Mechanical Engineering - Design and Management of Production Systems

Completed notes of the course

Complete course

095844 (new 059189) Design and Management of Production Systems •Theoretical key concepts •Collection of formulas •Collection of algorithms and procedures •Tables Author: Fabio Santoro Teachers and assistants:•Prof. Angela Tumino •Prof. Enrico Cagno •Prof. Sergio Terzi• Dr. Arianna Seghezzi •Dr. Alessandra Neri Academic Year: 2022-23 Preface This document is a summary of the course ofDesign and Management of Production System (cod. 095844) held by Professor Angela Tumino and Dr. Arianna Seghezzi. Extra theoretical content is added based on the lectures of Professor Enrico Cagno and Dr. Alessandra Neri. Besides the theoretical content there is also a collection of explained formulas, algorithms and tables useful to solve practical exercises. This collection is based on the lectures and practices of Professors Tumino and Cagno, also extra material is taken by the same course held by Professor Sergio Terzi. This course is divided principally in three main parts: 1.Introduction and performance analysis of a production system: Classification and performance analysis 2.Design of a fabrication production system: Job-shop, Manufacturing Cells and Trans- fer Lines 3.Design of an assembly production system: theoretical classification and assembly lines design 4.Management of production system: Introduction, Demand Forecasting, Inventory Management, Aggregate Planning, On-Demand Management and Scheduling(Contents link)DMPS Page 3 Contents I Introduction and performance analysis of production system9 1 Classification of Production Systems. . . . . . . . . . . . . . . . . . . . . . . . .11 1.1 Production: basis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.1.1 Process representation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.1.2 Activity analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.2 Production classification. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.2.1 by DEMAND. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.2.2 by NATURE OF PROCESS. . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.2.3 by METHOD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2 Performance Measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15 2.1 Performance Measurements System. . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2 Quality. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.3 Service. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.4 Flexibility. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.5 Productivity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.5.1 Production Performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.5.1.1 Traditional method. . . . . . . . . . . . . . . . . . . . . . . . . 18 2.5.1.2 OEE: Overall Equipment Effectiveness. . . . . . . . . . . . . . . 19 2.5.1.3 Production Rate. . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.5.1.4 Production Capacity. . . . . . . . . . . . . . . . . . . . . . . . . 21 2.5.2 Warehouse performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.5.2.1 Traditional metric. . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.5.2.2 ABC-ABC analysis. . . . . . . . . . . . . . . . . . . . . . . . . 22 II Design - Fabrication Systems23 3 Job-shops. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25 3.1 General description. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.2 Strengths. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.3 Weaknesses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.4 Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.4.1 Workload sizing approach: procedure. . . . . . . . . . . . . . . . . . . . . 26 4 Manufacturing Cells and Group Technology. . . . . . . . . . . . . . . . . . . .31 4.1 General description. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.2 Strengths. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.3 Weaknesses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 4.4 Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 4.5 Group Technology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.5.1 product classification. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33(Contents link)DMPS Page 5 CONTENTS 4.5.2 cell design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.5.2.1 ROC: Rank Order Clustering. . . . . . . . . . . . . . . . . . . . 34 4.5.2.2 SLC: Single Linkage Clustering (Similarity Coefficients). . . . . 35 5 Transfer Lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37 5.1 General description. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 5.2 Strengths. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 5.3 Weaknesses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 5.4 Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 5.4.1 Mono-product sizing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 5.4.2 Balancing models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405.4.2.1 Linear programming (optimization). . . . . . . . . . . . . . . . 41 5.4.2.2 Maximum fixed utilization rate (Heuristic). . . . . . . . . . . . 42 5.4.3 Multi-product sizing (hints). . . . . . . . . . . . . . . . . . . . . . . . . . 43 III Design - Assembly Systems45 6 Assembly Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .47 6.1 Classification. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 6.1.1 Layout configuration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 6.1.2 Product mix management. . . . . . . . . . . . . . . . . . . . . . . . . . . 48 6.1.3 Task organization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 6.1.4 Reciprocal movement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 6.2 Assembly Time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486.2.1 Work sampling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 6.2.2 Standard times. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 6.2.3 MTM (Motion Time Measurements). . . . . . . . . . . . . . . . . . . . . 49 6.3 Fixed position (manual). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 496.3.1 Strengths. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 6.3.2 Weaknesses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 6.3.3 Rough design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 6.4 Assembly Shop (manual). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 506.4.1 Transportation system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 6.4.2 Strengths. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 6.4.3 Weaknesses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 6.5 Assembly Cells (manual). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 6.6 Assembly Lines (manual). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516.6.1 Strengths. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 6.6.2 Weaknesses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 6.6.3 Line type. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516.6.3.1 Paced lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 6.6.3.2 Unpaced lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 6.6.4 Line Design (mono-product). . . . . . . . . . . . . . . . . . . . . . . . . . 52 6.6.4.1 Balancing technical ob jectives. . . . . . . . . . . . . . . . . . . 53 6.6.4.2 Balancing economical ob jectives. . . . . . . . . . . . . . . . . . 54 6.6.4.3 Line balancing models. . . . . . . . . . . . . . . . . . . . . . . . 55Maximum probability of incompletions. . . . . . . . . . . . . . . . 55 Kottas and Lau. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 6.7 Automated assembly. