the red peak. At their best, current MRP systems handle equipment failures by subtracting Time MTTR 10 MTTR 3 MTTR 1 Baseline WIP down time from available hours. Taking the percentage down time off the top assumes that repairs are frequent but short. You just expand the time to set up and run a lot. But this assumes that a long down time never occurs, and the random large backlog causes the lead-time problems. Failure to admit a possible problem is a failure to plan, which often turns into a plan to fail. If an APS ignores equipment failures, the entire red, yellow and green areas in Figure 1 will be ignored. If the APS includes a downtime set-aside, it assumes that the MTTR is small, with a worst-case scenario far better than the green area. But reality may be closer to the yellow or red areas in Figure 1. This problem often is addressed by scheduling equipment failures. Alas, that will happen only when you pick up a guinea pig by its tail. Note that guinea pigs don t have tails. This MTTR analysis can be used as an analogy to understand another issue. Viewed from a different perspective, a failure is just another lot arrival. The MTTR represents the setup and run time erp necessities Although many manufacturers complain about their ERP systems, they can be indispensable for planning production. Mfrtech.com has a few tips to help you decide on your next ERP purchase. Platform: While important, don t base your selection on platform alone because high-caliber functionality might compensate for the platform difference. Technology: The vendor should be on the leading edge to keep your system up to date. Number of vendors: Preferably, one vendor will design, develop, supply and support the package. Multiple vendors could cause system incompatibilities. Product demonstration: Take charge and try the product. Don t be afraid to enter a specific bill of material or other data to see how the system reacts. Buzz words: Don t focus on catch phrases. Implementation time: Time is money. Check estimates with previous customers. Customer referrals: A software vendor that can offer a variety of customer referrals is more likely to have many happier customers than those who cannot. Customer retention: Anything less than 80 percent should raise a flag to ask a question. Understand yourself: While it is always good to think where you want to be in five or more years, ensure that the system can handle where you are now. November

6 making mrp work probable success Figure 2. This probability of setup plus run time for a lot at a work center shows a realistic view of the time needed to complete manufacturing a lot. Probability for a lot instead of the down time. A larger lot size requires fewer lots to arrive, but each lot creates a bigger backlog of work. Increasing the lot size changes us from green to yellow to red areas in Figure 1. The figure simply displays the effect the lot size of one part has on the waiting time and WIP level of the other parts. Or stating it most clearly, the lot size of one part affects the waiting time of all the other parts. Current MRP/ERP software fails this basic reality test because they all assume that the lot size of one part has no effect on any other part s waiting time. Solution requirements Next, specify what a solution to the problem of estimating lead-times and setting lot sizes requires. First, it must include finite capacity, discussed above, and second, it must allow for random events. Better scheduling tools (APS, for example) will not work because they ignore the fundamental problem of random events (i.e., life happening). Although life would be easier to control without random events, it is better not to pretend they don t exist. As it turns out, including random events allows a solution to most of the problems outlined above. Adding random times for arrivals and times for lots let us determine how to change lot sizes as well as estimates of waiting times as utilization changes. Time Figure 2 shows a more realistic view of the time needed to complete a lot. The spread or width to the bell-shaped curve is added around the average or mean value. The figure displays the probability distribution for the time needed to complete a lot (i.e., setup time + run time per piece x lot size). The X-axis is the time, and the Y-axis is the probability that the X value is the actual time. You can see the standard bell-shaped curve with a mean in the middle and the sides spread out. The amount of spread is the standard deviation, or the plus-orminus term. If the time is assumed to be always and exactly the mean, the sides of the bell are collapsed into the mean, and it has a standard deviation of zero, which is unrealistic. The assumption of APS that the standard deviation is zero denies the second law of thermodynamics the existence of entropy. Including randomness in the analysis actually makes the mathematics easier and more accurate. The eventual solution should be extendible to include other factors such as equipment failures and labor sharing issues (i.e., three people running five machines). The solution should be understandable by the average industrial engineer. It must connect demand, capacity, lot sizes, setup and run times to utilization, WIP, and lead-time estimates. It must match real behavior so that a decrease in utilization at a critical machine is reflected by a decrease in the waiting time at that machine. It s not a myth This may sound like a search for the Holy Grail. But the requirements and problems with MRP can and have been addressed. The appropriate mathematics has been known for more than 100 years. For more than 30 years industrial engineering professors have been using it in the analysis of manufacturing systems. Software has been available in the marketplace for about 25 years, but it has not been widely adopted. The most important reason, as far as can be seen, is the lack of a tight connection to MRP/ERP systems. The issues with MRP regarding leadtimes and lot sizing only can be solved by MRP vendors, not MRP users. And the solutions have been available to MRP companies for years. Making a wider audience aware of the problems and limitations of current MRP software, along with the fact that solutions are available to vendors, could have a salutary effect. But this will happen only if the reader completes the circle. When users ask or demand better solutions, the MRP vendors will add them to the products they sell. d Since earning his Ph.D. at Harvard University, Gregory W. Diehl has spent his career consulting about the performance of manufacturing systems. He has designed and built software for consultants and analysts to use in the field of dynamics of manufacturing systems. Aaron J. Armstrong is an assistant professor of industrial engineering at the Milwaukee School of Engineering. He is a former supplier development engineer and engineering manager with John Deere, where he worked in supply chain optimization and the improvement of supplier manufacturing operations. 40 Industrial Engineer

