Sequencing Mixed Models & Unpaced Lines Active Learning Module 4 Dr. César O. Malavé Texas A&M University

Background Material Modeling and Analysis of Manufacturing Systems by Ronald G. Askin, Charles R. Standridge, John Wiley & Sons, Manufacturing Systems Engineering by Stanley B. Gershwin, Prentice – Hall,1994, Chapter 2. Any good manufacturing systems textbook which has detailed explanation on mixed models and unpaced lines.

Lecture Objectives At the end of this module, the students would be able to Explain the fundamentals of sequencing mixed models. Explain the basics of unpaced lines. Solve various problems related to these topics.

Time Management 3Assignment 9Unpaced Lines 5Summary 50 MinsTotal Time 10Team Exercise 15Sequencing Mixed Models 5Readiness Assessment Test (RAT) 3Introduction

Readiness Assessment Test (RAT) Discuss the basic features of Group Technology Layout and Just-In-Time Layout

RAT – Solution Group technology (GT) layout – Dissimilar machines are grouped into work centers or cells – Similar to process layout in that cells are designed to perform a specific set of processes –Similar to product layout in that cells are dedicated to a limited range of products Just-in-Time layout – Flow line similar to an assembly line Equipment and workstations arranged in sequence – Job shop or process layout Focus on simplifying material handling

Sequencing Mixed Models Several different products can be assembled simultaneously on the line. Products are generally classified as  Type 1 – Products with constant ratio of item task time to average item task time.  Type 2 – Products with independent station requirements.

Sequencing Mixed Models Let q j → Proportion of product type j, j=1,…,P t ij → Time to perform task I on product type j S k → Set of tasks assigned to workstation k An average feasibility is

For each item ‘j’, Q j items to be produced ‘r’ be the greatest common denominator of all Q j. Cycle repeats for r times to satisfy demand. Repeated cycle consists of N j = Q j / r Bottleneck station k b is the station with maximum total work. k b = argmax k C k X jn be 1 if item j is placed in nth position & 0 otherwise j(n) denotes the type of item placed nth Sequencing Mixed Models

Selecting the nth item to be entered in the line is to optimize the following problem Sequencing Mixed Models Subject to j = 1,.., p……… n = 1,.., N & j = 1,…, P... n = 1,.., N & k = 1,…, K … 0 or

Sequencing Constraints Constraints: 1  Ensures that all the products are produced. 2  Restricts the production rate of each product to be within s1 of its average time at all times. This controls production rate to suitably match utilization. 3  Limits maximum utilization at all times.

Step 0 : Initialization. Create a list of all products to be assigned during the cycle. This is List A Step 1 : Assign a Product. For n = 1,….,N from List A, create a List B of all product types that could be assigned without violating any constraint. From List B select the product type ( j*) that minimizes Add product type j* to the nth position. Remove a product type j* from A and if n < N, go to 1. Sequencing Heuristics

Sequencing Example Bottleneck station is assigned with workload of 68 seconds/cycle. Actual workload by model type for that station is provided in the table. ModelSales%Time Red Z Blue Q Black R RWB American

Example – Solution 1 Red, 1 Blue, 2 Black, 2RWB per cycle. Set s 1 = s 2 = 0.9 StageRed ZBlue QBlack RRWB American Assigned 11/6, 41/6, 01/3, 01/3, 2Black 21/3, 41/3, 0-1/3, 02/3, 2Blue 31/2, 4 - 0, 01, 2RWB 42/3, 2 -1/3, 21/3, 4Red /3, 22/3, 0RWB , 0 -Black

Team Exercise Three products are produced on the same line. One half of the demand is for A, the other half is evenly split between B & C. Find a repeating cycle without building unnecessary inventories or shortages. The following table gives the bottleneck machine times. ModelTime A100 B95 C105

Exercise – Solution Repeating Cycle : N A = 2, N B = 1, N C = 1, N = 4 Let Max Inventory(±) < 1 StageABCCum.Time (Excess) Assignment 1+0.5, , , (0)A 2*+1.0, 0+0.5, , (-5)B 3+0.5, , 0300 (0)C 40, (0)A * Assume A undesirable due to inventory accumulation

Unpaced Lines Let K - number of stations C - Cycle times S k - the sum of task times for tasks assigned to station k. k b - bottleneck machine All the times are deterministic

Unpaced Lines Let us divide the line into 2 lines as 1 to k b & k b +1 to K Station 1 to k-1 work faster than k b Each item has to spend s k b to avoid the inventory pile at each machine Throughput time for Line 2 is sum of all station times. Combining the lines, production time in system is

Unpaced Line - Illustration Let S 1 = 2, S 2 = 4, S 3 = 3 ItemEnter 1Leave 1Enter 2Leave 2Enter 3Leave 3Flow Time

Assignment Find a repeating cycle for entering product onto the mixed model line. Demand and the bottleneck process times are shown below. ProductDemandTime A B50040 C75045 D50050 E25055

Summary Assembly lines have greatly enhanced production because one objective : Producing good product Advances in computational speed makes it possible to find optimal solutions for many problems. Mixed model cases are handled by unpaced lines, has advantage of allowing variability in assembly times. Paced lines avoid need to remove and replace the products on the transport mechanism. Little work has been done on modeling the full range of practical consideration in assembly line design.