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58Page 6 DMPS(Contents link) CONTENTS IV Management59 7 Introduction to Production Planning. . . . . . . . . . . . . . . . . . . . . . . . .61 7.1 Hierarchical approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 617.1.1 Overview on aggregate planning. . . . . . . . . . . . . . . . . . . . . . . 62 7.1.2 Overview on material planning. . . . . . . . . . . . . . . . . . . . . . . . 62 7.1.3 Overview on production scheduling. . . . . . . . . . . . . . . . . . . . . . 63 7.2 Production management costs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 637.2.1 Labour cost. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 7.2.2 Stock-out cost. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 7.2.3 Setup cost. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 7.2.4 Inventory holding cost. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 8 Demand Forecasting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .67 8.1 Demand planning process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 8.2 Demand forecasting system and methodologies. . . . . . . . . . . . . . . . . . . 688.2.1 "Time Series" approaches. . . . . . . . . . . . . . . . . . . . . . . . . . . 688.2.1.1 Pros and Cons. . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 8.2.2 Causal approaches. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 698.2.2.1 Linear regression. . . . . . . . . . . . . . . . . . . . . . . . . . . 69 8.2.2.2 Pros and Cons. . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 8.2.3 Qualitative approaches. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 708.2.3.1 Pros and Cons. . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 8.2.4 Joint use of methodologies. . . . . . . . . . . . . . . . . . . . . . . . . . . 70 8.3 Forecasting process accuracy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 8.4 Demand Vs Sales forecast, analysis of the time series. . . . . . . . . . . . . . . . 728.4.1 Trend. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 8.4.2 Seasonality. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 8.4.3 Cyclicity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 8.5 Moving average. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 8.6 Exponential smoothing models: Brown. . . . . . . . . . . . . . . . . . . . . . . . 74 8.7 Exponential smoothing models: Holt-Winters. . . . . . . . . . . . . . . . . . . . 75 8.8 Implementation process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 9 Inventory Management. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .77 9.1 Decisions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 9.2 Ob jectives. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 9.3 Classification. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 789.3.1 EOQ-ROP model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 789.3.1.1 Relax hypothesis: finite production rate. . . . . . . . . . . . . . 79 9.3.1.2 Relax hypothesis: non-constant purchasing cost. . . . . . . . . . 79 9.3.1.3 Relax hypothesis: non-constant consumption and LT. . . . . . . 80 9.3.2 Fixed-Time period model. . . . . . . . . . . . . . . . . . . . . . . . . . . 81 9.3.3 Comparison fixed quantity - fixed time. . . . . . . . . . . . . . . . . . . . 82 9.3.4 Switch model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 10 Aggregate Planning. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .83 10.1 Strategies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 10.2 Techniques. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8410.2.1 Trial and error. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 10.2.2 Linear programming. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 10.2.3 Heuristic methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84(Contents link)DMPS Page 7 CONTENTS 11 On-demand Management/MRP. . . . . . . . . . . . . . . . . . . . . . . . . . . .85 11.1 Traditional"Pul l"approaches. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 11.2"Push"approach/Requirement based approach. . . . . . . . . . . . . . . . . . . 85 11.2.1 Procedure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 11.2.2 Unfeasibility strategies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 12 Scheduling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .87 12.1 Vocabulary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 12.2 Hypotheses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 12.3 Classification profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8812.3.1 Production system configuration. . . . . . . . . . . . . . . . . . . . . . . 88 12.3.2 Constraints. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 12.3.3 Parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 12.3.4 Ob jectives. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 12.3.5 Techniques. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9012.3.5.1 Algorithms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90Karg & Thompson. . . . . . . . . . . . . . . . . . . . . . . . . . . 90 Hodgson. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 Johnson (2 machines). . . . . . . . . . . . . . . . . . . . . . . . . . 92 Johnson (3 machines extensions). . . . . . . . . . . . . . . . . . . 92 Campbell, Dudeck and Smith. . . . . . . . . . . . . . . . . . . . . 93 12.3.6 Dispatching rules. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Processing or Set-up time. . . . . . . . . . . . . . . . . . . . . . . 93 Due Date. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 Processing time and Due date. . . . . . . . . . . . . . . . . . . . . 94 System status. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 Job status. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 Economic factors. . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 Weighted rules. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 V Appendices95 A Performance: list of causes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .97 A.1 Traditional method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 A.2 OEE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 B Tables PVsp and PVa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .99 C Standard Normal Distribution table. . . . . . . . . . . . . . . . . . . . . . . . .101 D Magee-Boodman Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .103 D.1 Ob jective. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 D.2 Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 D.2.1 Stock-holding and setup costs. . . . . . . . . . . . . . . . . . . . . . . . . 103 D.2.2 Optimal number of campaigns. . . . . . . . . . . . . . . . . . . . . . . . . 104 D.3 Limitations of the model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 D.4 Heuristic application for scheduling. . . . . . . . . . . . . . . . . . . . . . . . . . 