Planning. Dr. Richard Jerz rjerz.com

Planning. Dr. Richard Jerz rjerz.com Planning Dr. Richard Jerz 1 Planning Horizon Aggregate planning: Intermediate range capacity planning, usually covering 2 to 12 months. Long range Short range Intermediate range Now 2 months 1 Year 2 Stages

More information

Planning. Planning Horizon. Stages of Planning. Dr. Richard Jerz

Planning. Planning Horizon. Stages of Planning. Dr. Richard Jerz Planning Dr. Richard Jerz 1 Planning Horizon Aggregate planning: Intermediate range capacity planning, usually covering 2 to 12 months. Long range Short range Intermediate range Now 2 months 1 Year 2 Stages

More information

Infor CloudSuite Industrial Whatever It Takes - Advanced Planning & Scheduling for Today s Manufacturer

Infor CloudSuite Industrial Whatever It Takes - Advanced Planning & Scheduling for Today s Manufacturer Infor CloudSuite Industrial Whatever It Takes - Advanced Planning & Scheduling for Today s Manufacturer May 2017 CloudSuite Industrial Where Did APS Come From? APS grew out of the convergence of two movements.

More information

Drum Buffer-Rope. Skorkovský. Based on : R. Holt, Ph.D., PE

Drum Buffer-Rope. Skorkovský. Based on : R. Holt, Ph.D., PE Drum Buffer-Rope Skorkovský Based on : R. Holt, Ph.D., PE Traditional Approach: Divide and Conquer Division of Labor breaks down linkages complex systems into manageable chunks. Which is harder to manage?

More information

IT 470a Six Sigma Chapter X

IT 470a Six Sigma Chapter X Chapter X Lean Enterprise IT 470a Six Sigma Chapter X Definitions Raw Materials component items purchased and received from suppliers WIP work in process, items that are in production on the factory floor

More information

Operations and Supply Chain Management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology, Madras

Operations and Supply Chain Management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology, Madras Operations and Supply Chain Management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology, Madras Module - 01 Lecture - 08 Aggregate Planning, Quadratic Model, Demand and

More information

Operations and Supply Chain Management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology, Madras

Operations and Supply Chain Management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology, Madras Operations and Supply Chain Management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology, Madras Lecture - 24 Sequencing and Scheduling - Assumptions, Objectives and Shop

More information

Drum Buffer-Rope. Based on : R. Holt, Ph.D., PE

Drum Buffer-Rope. Based on : R. Holt, Ph.D., PE Drum Buffer-Rope Based on : R. Holt, Ph.D., PE Traditional Approach: Divide and Conquer Division of Labor breaks down linkages complex systems into manageable chunks. Which is harder to manage? Left or

More information

Managerial Economics Prof. Trupti Mishra S.J.M School of Management Indian Institute of Technology, Bombay. Lecture - 23 Theory of Cost (Contd )

Managerial Economics Prof. Trupti Mishra S.J.M School of Management Indian Institute of Technology, Bombay. Lecture - 23 Theory of Cost (Contd ) Managerial Economics Prof. Trupti Mishra S.J.M School of Management Indian Institute of Technology, Bombay Lecture - 23 Theory of Cost (Contd ) In today s session we will continue our discussion on the

More information

JUST IN TIME. Manuel Rincón, M.Sc. October 22nd, 2004

JUST IN TIME. Manuel Rincón, M.Sc. October 22nd, 2004 JUST IN TIME Manuel Rincón, M.Sc. October 22nd, 2004 Lecture Outline 1. Just-in-Time Philosophy 2. Suppliers Goals of JIT Partnerships Concerns of Suppliers 3. JIT Layout Distance Reduction Increased Flexibility

More information

How Real-time Dynamic Scheduling Can Change the Game:

How Real-time Dynamic Scheduling Can Change the Game: Iyno Advisors How Real-time Dynamic Scheduling Can Change the Game: New Software Approach to Achieving Stable Success in High-Change High-Mix Discrete Manufacturing By Julie Fraser Principal, Iyno Advisors

More information

Eliminating waste isn t enough; you have to reduce inputs to save money. lean accounting. By Reginald Tomas Yu-Lee.

