Class 28: Review for Final Exam OPSM301 Spring 2012 Class 28: Review for Final Exam

Logistics Exam on May 29, Tuesday ,between 9:30-11:30 in SOS Z31 (Sevgi Gönül Amphi) Please bring a pencil, erasor, calculator (these cannot be shared) 1 page of cheat-sheet is allowed (maximum A4 size, 2 sided, hand-written, no photocopy allowed) Please be in the exam room at 9:20 Please check your seat number at the door before entering the room

Exam Coverage Exam structure similar to the Midterm Chapters 1,2,3,4,5,6,7.1,7.2, 8, 9, 10.1-10.4 Lecture notes, class discussions, assignments Both qualitative and quantitative questions Practice with exercises at the end of chapters, and additional questions on the course website and F drive (or KUAIS) Solutions in the F:\COURSES\UGRADS\OPSM301\SHARE folder Will announce office hours before the exam

Overview of Topics Operations Strategy Process Flows Flow Time Strategic Fit, Trade-off, competitive dimensions,order winner-order qualifier, product-process matrix, process types Process Flows Little’s Law, Performance measures R,T,I Flow Time Activity times, Critical Path Capacity (Throughput Rate) Bottleneck, unit loads of resources, takt time, utilization,Gantt Chart Linear Programming- EXCLUDED Product mix, Employee scheduling, investment, transportation problems, binding constraint, shadow prices Inventory Management Trade-off between ordering cost vs holding cost, economic order quantity, reorder point, safety stock

The impact of variability Flow rate variability Safety inventory in manufacturing with inventory Safety capacity in service systems (queueing systems) Flow time variability Safety time Performance variability Statistical process control Project Management

Expected Areas for Questions Quantitative: Process Analysis Inventory management Waiting line management Project management Quality management Qualitative All of the above, and lean operations

Inventory Management EOQ Model Safety Stock as a function of Lead time, desired service level, and demand variability

Safety Inventory Using the Newsvendor formula: P(Demand<= Q) =Cu/(Cu+Co)=MB/(MB+MC) Marginal Analysis: What is the marginal value of ordering the next (n+1)th item?

What happens if I order one more unit (on top of Q = 2000)? Suppose you placed an order of 2000 units but you are not sure if you should order more. What happens if I order one more unit (on top of Q = 2000)? Sell the extra unit with probability …P(D>2000) DP = 200 (MB or Cu) Do not sell the extra unit with probability … P(D≤2000) DP =-65 (-MC or -Co) Expected profit from additional unit E(DP) = P(D>2000) 200-P(D ≤ 2000) 65 So? ... Order more or less than 2000?

Improving Supply Chain Performance: Improving Supply Chain Performance: The Effect of Pooling/Centralization Notes: J.A. Van Mieghem/Operations/Supply Chain Mgt

Learning Objectives: Centralization/pooling Chapter 7 Learning Objectives: Centralization/pooling Centralization reduces safety stocks (pooling) and cycle stocks (economies of scale) Can offer better service for the same inventory investment or same service with smaller inventory investment. Different methods to achieve pooling efficiencies: Physical centralization, Information centralization, Specialization, Commonality, Postponement/late customization. Cost savings are proportional to square root of # of locations pooled. Copyright © 2013 Pearson Education Inc. publishing as Prentice Hall

Causes of Delays and Queues High Unsynchronized Variability in Interarrival Times Processing Times High Capacity Utilization r = Ri / Rp, or Low Safety Capacity Rs = Rp – Ri, due to High Inflow Rate Ri Low Processing Rate Rp = c/ Tp (i.e. long service time, or few servers)

The Queue Length Formula Utilization effect Variability effect x where  Ri / Rp, where Rp = c / Tp, and CVi and CVp are the Coefficients of Variation (Standard Deviation/Mean) of the inter-arrival and processing times (assumed independent)

Operational Performance Measures processing waiting () Ri e.g 10 /hr R () 10 /hr Tw? 10 min, Rp=12/hr Flow time T = Tw + Tp (waiting+process) Inventory I = Iw + Ip Flow Rate R = Min (Ri, Rp) Stable Process = Ri < Rp,, so that R = Ri Little’s Law: I = R  T, Iw = R  Tw, Ip = R  Tp Capacity Utilization = Ri / Rp < 1 Safety Capacity = Rp – Ri Number of Busy Servers = Ip= c = Ri  Tp

Economics of Waiting Line Systems Total Cost= Waiting Cost + Service Cost cost of waiting = # customers in line x cost per unit time per customer = Iw x c OR, if total time in the system is costly: = I x c cost of service = cost per server per unit time x # of servers

Effect of Pooling Pooled service capacity reduces waiting Ri/2 Server 1 Queue 1 Server 2 Queue 2 Ri/2 Ri Ri/2 Server 1 Pooled service capacity reduces waiting Ri Queue Server 2

Key Points: The role of variability Note there is no buffer between stages: Capacity/hr: Capacity/hr: 6/hr 6units/hr 6units/hr 4 or 8/hr 4 or 8/hr 5/hr 2 or 10 2 or 10 4/hr 0 or 12 0 or 12 3/hr As variability increases, throughput (rate) decreases

Dependent Events: Products require more than one step Statistical Fluctuations: Machine and human variations; errors; raw material quality problems; Dependent Events + Statistical Fluctuations Reduced Production Whenever we have dependent events, their fluctuations don’t average out; they accumulate Note that this has significant implication for JIT production systems (systems with very small buffers)– what are they? Need to reduce variability Still need some buffers. Idea can be applied to supply chains as well – Stations are like companies. Actions ? -Reduce variability -Increase buffer (inventory)

Seven Tools for TQM

Lean Operations Paradigm of Lean Operations: Synchronization Tools Strive for the ideal by eliminating waste This is a total business management system Synchronization Tools Reduced batch sizes Pull production control systems (vs. push)—JIT & Kanban control Quality at the source Resource pooling Level loading (Heijunka) Layout: Cellular operations Set up a System for Continuous Improvement Reduce variability (standard operating procedures) Increase visibility (river analogy) Improve human infrastructure J.A. Van Mieghem/Operations/Lean Ops

Key Principles of Process Management Identify and improve bottlenecks (flow rate) Identify and improve critical path (flow time) Eliminate variability as much as possible Eliminate resource interference Use pooling when beneficial: Centralize inventories, use a single line in waiting systems, integrate tasks Postpone differentiation