105Page 8 DMPS(Contents link) Part I Introduction and performance analysisof production system(Contents link)DMPS Page 9 1|Classification of Production Systems 1.1Production: basis Definition of production system: combination of the production process and all management subsystems contributing to make the transformation. Definition of production process: the transformation consists into evolve starting material to make products from both technological (chemical-physical) and economical point of view (this transformation can be driven by different methods i.e. long rest cheese increases its value and improves its properties just resting in a warehouse)Definition of ID code : the products can be identified by unique identification code (optical bar code, RIFD,...) Bill of Materials (BOM): is the list of material, parts and sub-assemblies needed to produce one unit of product (utilization coefficient and scrap rate) 1.1.1Process representation•Layout diagram: map, more or less detailed, of the plant •Flow diagram: graphical representation of the logic flow of the products •Technological diagram: used to represents the technological steps (generic symbols). There could be different process flows: Linear, Analytic and Synthetic flows. Continuous and Discontinuous flow depending if there is or not different production rates. Usually in discontinuous flows it is necessary to adopt buffers in order to cooperate with different production rates.(Contents link)DMPS Page 11 CHAPTER 1. CLASSIFICATION OF PRODUCTION SYSTEMS 1.1.2Activity analysis An activity can be classified as it adds or non-adds value to the final product: •added-value: processing time and service time (all activities that customer are willing to pay for) •non-added value: inspection time, idle time and transfer time (basically some of them can be seen as unnecessary form the customer prospective) 1.2Production classification1.2.1by DEMAND this classification tries to explain how much time is required to respond to the customer demand •Production to stock(MTS-made to stock): put the products into a warehouse waiting for customer demand (e.g. fasteners) •Production to order: the production starts with the customer order. This can be repeat (standard products) or single (unique products) Programming Index=I P=time that customer is willing to waitLead Time ( I P >1production to order I P≤1mandatory production to stock for IKEA productsI P= 0(the product is bought and picked instantly) Different levels of production: 1.ETO(engineer to order): this must be done for new product, typical for a unique product. The engineering process is sub jected to a very high lead time due to uncertainties in the design process and it implies to be quite costlyPage 12 DMPS(Contents link) CHAPTER 1. CLASSIFICATION OF PRODUCTION SYSTEMS 2.PTO(purchase to order): all the design processes are already done with the respective BOM. When the customer order the product the company purchases all the raw materi- als needed. This happens when the raw materials are quite expensive or when they are perishable, so the cost of the warehouse is not feasible 3.MTO(make to order): this is applied when there are high cost components, an unpre- dictable customer demand and a high level of customization. This process contains also fabrication processes 4.ATO(assembly to order): all the components are put into a warehouse. It is up to the customer to choose different type of sub-assemblies. It is easier to forecast the demand 5.MTS(make to stock): all the products are already produced and stocked waiting to the customer demand. This type of production is done on standard products (i.e. fasteners) and it is also done a forecast analysis. (demand>forecast stockouts demand P∗ Open a new station If it is not assigned any explicit value forP∗ , assumeP∗ = 10%StatOptT kP TkRT kP σ2 kz kΦ( z k)P kAlloc.Avail. Opts. (Contents link)DMPS Page 55 CHAPTER 6. ASSEMBLY SYSTEMS Kottas and Lau Hypothesis: •Constraints areC Tand precedences •time to complete a task is distributed as normal distribution •time to complete a task is independent from previous ones •unfinished products go on •each worker is paid without considering unbalancing •cost to complete and operation is independent form its progress Definitions: •Available operations: operations with predecessors allocated to a workstation •Desirable operations: available operation for whichL k> P k· I kwhere: –L k: is the cost of the task kto open a new station –P k: is the probability of incompletion of the task k –I k: is the cost of incompletion of the task kand all its followers: Ik= I∗ k+X rI ∗ r ∗ris the set of followers ofk ∗I∗ kis the cost of incompletion of task k ∗I∗ kis the cost of incompletion of rtasks •Critical operations: available operation for whichL k≤ P k· I kand also the station is currentlyempty •Non-Desirable operations: available operation for whichL k≤ P k· I kbut the station is not empty •Sure operations: desirable operation for whichP k∼ 0( 0.5and the seasonality periodLwill assume the value of thatk. The coefficient of seasonality of a generic periodiis calculated as the as the ratio between the value of the demand in that period and the average value of the demand of that period Si=D iA i If there is seasonality, it is possible to apply some method calleddepuration, to eliminate it and analyze the time-series with other criteria 8.4.3Cyclicity The cyclicity is a generalization of seasonality because it is characterized by rises and falls not at fixed periods. The fluctuation is usually longer than seasonality (2 years). Cyclicity can be affected by macro-economic cycles 8.5Moving average The forecast for the periodt+ 1is computed with the moving average from the periodtfor the lastkperiods Ft+1= M A(k) t=1k k X i=1D t−i we can make some observation about this analysis1.Reactivity of the model: for dif- ferent variations of the demand over time, we need to have a model more or less reactive (k>k) •highk: the contribution of each single value of the time series is low (low reactivity) •lowk: the contribution of each single value of the time series is high (high reactivity)2.Moving average cannot be used to forecast with long time horizon 3.Moving average cannot be used when the time series is characterized by trend and/orseasonality because it will not take in consideration those effects(Contents link)DMPS Page 73 CHAPTER 8. DEMAND FORECASTING 8.6Exponential smoothing models: Brown The Brown smoothing models tries to forecast the future demand (F t+1) considering two effects: the actual demand of the current period (D t) and the forecasted demand of the same current period based on past forecasting analysis (F t). These three variables are related with a smoothing coefficientα∈[0,1]: Ft+1= α·D t+ (1 −α)·F t Observations of this model: 1.The initialization of the Brown’s model is based on the theory of mathematical series: Ft+1= α·D t+ (1 −α)·F t Ft= α·D t−1+ (1 −α)·F t−1 Ft−1= α·D t−2+ (1 −α)·F t−2 . . .      ⇒ F t+1=n −1 X i=0α ·(1−α)i ·D t−i withnas the number of past actual demand values 2.The choice of the smoothing coefficientαis: •highα: implies high reactivity model in which the forecast tends to consider more the value of the last actual demand than the past forecasting (previous demands) •lowα: implies low reactivity model in which the forecast tends to consider more the value of the past data over the more recent oneDepending on the type of behaviour of the demand, it is possible to choose an appropriate value for the smoothing coefficient 3.Brown’s model cannot be used when the time series is characterized by trend and/orseasonality because it will not take in consideration those effectsPage 74 DMPS(Contents link) CHAPTER 8. DEMAND FORECASTING 8.7Exponential smoothing models: Holt-Winters The Holt-Winters model takes in consideration also the effects of trend and seasonality of the demand to make a forecast. The forecast for the immediate next period (F t+1) is formulated by the values of the average demand (A t) and trend ( T t) of the current period. It also consider the effect of the seasonality of the same period of the forecasting (S t+1−L), but shifted back of the value of the seasonality period (L): Ft+1= ( A t+ T t) ·S t+1−L It is possible to forecast also with long time horizon, shifting the