Eliminating waste isn t enough; you have to reduce inputs to save money. lean accounting. By Reginald Tomas Yu-Lee. Eliminating waste isn t enough; you have to reduce inputs to save money Proper lean accounting By Reginald Tomas Yu-Lee October 2011 39 proper lean accounting rom its inception, lean has been about cost

More information

Operations and Supply Chain Management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology, Madras

Operations and Supply Chain Management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology, Madras Operations and Supply Chain Management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology, Madras Lecture - 23 Safety Stock Reduction Delayed Product Differentiation, Substitution

More information

Optimizing Inplant Supply Chain in Steel Plants by Integrating Lean Manufacturing and Theory of Constrains through Dynamic Simulation

Optimizing Inplant Supply Chain in Steel Plants by Integrating Lean Manufacturing and Theory of Constrains through Dynamic Simulation Optimizing Inplant Supply Chain in Steel Plants by Integrating Lean Manufacturing and Theory of Constrains through Dynamic Simulation Atanu Mukherjee, President, Dastur Business and Technology Consulting,

More information

The Five Focusing Steps

The Five Focusing Steps Back to Basic TOC The Five Focusing Steps Presented by: Eli Schragenheim Blog: www.elischragenheim.com elischragenheim@gmail.com Date: January 27, 2018 The power of having an insight Having an insight

More information

Online Student Guide Total Productive Maintenance

Online Student Guide Total Productive Maintenance Online Student Guide Total Productive Maintenance OpusWorks 2016, All Rights Reserved 1 Table of Contents LEARNING OBJECTIVES... 2 INTRODUCTION... 2 MEETING CUSTOMER DEMAND... 2 UNPLANNED DOWNTIME... 3

More information

Demand Driven Fulfillment Identifying Potential Benefits

Demand Driven Fulfillment Identifying Potential Benefits VASFT022 VARGO White Paper Page 1 VASFT022 Demand Driven Fulfillment Identifying Potential Benefits VASFT022 VARGO White Paper Page 2 Demand Driven Fulfillment is a term describing the execution of the

More information

Saving an Extended Enterprise: A CEO s Experience

Saving an Extended Enterprise: A CEO s Experience Saving an Extended Enterprise: A CEO s Experience by Mathew Lovejoy President Acme Alliance Northbrook, Illinois Acme Alliance is a job shop aluminum die-casting company with a factory and headquarters

More information

Capability White Paper Prescriptive Maintenance

Capability White Paper Prescriptive Maintenance Capability White Paper Prescriptive Maintenance How will it make managing your assets better, faster, smarter, more comprehensive and affordable? Introduction This is an overview for those folks who do

More information

Outline. Push-Pull Systems Global Company Profile: Toyota Motor Corporation Just-in-Time, the Toyota Production System, and Lean Operations

Outline. Push-Pull Systems Global Company Profile: Toyota Motor Corporation Just-in-Time, the Toyota Production System, and Lean Operations JIT and Lean Operations Outline Push-Pull Systems Global Company Profile: Toyota Motor Corporation Just-in-Time, the Toyota Production System, and Lean Operations Eliminate Waste Remove Variability Improve

More information

Inventory and Variability

Inventory and Variability Inventory and Variability 1/29 Copyright c 21 Stanley B. Gershwin. All rights reserved. Inventory and Variability Stanley B. Gershwin gershwin@mit.edu http://web.mit.edu/manuf-sys Massachusetts Institute

More information

Operation and supply chain management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology Madras

Operation and supply chain management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology Madras Operation and supply chain management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology Madras Lecture - 37 Transportation and Distribution Models In this lecture, we

More information

use lean lot sizing to prepare for economic recovery

use lean lot sizing to prepare for economic recovery ANtiCiPAtiNg the reemergence of demand use lean lot sizing to prepare for economic recovery By Steve CiMorelli, CfPiM Over the past 12 to 18 months, much has been written about manufacturers cutting inventories

More information

Think ROI, Not Cost When Evaluating ERP Software

Think ROI, Not Cost When Evaluating ERP Software Think ROI, Not Cost When Evaluating ERP Software BY ADAM GRABOWSKI DIRECTOR, MARKETING AND COMMUNICATIONS We simplify your manufacturing. When considering Enterprise Resource Planning (ERP) software for

More information

PRODUCTION ACTIVITY CONTROL (PAC)

PRODUCTION ACTIVITY CONTROL (PAC) PRODUCTION ACTIVITY CONTROL (PAC) Concerns execution of material plans Contains shop floor control (SFC), and vendor scheduling and follow-up SFC encompasses detailed scheduling and control of individual

More information

Flow and Pull Systems

Flow and Pull Systems Online Student Guide Flow and Pull Systems OpusWorks 2016, All Rights Reserved 1 Table of Contents LEARNING OBJECTIVES... 4 INTRODUCTION... 4 BENEFITS OF FLOW AND PULL... 5 CLEARING ROADBLOCKS... 5 APPROACH

More information

Drum-Buffer-Rope in PlanetTogether Galaxy

Drum-Buffer-Rope in PlanetTogether Galaxy Drum-Buffer-Rope in PlanetTogether Galaxy This document provides background on Theory of Constraints and Drum-Buffer-Rope scheduling. It describes how to assess whether the DBR approach is appropriate

More information

Cut Your PPC Campaigns Down To Size

Cut Your PPC Campaigns Down To Size Cut Your PPC Campaigns Down To Size What if you could learn to trim your PPC campaigns down to a more manageable and efficient size? While simultaneously raising your conversion rates? Well, guess what?

More information

Lecture 12. Introductory Production Control

Lecture 12. Introductory Production Control Lecture 12 Introductory Production Control 167 Where we ve come from: Models of Manufacturing Systems: Deterministic, Queuing, Simulation Key ideas: Some WIP useful for buffering stations, but More WIP

More information

Best practices in demand and inventory planning

Best practices in demand and inventory planning whitepaper Best practices in demand and inventory planning WHITEPAPER Best Practices in Demand and Inventory Planning 2 about In support of its present and future customers, Aptean sponsored this white

More information

OM (Fall 2016) Outline

OM (Fall 2016) Outline Lean Operations Outline Global Company Profile: Toyota Motor Corporation Lean Operations Lean and Just-in-Time Lean and the Toyota Production System Lean Organizations Lean in Services 2 Toyota Motor Corporation

More information

Best Practices in Demand and Inventory Planning

Best Practices in Demand and Inventory Planning W H I T E P A P E R Best Practices in Demand and Inventory Planning for Chemical Companies Executive Summary In support of its present and future customers, CDC Software sponsored this white paper to help

More information

FEATURES IN TRIMIT FURNITURE 2017

FEATURES IN TRIMIT FURNITURE 2017 FEATURES IN TRIMIT FURNITURE 2017 This document provides an overview of the most important features available in TRIMIT Furniture, as they are available in version 2017 of December 2016. The purpose of

More information

The 5 Reasons YOUR ERP SOFTWARE NEEDS TO PROVIDE A NESTING INTERFACE BY SILAS FULSOM, GLOBAL SHOP SOLUTIONS PRODUCT OWNER, R&D CUSTOM DEVELOPMENT TEAM

The 5 Reasons YOUR ERP SOFTWARE NEEDS TO PROVIDE A NESTING INTERFACE BY SILAS FULSOM, GLOBAL SHOP SOLUTIONS PRODUCT OWNER, R&D CUSTOM DEVELOPMENT TEAM The 5 Reasons YOUR ERP SOFTWARE NEEDS TO PROVIDE A NESTING INTERFACE BY SILAS FULSOM, GLOBAL SHOP SOLUTIONS PRODUCT OWNER, R&D CUSTOM DEVELOPMENT TEAM We simplify your manufacturing. In today s highly

More information

Case Study. Cosma International improves systems through collaboration with Solarsoft. Customer Spotlight.

Case Study. Cosma International improves systems through collaboration with Solarsoft.  Customer Spotlight. Case Study Cosma International improves systems through collaboration with Solarsoft Customer Spotlight Victor Manufacturing (Cosma) Tier-1 supplier of automotive assemblies A division of Magna International

More information

Managing stock levels: materials management and inventory control

Managing stock levels: materials management and inventory control 16 Managing stock levels: materials management and inventory control Prerequisites Objectives Introduction For part of this chapter you will find it useful to have some knowledge of the normal distribution

More information

ThermoFab and DBR: Manufacturing At Warp Speed. A White Paper Report

ThermoFab and DBR: Manufacturing At Warp Speed. A White Paper Report ThermoFab and DBR: Manufacturing At Warp Speed A White Paper Report June 2004 You probably know ThermoFab as a leading custom thermoforming provider of high-quality plastic enclosures for a wide range

More information

Chapter 8 Script. Welcome to Chapter 8, Are Your Curves Normal? Probability and Why It Counts.

Chapter 8 Script. Welcome to Chapter 8, Are Your Curves Normal? Probability and Why It Counts. Chapter 8 Script Slide 1 Are Your Curves Normal? Probability and Why It Counts Hi Jed Utsinger again. Welcome to Chapter 8, Are Your Curves Normal? Probability and Why It Counts. Now, I don t want any

More information

Reading Essentials and Study Guide

Reading Essentials and Study Guide Lesson 3 Cost, Revenue, and Profit Maximization ESSENTIAL QUESTION How do companies determine the most profitable way to operate? Reading HELPDESK Academic Vocabulary generates produces or brings into

More information

Metrics Madness. What Gets Measured Gets Managed? Examining the Gaps Between Managers Beliefs About Metrics and What Workers Actually Do

Metrics Madness. What Gets Measured Gets Managed? Examining the Gaps Between Managers Beliefs About Metrics and What Workers Actually Do Metrics Madness What Gets Measured Gets Managed? Examining the Gaps Between Managers Beliefs About Metrics and What Workers Actually Do Unpublished Research, 2007-2012 February 2018 bobemiliani www.bobemiliani.com

More information

Visual Planner. Production Planning and Scheduling Solution for Exact Macola Progression and ES