period bym: Ft+m= ( A t+ m·T t) ·S t+m−L The variablesA t, T tand S tare evaluated as follow: At= α·D tS t−L+ (1 −α)·(A t−1+ T t−1) Tt= γ·(A t− A t−1) + ( γ−1)·T t−1 St= β·D tA t+ (1 −β)·S t−L These variable are initialized consideringnperiods: A0= A year1+n2 · T 0 T0=A year2− A year1n S0,i=S i,year1− S i,year22 All these formulation are based considering a yearly seasonalityL= 12months 8.8Implementation process(Contents link)DMPS Page 75 9|Inventory Management Inventory management is based on material production/purchase in order to replenish stocks. This is a"pul l"stock based strategy. Inventories can be final products or raw materials/compo- nents with high demand and used for different products. It is possible to evaluate the inventory performance looking for: •Effectiveness: meet customer demands by reducing the stock-out risk. There can be uncertainties given by non-deterministic parameters like demand and lead time: –safety stock: are made for absorb uncertainties –seasonal stock: is the capacity of design •Efficiency: help the plant by reducing the total cost acting on: –purchasing cost (the unitary cost for large quantities is lower) –transportation cost (distribution) –production cost (higher quantity for each lot implies lower setups) The inventory approach must be used when:1.Demand stationary or constant over time 2.It is possible to foresee the demand with high accuracy 3.Previous operations are high flexible 9.1Decisions The decisions made about inventory management can deal with:1.Replenishing policy: it is decided when and how much quantity to order. This has impact on stock holding cost, order cost and it has effect on the operations after the stock. This decisions depend on previous operations and on warehouse capacity 2.Control level: it depends on how often it is checked the actual level of stocks. An automated monitoring system requires technology support and it is very expensive than a human evaluation 9.2Ob jectives The ob jectives of inventory management is to minimize the total cost and maximize the service level for the next operations. These ob jectives are functions of: •Stock holding cost •Ordering cost •Cost of control •Cost of service level for next operations(Contents link)DMPS Page 77 CHAPTER 9. INVENTORY MANAGEMENT 9.3ClassificationThere are two main characteristics for an inventory management model: 1.The quantity to order 2.The time interval of order issuing Models can depend also on which type of actual inventory level monitoring system they require (continuous or discrete con- trol) and also if the order of each item depends or not on orders of other items. It can be different items must be ordered together (combined order). We will analyze deeply two models for: 1.Quantity fixed and variable interval (EOQ-ROP) 2.Quantity variable and fixed interval (Fixed-Time period) 9.3.1EOQ-ROP modelThe "Equivalent Order Quantity- Reorder Point"model is character- ized by a fixed quantity to order E OQin order to minimize the to- tal cost with the condition that all items can be purchased separately. These orders are made with a vari- able time interval when the inven- tory availability level reaches a cer- tain point namedROP. This sys- tem requires a continuous monitor- ing of the actual inventory level. At the basic design we consider- ing all parameters as deterministic, the replenishing rate is infinite (instantaneous) and the purchasing cost is constant and not de- pendent on the quantity. TheROPcan be evaluated as the quantity of items that are consumed on lead time.dis the consumption rate and it is supposed constant in each order. TheE OQ can be evaluated by minimization of the total cost which can be divided into: a)Purchasing cost(C p): depends on the annual demand D a[unit/year] and the unitary purchasing costp[e/unit]: Cp= D a· p b)Inventory holding cost(C stock): depends on capital cost c m%[%/year], the unitary stock valuep[e/unit] and the average inventory level [unit] Cstock= c m%· p·Q2 Page 78 DMPS(Contents link) CHAPTER 9. INVENTORY MANAGEMENT c)Order issuing cost(C o): depends on the unitary order cost o[e/order] and the number of ordersD a/Q [order/year]: Co= o·D aQ The goal is find a certain quantityE OQ=Q∗ [unit/batch] that minimize the overall cost: E OQ=s2 ·o·D ac m%· p The number of batches and the average reordering time are: #batches=D aE OQ T =period# batches 9.3.1.1Relax hypothesis: finite production rateIf the production rate r[unit/period] becomes finite the expression for theE OQchanges: E OQ=v u u u t2 ·o·D acm %·P· 1−D ar ·H whereH[period] is the time requested to produce the quan- tity. The production ratermust be not lower than the consumption rated(Generally theE OQwith finite rate is higher than with infinite rate). Ifr=dit is a just in time production with no inventories while ifr < dthere are stock-outs. 9.3.1.2Relax hypothesis: non-constant purchasing costThe purchasing cost pcan be non-constant and it usu- ally reduces when large quantity is increasing granting dis- counts. It is necessary to: 1.Evaluate theE OQ ifor each different purchasing cost pi 2.Verify ifE OQ iis feasible in the quantity interval, otherwise theE OQ ibecomes the interval limit At the end, take theE OQ iwith minimum cost(Contents link)DMPS Page 79 CHAPTER 9. INVENTORY MANAGEMENT 9.3.1.3Relax hypothesis: non-constant consumption and LTThe hypothesis of determin- istic parameters is no longer active and the parameters takes in consideration un- certainties both about con- sumption rate and the real lead time. This means that it is necessary to introduce the Safety Stocks (S S). The main ob jective ofS Sis to prevent stock-outs due to different consumption rate during lead time. They depends on uncertainties of demand con- sumption and lead time duration, this allows the warehouse to be more reliable. We assume all uncertainties can be described with standard normal distribution. The safety stocks increases theROP ROP=d·LT+S S •d[unit/period]: average consumption rate •LT[period]: average lead time •S S[unit]: safety stocks S S=k·σ d,LTσ d,LT=qLT ·σ2 d+ σ2 LT· d2 •k: service level factor (the minimum value of standard distribution to fulfill the service level requiredC) •LT[period]: lead time (same unit of measure ofd) •σ d: standard deviation of demand •σ LT: standard deviation of lead time (same unit of measure of dand not the opposite)Page 80 DMPS(Contents link) CHAPTER 9. INVENTORY MANAGEMENT 9.3.2Fixed-Time period modelThis model is characterized by: 1.the time between two ordersis kept fixed 2.the ordered quantity is vari-able due to the actual value of inventories at the moment of order 3.it uses a simpler control ofthe actual stock level (dis- continuous) 4.the orders are usually com-bined by different items The goal is to optimize the value of the periodTin order to minimize the total cost. OL=d·(T+LT) +S S T=s2 ·oc m%· p·D a! •OL[unit]: ob jective level •d[unit/period]: average demand consumption •T+LT[period]: period to cover (consumption+lead time) •S S[unit]: safety stocks S S=k·σ D,T+LTσ D,T+LT=q( T+LT)·σ2 D+ σ2 T+LT· d2 •k: probability coefficient target •T[period]: reorder time (same unit of measure ofD) •LT[period]: lead time (same unit of measure ofD) •σ D: standard deviation of demand •σ T+LT: standard deviation of overall period (same unit of measure of d) Cp= D a· P C o= o·#batches C inv= cm%·P· d·(T+LT)2 + S S(Contents link)DMPS Page 81 CHAPTER 9. INVENTORY MANAGEMENT 9.3.3Comparison fixed quantity - fixed time9.3.4Switch model Switch models can combine the advantages of the two single model presented although they are