Visual Planner. Production Planning and Scheduling Solution for Exact Macola Progression and ES Visual Planner Production Planning and Scheduling Solution for Exact Macola Progression and ES Today s Business Challenges Keeping direct material costs down Difficulty accurately assessing capacity and

More information

Manufacturing Systems Management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology, Madras

Manufacturing Systems Management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology, Madras Manufacturing Systems Management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology, Madras Lecture - 28 Basic elements of JIT, Kanban systems In this lecture we see some

More information

A Diagnostic Approach to Scheduling

A Diagnostic Approach to Scheduling Harish C Bahl * Neelam Bahl California State University, Chico, CA, U.S.A. Several algorithms and methodologies have been proposed for a variety of environments. In this paper, we suggest a diagnostic

More information

Question 2: How do we make decisions about inventory?

Question 2: How do we make decisions about inventory? uestion : How do we make decisions about inventory? Most businesses keep a stock of goods on hand, called inventory, which they intend to sell or use to produce other goods. Companies with a predictable

More information

There are three options available for coping with variations in demand:

There are three options available for coping with variations in demand: Module 3E10 Operations management for Engineers - Crib 1 (a) Define the theoretical capacity of a manufacturing line. Explain why the actual capacity of a manufacturing line is often different from its

More information

Planning. Planning Horizon. Stages of Planning. Dr. Richard Jerz

Planning. Planning Horizon. Stages of Planning. Dr. Richard Jerz Planning Dr. Richard Jerz 1 Planning Horizon Aggregate planning: Intermediate-range capacity planning, usually covering 2 to 12 months. Long range Short range Intermediate range Now 2 months 1 Year 2 Stages

More information

By: Adrian Chu, Department of Industrial & Systems Engineering, University of Washington, Seattle, Washington November 12, 2009.

By: Adrian Chu, Department of Industrial & Systems Engineering, University of Washington, Seattle, Washington November 12, 2009. OPT Report By: Adrian Chu, Department of Industrial & Systems Engineering, University of Washington, Seattle, Washington 98195. November 12, 2009. The Goal Every manufacturing company has one goal to make

More information

Advanced Manufacturing Laboratory Department of Industrial Engineering. Sharif University of Technology

Advanced Manufacturing Laboratory Department of Industrial Engineering. Sharif University of Technology Advanced Manufacturing Laboratory Department of Industrial Engineering Sharif University of Technology Session #16 Instructor Omid Fatahi Valilai, Ph.D. Industrial Engineering Department, Sharif University

More information

FEATURES IN TRIMIT FURNITURE BASED ON BUSINESS CENTRAL

FEATURES IN TRIMIT FURNITURE BASED ON BUSINESS CENTRAL FEATURES IN TRIMIT FURNITURE BASED ON BUSINESS CENTRAL Date: 14-12-2018 This document provides an overview of the most important features available in TRIMIT Furniture based on Microsoft Dynamics 365 Business

More information

MANUFACTURING RESOURCE PLANNING AND ENTERPRISE RESOURCE PLANNING SYSTEMS: AN OVERVIEW

MANUFACTURING RESOURCE PLANNING AND ENTERPRISE RESOURCE PLANNING SYSTEMS: AN OVERVIEW MANUFACTURING RESOURCE PLANNING AND ENTERPRISE RESOURCE PLANNING SYSTEMS: AN OVERVIEW Al-Naimi Assistant Professor Industrial Engineering Branch Department of Production Engineering and Metallurgy University

More information

Traditional ERP Systems Don t Fit Dairy.

Traditional ERP Systems Don t Fit Dairy. Traditional ERP Systems Don t Fit Dairy. The Retail Consolidation Effect Now more than ever, management wants to know what it actually costs to produce their product. It started in other industries and

More information

INVENTORY MANAGEMENT

INVENTORY MANAGEMENT INVENTORY MANAGEMENT Professor Robert Saltzman Operations Analysis Inventory What is it? Idle goods, waiting to be used or sold Inventory can take many forms: Finished Goods: Food, clothes, cars, electronics,

More information

GE Digital Executive Brief. Enhance your ability to produce the right goods in time to satisfy customer demand

GE Digital Executive Brief. Enhance your ability to produce the right goods in time to satisfy customer demand Enhance your ability to produce the right goods in time to satisfy customer demand Traditionally, successful production has relied heavily on skilled personnel. Experienced employees installed equipment

More information

Master Production Scheduling: from possible to profitable

Master Production Scheduling: from possible to profitable Management briefing Master Production Scheduling: from possible to profitable How to improve production planning in an increasingly complex manufacturing environment PRODUCTION PLANNING Planning for profitability

More information

ORION RESOURCES Solving the puzzle of smart hiring. Retained Search Quality A La Carte

ORION RESOURCES Solving the puzzle of smart hiring. Retained Search Quality A La Carte ORION RESOURCES info@orionresources.com 206-382- 8400 Solving the puzzle of smart hiring. At Orion, we think it s time for some much needed innovation in recruiting. Why? Because standard recruiting services