very complexPage 82 DMPS(Contents link) 10|Aggregate Planning The aggregate planning is a mid- term that takes as input data form accounting and customer de- mands, these data are elabo- rated with production resources and produces as output the Master Production Schedule (MPS). The MPS is a table that contains the quantity only of finished products (aggregated information) without considering materials and sub-components. This table covers the time horizon of 1 month or 1 year and the time bucket (each column) of 1 week or 1 month. In the MPS are evaluated for each period like: Quantity of stocks (average inventory level), Stock-outs or backlogs, Production (standard time and overtime), Outsourcing/Purchasing and Setups 10.1StrategiesThere are many strategies for production, but there are two main of them: •Level plan: this type of strategy con- sists to produce a fixed quantity of prod- ucts all over the time horizon. It is re- quired the presence of a medium-big size warehouse to store the finished products. When production is higher than demand, products are put into the warehouse and they are taken out when production is lower than demand. This type of strat- egy is mandatory to be used when the plant is not so flexible in term of quantity and setup costs of changing production rate are very high. It is also recommended to be used when the demand is very stable (mature products). In case of unfeasibilities (demand higher than production and the warehouse is empty) it could occurs in backlogs (recoverable) and stock-outs (non recoverable). The production quantity is equal to the average demand •Chase plan: with this strategy the production follows exactly the demand, so in theory there is no inventory of good products (no warehouse cost). To apply this strategy the production plant must be flexible in term of quantity and it must be applied when products cannot be stored. If demand becomes higher than forecasted one, there will be stock-outs. Real strategies are usually a combination of these two models, but The choice should also take into account eventual constraints (e.g. maximum production capacity)(Contents link)DMPS Page 83 CHAPTER 10. AGGREGATE PLANNING 10.2Techniques 10.2.1Trial and error This technique is manual and consists into applying different type of strategies to produce dif- ferent plans (trials), then it is chosen the one with low cost. 10.2.2Linear programming This is an optimization technique to fine the most cheaper solution, but it is very difficult to find a solution because the variables are integer and not continuous 10.2.3Heuristic methods There are various heuristic (not optimistic) methods: •Wagner-Whitin: help to evaluate inventories and setups but without constraints on production capacity •Karni-Roll: evolution of Wagner-Whitin considering also constraints on production ca- pacity •Aucamp •Magee-Boodman model: this model is analyzed in chapterDat page103Page 84 DMPS(Contents link) 11|On-demand Management/MRP The material planning is a short-medium time planning in which it takes as input the Master Production Schedule and uses the quantity of goods to decide how much and when manage and produce raw material and components. There are 2 approaches: 11.1Traditional"Pul l"approaches This approach is based on inventory management (EOQ, Fixed T and switch models) when ma- terial production/purchase is based on replenishing stocks, but respect to inventory management, materials and components have different hypotheses: •the demand is no longer independent because the quantity of components/material is re- lated on the quantity of goods (MPS), so it is not possible to use normal distribution •the demand is not stationary and this implies that with inventory models we are going to pay inventories also when it would not be necessary •the assumption of smooth and gradual stock consumption cannot be still considered 11.2"Push"approach/Requirement based approach This approach consists into order material and components to satisfy the finished product re- quirements. It means that based on the MPS we are going to order when and the quantity needed. This approach requires also a lot of information: 1.Master Production Schedule: given from aggregate planning 2.Product information: •source (internal production, outsourcing,...) •scrap production rate expected for each component and material 3.BOM (Bill Of Materials): in this case it is consider the BOM related on manufacturing process: •coefficients of use •process scrap rate (related to the assembly) •lead timeLTcorrection: not all materials and components are required at the same time, so they can be ordered when each of them is actually needed 4.Management information: this is related to inventory: •fixed (quite fixed): Lead Time, Safety Stocks and batch production policy •variable: actual inventory level and order in progress(Contents link)DMPS Page 85 CHAPTER 11. ON-DEMAND MANAGEMENT/MRP 11.2.1ProcedureComponent12. . .. . .Ndescription Gross Requirementdemand of each component Initial Availability (without SS) Net Requirementthis can’t be negative Net Requirement adj scrapsNet Requirement 1 −product scrap rateOrder In Progress (OIP) Net Requirement adj OIPthis can’t be negative Lot-sized RequirementEOQ or L4L or other Order to Issuethe order is anticipated by LT notes: •Net requirement = Gross - (Initial availability (without SS)- eventual Reserved stocks) •product scrap rateis the rate during production of a specific component •assembly scrap rateis the rate that has to be applied to the gross requirement of the sub-level component during assembly •Some sub-components may have negativeLT sbecause the are used in the process later 11.2.2Unfeasibility strategies In case of unfeasibility, the order are required to be issued before the first period. There are some adjustments that can be made, but they must be applied from children to parents one level at the time: •Use Safety StocksS S •Reduce Lead TimeLT •Change lot-sizing policy (the best is L4L) •Purchase a the component from a external supplierPage 86 DMPS(Contents link) 12|Scheduling Production scheduling consists into decide what, how, when and where to produce on a short-term time horizon. It takes data from aggregate planning and material planning in order to decide the most efficient sequence of operations in production. This type of planning is very detailed and it requires a lot of data, but it is affected by uncertainties: •Variability: product variants and urgent jobs (a big client can request an extra job to be done in short time, this leads to re-organization) •Unpredictability: failures •Uncertainty: working times that depends on automation level It is also necessary to decide the final ob ject as efficiency (manage better the resources) or effectiveness (respect customer meets). Nowadays it is increased the automation level with also technology information during production process. All the data must be processed and transmitted very quickly. The output is the production schedule at it usually under the form of the Gantt’s diagram, where each job is assigned to a specific machine in each precise time 12.1Vocabulary•Job: working unit composed by a certain number of items. This is related to production batch and it is usually different from client’s order. It is an internal decision •Order: quantity of items required by the customer (external) •Routing: sequence of phase production •Preemption: stopping of the processing of one job on a machine in order to process another one that is more urgent •Passing: overtaking between jobs waiting to be