More information

The Structure of Costs in the

The Structure of Costs in the The Structure of s in the Short Run The Structure of s in the Short Run By: OpenStaxCollege The cost of producing a firm s output depends on how much labor and physical capital the firm uses. A list of

More information

5 Key Metrics Every Call Center Manager Should Master

5 Key Metrics Every Call Center Manager Should Master 5 Key Metrics Every Call Center Manager Should Master Why It Matters to have the Right Metrics as a Call Center Manager There are a lot of reasons that call center managers should keep working to find

More information

Lesson-9. Elasticity of Supply and Demand

Lesson-9. Elasticity of Supply and Demand Lesson-9 Elasticity of Supply and Demand Price Elasticity Businesses know that they face demand curves, but rarely do they know what these curves look like. Yet sometimes a business needs to have a good

More information

Lean Operations. PowerPoint slides by Jeff Heyl. Copyright 2017 Pearson Education, Inc.

Lean Operations. PowerPoint slides by Jeff Heyl. Copyright 2017 Pearson Education, Inc. Lean Operations 16 PowerPoint presentation to accompany Heizer, Render, Munson Operations Management, Twelfth Edition Principles of Operations Management, Tenth Edition PowerPoint slides by Jeff Heyl 16-1

More information

Learning Objectives. Scheduling. Learning Objectives

Learning Objectives. Scheduling. Learning Objectives Scheduling 16 Learning Objectives Explain what scheduling involves and the importance of good scheduling. Discuss scheduling needs in high-volume and intermediate-volume systems. Discuss scheduling needs

More information

Microsoft Dynamics GP. Manufacturing Core Functions

Microsoft Dynamics GP. Manufacturing Core Functions Microsoft Dynamics GP Manufacturing Core Functions Copyright Copyright 2010 Microsoft. All rights reserved. Limitation of liability This document is provided as-is. Information and views expressed in this

More information

Justifying Advanced Finite Capacity Planning and Scheduling

Justifying Advanced Finite Capacity Planning and Scheduling Justifying Advanced Finite Capacity Planning and Scheduling Charles J. Murgiano, CPIM WATERLOO MANUFACTURING SOFTWARE 1. Introduction How well your manufacturing company manages production on the shop

More information

THE IMPROVEMENTS TO PRESENT LOAD CURVE AND NETWORK CALCULATION

THE IMPROVEMENTS TO PRESENT LOAD CURVE AND NETWORK CALCULATION 1 THE IMPROVEMENTS TO PRESENT LOAD CURVE AND NETWORK CALCULATION Contents 1 Introduction... 2 2 Temperature effects on electricity consumption... 2 2.1 Data... 2 2.2 Preliminary estimation for delay of

More information

RFID Transformative Technology. A Radley Corporation White Paper

RFID Transformative Technology. A Radley Corporation White Paper RFID Transformative Technology A Radley Corporation White Paper Table of Contents CONTEXT... 5 THE HEAT IS ON: IoT & THE PRESSURE OF CHANGE... 5 THE BLACK SHEEP OF TECHNOLOGY: RFID MISCONCEPTIONS... 5

More information

Fifteen Undeniable Truths About Project Cost Estimates, or Why You Need an Independent Cost Estimate

Fifteen Undeniable Truths About Project Cost Estimates, or Why You Need an Independent Cost Estimate iparametrics, LLC Headquarters 2325 Lakeview Parkway, Suite 200 Alpharetta, GA 30009 Fifteen Undeniable Truths About Project Cost Estimates, or Why You Need an Independent Cost Estimate www.iparametrics.com

More information

Process design Push-pull boundary 35C03000 Process Analysis and Management Max Finne, Assistant Professor of Information and Service management

Process design Push-pull boundary 35C03000 Process Analysis and Management Max Finne, Assistant Professor of Information and Service management Process design Push-pull boundary 35C03000 Process Analysis and Management Max Finne, Assistant Professor of Information and Service management Arrangements for lectures 9 and 10 In class Studying outside

More information

Management of Inventory Systems Prof. Pradip Kumar Ray Department of Industrial and Systems Engineering Indian Institute of Technology, Kharagpur

Management of Inventory Systems Prof. Pradip Kumar Ray Department of Industrial and Systems Engineering Indian Institute of Technology, Kharagpur Management of Inventory Systems Prof. Pradip Kumar Ray Department of Industrial and Systems Engineering Indian Institute of Technology, Kharagpur Lecture - 41 Basics of Purchasing Management So, during

More information

What is ERP? Source: Wikipedia

What is ERP? Source: Wikipedia Brad Staats What is ERP? Enterprise resource planning (ERP) systems integrate internal and external management information across an entire organization. The purpose of ERP is to facilitate the flow of

More information

Descriptive Statistics Tutorial

Descriptive Statistics Tutorial Descriptive Statistics Tutorial Measures of central tendency Mean, Median, and Mode Statistics is an important aspect of most fields of science and toxicology is certainly no exception. The rationale behind

More information

Why Should You Invest in IQMS MES Tools: RealTime Production and Process Monitoring?