processed, for urgency reasons (have different sequence on different machines) •Due Date (DD): date in which a job should be completed –EDD- Earliest Due Date: earliest planned date an job may be completed –LDD- Latest Due Date: latest planned date an job may be completed –ESD- Earliest Starting Date: earliest planned date at which it is possible to start working the job –LSD- Latest Starting Date: latest planned date at which it is possible to start working the job –Slack=DD-Processing time-ESD(Contents link)DMPS Page 87 CHAPTER 12. SCHEDULING 12.2Hypotheses The hypotheses we make in this course are:1.What is already planned, it cannot be changed (e.g. what decided in the MPS or MRPand other fixed quantities like due date 2.The resource availability are fully known (production capacity) 3.The critical resources are only the machines (assume workers always available) 4.Job are completely define (setup and processing times and machines are known) and noalternative routings are allowed 5.The transportation time between two machines is considered negligible 6.There is no decoupling point 7.One job can be processed only on one machine at time (no parallel stations) 8.Inventory costs are negligible 12.3Classification profile The scheduling planning can be classified on independent variables:12.3.1Production system configuration •Single machine: there is only one machine and it is necessary to decide the sequence of jobs to be processed •Parallel machines: each job can be performed only on one machine. There can be more machines and they can be equal or just very similar •Flow shop: a series of machines is a line. Each machine performs a specific operation and all jobs have the same routing •Job shop: a job can be processed on one or more machines in the same shop (each job can have different routings) •Open shop: it consists in many machines that can perform different tasks. Job routing is not fixed a prioriPage 88 DMPS(Contents link) CHAPTER 12. SCHEDULING 12.3.2Constraints•Setup times: they can be dependent or independent from the sequence of jobs and machine •Preemption allowed or not •Passing allowed or not •Processing time deterministic or stochastic 12.3.3Parameters First we define few symbols: -N: jobs number -j: job’s index -M: machines number -i: machine’s index -t i,j: processing time of job jon machinei- d j: due date of job j -I j: actual starting date of job j -C j: actual completion date of job j -S U i,j: setup time of job jon machinei the parameters are:•Lateness(for jobj):L j= C j− d j. it can be positive (late) and negative (anticipated) •Tardiness(for jobj):T j= max(0, L j) . only non-negative delay is considered •Flow-time(for jobj:F j= C j− I j. Lead time of job j •Average lateness:LM j=1N N P j=1L j •Average tardiness:T M j=1N N P j=1T j •Average flow-time:F M j=1N N P j=1F j •Number of tardy jobs: number of jobs witT j> 0 •Makespan:M AK= max j( C j) −min j( I j) •Saturation coefficientof machinei:T S i=1M AK N P j=1t i,j •Average saturation coefficient:T S M=1M ·M AKM P i=1N P j=1t i,j •Work In Progress:W I P=1max jC j− min jI jmax jC j P t=min jI j •Total setup time:S U T=M P i=1N P j=1S U i,j(Contents link)DMPS Page 89 CHAPTER 12. SCHEDULING 12.3.4Ob jectives Scheduling ob jectives can be: •Minimize average lateness •Minimize average tardiness •Minimize average flow-time •Minimize number of late jobs •Minimize makespan •Minimize the average saturation coefficient 12.3.5TechniquesThere are two main approaches 1.Operative Planning-based: this is characterized by algorithms that take all the neces- sary data and give a detailed schedule plan (some of this algorithms can be optimistic or heuristic) 2.Production control-based: it is a more dynamic planning based on production decisions. It is solved with heuristic algorithms based on dispatching rules (regole di carico) 12.3.5.1Algorithms Karg & Thompson •System configuration: –Single machine –Sequence dependent set-upS U j k •Other constraints: –no preemption (means no stop of processing of one job on a machine in order to process a more urgent job) •Ob jective: minimum total set-up time •Type of algorithm: Euristic (non-optimized)Page 90 DMPS(Contents link) CHAPTER 12. SCHEDULING Algorithm:1.From the list of jobs, select "randomly" 2 jobs (A and B)NB! A first and B after 2.Choose another job from the others available 3.Compute the setup time from all combinations of order of the selected jobs:NB! : •Ais always he first element of the list •The combination of the set-up time goes to a complete cycle (also the last job of the list to job A, the initial one) 4.Select the order of jobs with the minimum set-up time from the point 3 5.Repeat from the point 2 till the list of available job is emptyNB: the order chosen in point 4 cannot be changed, the new job select along the entire list Hodgson•System configuration: –Single machine –No set-ups or sequence independent set-ups (the processing time is not affected by the sequence of operations) •Other constraints: –no preemption (means no stop of processing of one job on a machine in order to process a more urgent job) •Ob jective: minimum number of tardy jobs (it doesn’t evaluate the level of tardiness) •Type of algorithm: Optimization Algorithm:1.Create two lists: •L: empty list of tardy jobs •E: list of non-tardy jobs (all the jobs) 2.Sort the listEby increasingDD(Due-Date/Delivery-Date) 3.Put, one by one, the elements ofEon a time-line till we find a job withC D(completion- date) after theDD 4.Select, from the list of jobs on the time-line, the job the the longest processing time. Thisjob is placed in the tarty-jobs listL(It is not necessary the last one) 5.Repeat from point 3 till we find a list of non-tardy jobs with allC DsbeforeDDs The solution is composed by the two lists:•non-tardy jobs listEis sorted by definition •the list of tardy jobs listLis not defined, it is necessary to change the order to find the final solution that costs less in term of penalty delay costs(Contents link)DMPS Page 91 CHAPTER 12. SCHEDULING Johnson (2 machines)•System configuration: –Flow-shop with only two machines (machine 1 and machine 2) –No set-ups or sequence independent set-ups (the processing time is not affected by the sequence of operations) •Other constraints: –no preemption (means no stop of processing of one job on a machine in order to process a more urgent job) –no passing (means the same sequence of jobs for all the machines) •Ob jective: minimum makespan (maximum saturation of machines) •Type of algorithm: Optimization Algorithm:1.Create an empty list as long as the number of jobs (sequence list) 2.Create a list of available jobs 3.Find the jobjwith the shortest processing time for any machine 4.If the processing time of the machine 1M1is shorter than the time of machine 2M2, put the jobjin the first spare place (empty element) from the left of the sequence list, otherwise put the jobjthe first spare place from the right of the sequence list 5.Remove the jobjfrom the list of available jobs list 6.Repeat from point 3 till the available jobs list is empty Johnson (3 machines extensions) If we have a flow shop of 3 machinesM1−M2−M3: 1.Perform the Johnson’s algorithm considering the machinesM1−M2 2.Perform the Johnson’s algorithm considering the machinesM2−M3 If the two sequences are identical, they are optimal solution otherwise, we cannot assess an optimal solutionPage 92 DMPS(Contents link) CHAPTER 12. SCHEDULING Campbel l, Dudeck and Smith•System configuration: –Flow-shop ofMmachines –No set-ups or sequence independent set-ups (the processing time is not affected by the sequence of operations) •Other constraints: –no preemption (means no stop of processing of one job on a machine in order to process a more urgent job) –no passing (means the same sequence of jobs for all the machines) •Ob jective: minimum makespan (maximum saturation of machines) •Type of algorithm: heuristic Algorithm:1.GenerateM−1couples of dummy (or fake) machines summing up for each job the pro- cessing times of the firstkmachines and of the lastk(k= 1,2, ..., M−1) 2.Find the optimal sequence for each couple of dummy machines applying Johnson’s algo-rithm 3.Calculate the makespan of each of the found sequences and choose the shortest one 12.3.6Dispatching rules Dispatching rules are an easy alternative to optimization criteria, in particular when the system is highly dynamic an the operation sequence can be changed at the end of each operations. These rules are heuristic and the main concept is: when a machine becomes available, choose the best available job by priority rules. These rules are different and depends on the final ob jective we want to achieve. Dispatching rules can be distinguished depending on the fact the priority can change at the end of each operation: •Static rule: for each machine the priority order is fixed once and doesn’t change •Dynamic rule: at the end of each operation, the priority order is computed again They can also be classified depending in which region are applied:•Global rule: the priority is computed based on all remaining operations on each machine •Local rule: the priority is computed based only on the next operation on that machine Processing or Set-up time-SPT(shortest processing time): it is a static and local rule on a specific machine with a good result of average flow-time but with the risk of delay of longest jobs -LPT(longest processing time) -TSPT(truncated shortest processing time): as SPT with a waiting time threshold -LWKR(least work remaining): minimum residual processing time. It is a dynamic and global rule(Contents link)DMPS Page 93 CHAPTER 12. SCHEDULING -TWORK(total processing time): minimum total processing time. It is a static and global rule -MSUT(minimum setup time): minimum setup time on a machine. It is a static and local rule Due Date-EDD(earliest due date): it is a static and local rule. It is good in terms of number of tardy jobs but it penalizes longest jobs -OPNDD(operation due date): it is a static and global rule. The first job is the one with early OPNDD. machinekand jobj ∗equal parts:OP N DD j=DD j− start time j# operations ∗proportional to processing time:OP N DD j,k=DD j− start time jP kt p,j,k· t p,j,k Processing time and Due date-MST(minimum slack time): it is dynamic and global rule.slack=DD−present time− residual processing time -S/OPN(slack per operation): it is dynamic and global rule.S/OP N=slack# residual operations the first job with lowest S/OPN. It is good in term of punctuality System status-NINQ(Number In Next Queue): min. number of jobs already queued for the next oper- ation -WINQ(Work In Next Queue): min. total processing time already queued for the next operation Job status-FIFO(first in first out) -LIFO(last in first out) -FISFS(First In the System First Served): the first job that entered the system for the first time -FROP(Fewest Remaining Operations): min. number of residual operations -MROP(Most Remaining Operations): max. number of residual operations Economic factors-COVERT: max. ratio = delay cost/residual time Weighted rules-SPT/LWKRminαP T+ (1−α)RT(P T: processing time.RT: residual processing time)Page 94 DMPS(Contents link) Part V Appendices(Contents link)DMPS Page 95 A|Performance: list of causes A.1Traditional methodCauseType StrikesT S TUnion assemblyT S TAbsenteeismT OCoffee breakT OLack of informationT OLunch breakT OMan-machine interferenceT OPhysiological stopsT OServomechanism waiting timeT OShift changeT OStand-by for another machine waitT OInappropriate chemical of materialT LMLach of materialT LMLack of energyT LMLack of material machine-sideT LMMaintenanceT MMaintenance waitT MSpare parts waitT MBreak of machineT FBreak of mandrelT FBreak of motorT FBreak of refrigerantT FGeneral failureT FSamplesT P RTest/trialsT P RComponent changeoverT SGeneral micro-shutdownsT SMachine settingT SPlant cleaningT SProduct changeT SSubstitution toolT STooped up of component feedersT SUtensils and equipment changeT S(Contents link)DMPS Page 97 APPENDIX A. PERFORMANCE: LIST OF CAUSES A.2OEECauseType StrikesT S tUnion assemblyT S tUnion meetingsT S tLack of ordersT LOSamplesT P TTrialsT P TPlanned maintenanceT MPreventive maintenanceT MScheduled maintenanceT MSpare parts wait (periodic replacement)T MBreack of component in machine 1T FBreack of component in machine 2T FBreak of mandrelT FBreakdown maintener interventionT FBreakdown operator interventionT FGeneral failureT FComponents changeoverT SEquipment changeT SFormat changeT SGeneral micro-shoutdownsT SMachine settingT SMachine shutdownT SMachine startingT SMachine tool cleaningT SMinor regulationsT SPlant cleaningT SProduct changeT SRoom sterilizationT SSetting of the machineT SSubstitution of mouldT SSubstitution toolsT STime of coils loadingT SInappropriate material in productionT LMLack of energyT LMLack of material machine sideT LMLack of material machine sideT LMPage 98 DMPS(Contents link) B|Tables PVsp and PVa PVsp(i,n)= (1 +i)− n1%2%3%4%5%6%7%8%9%10%11%12%13%14%15% 10.9900.9800.9710.9620.9520.9430.9350.9260.9170.9090.9010.8930.8850.8770.870 20.9800.9610.9430.9250.9070.8900.8730.8570.8420.8260.8120.7970.7830.7690.756 30.9710.9420.9150.8890.8640.8400.8160.7940.7720.7510.7310.7120.6930.6750.658 40.9610.9240.8880.8550.8230.7920.7630.7350.7080.6830.6590.6360.6130.5920.572 50.9510.9060.8630.8220.7840.7470.7130.6810.6500.6210.5930.5670.5430.5190.497 60.9420.8880.8370.7900.7460.7050.6660.6300.5960.5640.5350.5070.4800.4560.432 70.9330.8710.8130.7600.7110.6650.6230.5830.5470.5130.4820.4520.4250.4000.376 80.9230.8530.7890.7310.6770.6270.5820.5400.5020.4670.4340.4040.3760.3510.327 90.9140.8370.7660.7030.6450.5920.5440.5000.4600.4240.3910.3610.3330.3080.284 100.9050.8200.7440.6760.6140.5580.5080.4630.4220.3860.3520.3220.2950.2700.247 110.8960.8040.7220.6500.5850.5270.4750.4290.3880.3500.3170.2870.2610.2370.215 120.8870.7880.7010.6250.5570.4970.4440.3970.3560.3190.2860.2570.2310.2080.187 130.8790.7730.6810.6010.5300.4690.4150.3680.3260.2900.2580.2290.2040.1820.163 140.8700.7580.6610.5770.5050.4420.3880.3400.2990.2630.2320.2050.1810.1600.141 150.8610.7430.6420.5550.4810.4170.3620.3150.2750.2390.2090.1830.1600.1400.123 160.8530.7280.6230.5340.4580.3940.3390.2920.2520.2180.1880.1630.1410.1230.107 170.8440.7140.6050.5130.4360.3710.3170.2700.2310.1980.1700.1460.1250.1080.093 180.8360.7000.5870.4940.4160.3500.2960.2500.2120.1800.1530.1300.1110.0950.081 190.8280.6860.5700.4750.3960.3310.2770.2320.1940.1640.1380.1160.0980.0830.070 200.8200.6730.5540.4560.3770.3120.2580.2150.1780.1490.1240.1040.0870.0730.061 210.8110.6600.5380.4390.3590.2940.2420.1990.1640.1350.1120.0930.0770.0640.053 220.8030.6470.5220.4220.3420.2780.2260.1840.1500.1230.1010.0830.0680.0560.046 230.7950.6340.5070.4060.3260.2620.2110.1700.1380.1120.0910.0740.0600.0490.040 240.7880.6220.4920.3900.3100.2470.1970.1580.1260.1020.0820.0660.0530.0430.035 250.7800.6100.4780.3750.2950.2330.1840.1460.1160.0920.0740.0590.0470.0380.030(Contents link)DMPS Page 99 APPENDIX B. TABLES PVSP AND PVA PVa:=1 + (1 + i)− ni 1%2%3%4%5%6%7%8%9%10%11%12%13%14%15% 10.9900.9800.9710.9620.9520.9430.9350.9260.9170.9090.9010.8930.8850.8770.870 21.9701.9421.9131.8861.8591.8331.8081.7831.7591.7361.7131.6901.6681.6471.626 