Why Should You Invest in IQMS MES Tools: RealTime Production and Process Monitoring? Why Should You Invest in MES Tools: RealTime Production and Process Monitoring? In manufacturing, your money is made on the shop floor. Real-time data is power in helping to identify and then proactively

More information

SteamDestroyer. The Ultimate Guide to Free Steam Games

SteamDestroyer. The Ultimate Guide to Free Steam Games SteamDestroyer The Ultimate Guide to Free Steam Games Table of Contents I. What you can expect II. Requirement III. General Method Overview Steam Gifts IV. General Method Overview - TF2 Keys V. Steam Keys

More information

Mechanical Engineering 101

Mechanical Engineering 101 Mechanical Engineering 101 University of California, Berkeley Lecture #10 1 Today s lecture Supply Chain Management (SCM) Variance acceleration Safety stock Raw materials factory wholesaler retailer customer

More information

THE COST OF INTERNAL VARIETY: A NON-LINEAR OPTIMIZATION MODEL

THE COST OF INTERNAL VARIETY: A NON-LINEAR OPTIMIZATION MODEL INTERNATIONAL DESIGN CONFERENCE - DESIGN 2006 Dubrovni - Croatia, May 5-8, 2006. THE COST OF INTERNAL VARIETY: A NON-LINEAR OPTIMIZATION MODEL T. Nowa and M. Chromnia eywords: design for variety, cost

More information

Reading Essentials and Study Guide

Reading Essentials and Study Guide Lesson 3 Using Economic Models ESSENTIAL QUESTION In what ways do people cope with the problem of scarcity? Reading HELPDESK Academic Vocabulary mechanism process or means by which something can be accomplished

More information

5.3 Supply Management within the MES

5.3 Supply Management within the MES Technical 6x9 / Manufacturing Execution Sytems (MES): Design, Planning, and Deployment / Meyer / 0-07-162383-3 / Chapter 5 Core Function Production Flow-Oriented Planning 85 Customer data (e.g., customer

More information

7 ways to improve your Production Planning using SAP Business One integration

7 ways to improve your Production Planning using SAP Business One integration 7 ways to improve your Production Planning using SAP Business One integration At the core of any business' success story, you will find sound planning. It goes without saying that planning is the most

More information

Why Should You Invest in IQMS MES Tools: RealTime Production and Process Monitoring?

Why Should You Invest in IQMS MES Tools: RealTime Production and Process Monitoring? Why Should You Invest in IQMS MES Tools: RealTime Production and Process Monitoring? In manufacturing, your money is made on the shop floor. Real-time data is power in helping to identify and then proactively

More information

Operations and Supply Chain Management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology, Madras

Operations and Supply Chain Management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology, Madras Operations and Supply Chain Management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology, Madras Lecture - 20 Disaggregation Time Varying Demand, Safety Stock ROL for

More information

2012 MPS Qualify Exam

2012 MPS Qualify Exam 2012 MPS Qualify Exam The examination will be four hours long. There will be eight questions in all. Students must select 7 out of 8 questions to answer. The exam is open book and open notes. The students

More information

Reading Essentials and Study Guide

Reading Essentials and Study Guide Lesson 3 Using Economic Models ESSENTIAL QUESTION In what ways do people cope with the problem of scarcity? Reading HELPDESK Academic Vocabulary mechanism process or means by which something can be accomplished

More information

Managerial Accounting Prof. Dr. Varadraj Bapat Department of School of Management Indian Institute of Technology, Bombay

Managerial Accounting Prof. Dr. Varadraj Bapat Department of School of Management Indian Institute of Technology, Bombay Managerial Accounting Prof. Dr. Varadraj Bapat Department of School of Management Indian Institute of Technology, Bombay Lecture - 31 Standard Costing - Material, Labor and Overhead Variances Dear students,

More information

Leading Automotive Supplier Accelerates Lean Operations with EnterpriseIQ

Leading Automotive Supplier Accelerates Lean Operations with EnterpriseIQ Leading Automotive Supplier Accelerates Lean Operations with EnterpriseIQ Automotive Suppliers Advantage Competing in an industry where a large number of suppliers vie for comparatively fewer customers,

More information

2 Production Planning

2 Production Planning 1 2 Production Planning "The wise man must be wise before, not after, the event." (Epicharmus, approx. 550 BC 460 BC) In this chapter I will present the basic planning approaches used in the SAP system.

More information

BREAK FREE FROM CELLS ESCAPE FROM SPREADSHEETS

BREAK FREE FROM CELLS ESCAPE FROM SPREADSHEETS 0845 345 3300 tellmemore@theaccessgroup.com www.theaccessgroup.com BREAK FREE FROM CELLS ESCAPE FROM SPREADSHEETS EXPERIENCE THE POWER OF ADVANCED PLANNING AND SCHEDULING SYSTEMS Executive summary Despite

More information

Chapter 27 Lean production

Chapter 27 Lean production Chapter 27 Lean production The idea of lean production encompasses theories of modern Japanese industrial management that are all designed to achieve the reduction and removal of waste within a business.

More information

Welcome to Principles of Lean Manufacturing

Welcome to Principles of Lean Manufacturing v3.0 The LE101 Experience Welcome to Principles of Lean Manufacturing 2018 Time Wise Solutions. All rights reserved. The Real World Your External Customers What do they expect from you? Where do you fall

More information

Dr. Eli Goldratt Unplugged

Dr. Eli Goldratt Unplugged Dr. Eli Goldratt Unplugged This is part one of SCDigest editor Dan Gilmore s interview with Dr. Eli Goldratt, father of the Theory of Constraints, and author of The Goal and several other influential books

More information

Innovative Marketing Ideas That Work

Innovative Marketing Ideas That Work INNOVATIVE MARKETING IDEAS THAT WORK Legal Disclaimer: While all attempts have been made to verify information provided in this publication, neither the Author nor the Publisher assumes any responsibility

More information

Lecture - 44 Supply Chain

Lecture - 44 Supply Chain Economics, Management and Entrepreneurship Prof. Pratap. K. J. Mohapatra Department of Industrial Engineering and Management Indian Institute of Technology Kharagpur Lecture - 44 Supply Chain Good morning.

More information

How I ve Built A $100K/Year Business Whilst Working Full Time

How I ve Built A $100K/Year Business Whilst Working Full Time How I ve Built A $100K/Year Business Whilst Working Full Time How a Trained Computer Engineer Works 2 Hours A Day and Makes 5X More Money Than He Earns In His Full Time Job! Hi, and welcome to another

More information

Production Scheduling

Production Scheduling PRODUCTION SCHEDULING Production Scheduling The Manufacturing Quandary Quandary is a state of perplexity or uncertainty over what to do in a difficult situation. Production scheduling is expected to satisfy

More information

Production Scheduling

Production Scheduling PRODUCTION SCHEDULING Production Scheduling The Manufacturing Quandary Quandary is a state of perplexity or uncertainty over what to do in a difficult situation. Production scheduling is expected to satisfy

More information

Order Fulfillment businesses

Order Fulfillment businesses Order Fulfillment businesses R Rakuten SUPER LOGISTICS Table of Contents Chapter 1 1 $ Dangers of DIY Order Fulfillment Chapter 2 1 $ Know Your Needs Chapter 3 1 $ Does It Make Sense to Outsource Chapter

More information

COST THEORY. I What costs matter? A Opportunity Costs

COST THEORY. I What costs matter? A Opportunity Costs COST THEORY Cost theory is related to production theory, they are often used together. However, here the question is how much to produce, as opposed to which inputs to use. That is, assume that we use

More information

Chapter 4. Models for Known Demand

Chapter 4. Models for Known Demand Chapter 4 Models for Known Demand Introduction EOQ analysis is based on a number of assumptions. In the next two chapters we describe some models where these assumptions are removed. This chapter keeps

More information

Make-to-Stock under Drum-Buffer-Rope and Buffer Management Methodology

Make-to-Stock under Drum-Buffer-Rope and Buffer Management Methodology I-09 Elyakim M. Schragenheim Make-to-Stock under Drum-Buffer-Rope and Buffer Management Methodology WHY MAKE-TO-STOCK? At least from the theory of constraints (TOC) perspective this is a valid question.

More information

A beginners guide to moving to an ERP

A beginners guide to moving to an ERP A beginners guide to moving to an ERP 2 Contents This paper is for companies considering an ERP and looking to justify the investment in new technology. This paper will provide methods to identify and

More information

Design Like a Pro. Boost Your Skills in HMI / SCADA Project Development. Part 3: Designing HMI / SCADA Projects That Deliver Results

Design Like a Pro. Boost Your Skills in HMI / SCADA Project Development. Part 3: Designing HMI / SCADA Projects That Deliver Results INDUCTIVE AUTOMATION DESIGN SERIES Design Like a Pro Boost Your Skills in HMI / SCADA Project Development Part 3: Designing HMI / SCADA Projects That Deliver Results The end of a project can be the most

More information

Operations and Supply Chain Management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology, Madras

Operations and Supply Chain Management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology, Madras Operations and Supply Chain Management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology, Madras Module - 1 Lecture - 7 Aggregate Planning, Dynamic Programming, Backordering

More information

MBF1413 Quantitative Methods

MBF1413 Quantitative Methods MBF1413 Quantitative Methods Prepared by Dr Khairul Anuar 1: Introduction to Quantitative Methods www.notes638.wordpress.com Assessment Two assignments Assignment 1 -individual 30% Assignment 2 -individual

More information