32.9412.8842.8292.7752.7232.6732.6242.5772.5312.4872.4442.4022.3612.3222.283 43.9023.8083.7173.6303.5463.4653.3873.3123.2403.1703.1023.0372.9742.9142.855 54.8534.7134.5804.4524.3294.2124.1003.9933.8903.7913.6963.6053.5173.4333.352 65.7955.6015.4175.2425.0764.9174.7674.6234.4864.3554.2314.1113.9983.8893.784 76.7286.4726.2306.0025.7865.5825.3895.2065.0334.8684.7124.5644.4234.2884.160 87.6527.3257.0206.7336.4636.2105.9715.7475.5355.3355.1464.9684.7994.6394.487 98.5668.1627.7867.4357.1086.8026.5156.2475.9955.7595.5375.3285.1324.9464.772 109.4718.9838.5308.1117.7227.3607.0246.7106.4186.1455.8895.6505.4265.2165.019 1110.3689.7879.2538.7608.3067.8877.4997.1396.8056.4956.2075.9385.6875.4535.234 1211.25510.5759.9549.3858.8638.3847.9437.5367.1616.8146.4926.1945.9185.6605.421 1312.13411.34810.6359.9869.3948.8538.3587.9047.4877.1036.7506.4246.1225.8425.583 1413.00412.10611.29610.5639.8999.2958.7458.2447.7867.3676.9826.6286.3026.0025.724 1513.86512.84911.93811.11810.3809.7129.1088.5598.0617.6067.1916.8116.4626.1425.847 1614.71813.57812.56111.65210.83810.1069.4478.8518.3137.8247.3796.9746.6046.2655.954 1715.56214.29213.16612.16611.27410.4779.7639.1228.5448.0227.5497.1206.7296.3736.047 1816.39814.99213.75412.65911.69010.82810.0599.3728.7568.2017.7027.2506.8406.4676.128 1917.22615.67814.32413.13412.08511.15810.3369.6048.9508.3657.8397.3666.9386.5506.198 2018.04616.35114.87713.59012.46211.47010.5949.8189.1298.5147.9637.4697.0256.6236.259 2118.85717.01115.41514.02912.82111.76410.83610.0179.2928.6498.0757.5627.1026.6876.312 2219.66017.65815.93714.45113.16312.04211.06110.2019.4428.7728.1767.6457.1706.7436.359 2320.45618.29216.44414.85713.48912.30311.27210.3719.5808.8838.2667.7187.2306.7926.399 2421.24318.91416.93615.24713.79912.55011.46910.5299.7078.9858.3487.7847.2836.8356.434 2522.02319.52317.41315.62214.09412.78311.65410.6759.8239.0778.4227.8437.3306.8736.464Page 100 DMPS(Contents link) C|Standard Normal Distribution table Φ(z) =P(x≤z)z0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.00.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.10.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.20.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 0.30.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517 0.40.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.50.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.60.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.70.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.80.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.90.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 1.00.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 1.10.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830 1.20.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015 1.30.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.40.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.50.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 1.60.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 1.70.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.80.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.90.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 2.00.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 2.10.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 2.20.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890 2.30.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916 2.40.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 2.50.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 2.60.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 2.70.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 2.80.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.90.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 3.00.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990 3.10.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993 3.20.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 3.30.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 3.40.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 3.50.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 3.60.9998 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 3.70.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 3.80.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 3.91.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 (Contents link)DMPS Page 101 D|Magee-Boodman Model Magee-Boodman model is an heuristic model for aggregate planning based on inventory manage- ment. It is a multi-product single-machine in which it is evaluated the best sequence of operation of different product families. It considers also a statistically determined stationary demand D.1Ob jective The ob jective of the model is to determine the optimal number of campaigns (number of pro- duction cycles)n 0to perform in the time horizon in order to minimize the total cost. The costs that are considered are the stock-holding cost and the setup cost D.2Model In general, this model is used to manage a multi-product production. We define here the sym- bology: •k: product index •H: total available working days/hours in a year. It doesn’t depend on the product •r(k): production rate of the productk. In general it is considered finite •D(k): annual demand for productk •C m: stock-holding ownership rate. Also this doesn’t depend on the product, but it is based on the stock-holding expensive rate and the opportunity rate •p(k): variable production cost of the productk •a(k): setup cost of the productk. It depends on the production sequence, but it doesn’t consider the time lost to do the setup operation. The setup cost from the productAto productBcan be different from productCto productA. It is possible to choose an optimal sequence of operations that remains constant for each campaign. A simple technique is to following the rule applied in the practice session D.2.1Stock-holding and setup costs The total stock holding cost and the total setup cost are: Cstock,tot=K X k=1p (k)·C m·D(k)· 1−D (k)r (k)·H2 ·n 0C setup,tot= n 0·K X k=1a (k)(Contents link)DMPS Page 103 APPENDIX D. MAGEE-BOODMAN MODEL D.2.2Optimal number of campaigns Considering the expressions of the stock-holding and setup cost, it is possible to identify the optimal number of campaignsn 0: n0=v u u u u u u tK P k=1p (k)·C m·D(k)· 1−D (k)r (k)·H2 ·K P k=1a (k) (n 0can be not integer) with the corresponding order quantity for each campaign (with and without considering the effect of the finite production rate): Q0( k) =D (k)n 0Q 0( k) =D (k)n 0· 1−D (k)r (k)·H D.3Limitations of the model The Magee-Boodman model have 5 limitations:1."Degenerate" campaigns: this means that sometimes it isn’t economically convenient to produce all products in all campaigns. In particular, for some product, it can be better to be produced one campaign yes and one not. These products are characterized by: •Low annual demand •High setup cost compared to the other products. To evaluate if it is necessary to apply degenerate cam- paigns to some products it is possible to compare the order quantity withE OQ(without considering the finite production rate): E OQ(k) =s2 ·D(k)·o(k)C m ·p(k)Q 0( k) =D (k)n 0 or, to be more precise, considering the finite production rate: E OQ(k) =v u u u t2 ·D(k)·o(k)C m ·p(k)· 1−D (k)r (k)·H Q 0( k) =D (k)n 0· 1−D (k)r (k)·H If not specified, it is possible to consider the ordering costo(k)equal to the setup cost a(k). For each productk, if the relationE OQ(k)≫Q 0( k)(considerE OQ(k)≥2·Q 0( k)), it means that it should be considered to apply a degenerate campaign for productk. It is nec