Sequencing Mixed Models & Unpaced Lines

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

2. Background Material • Modeling and Analysis of Manufacturing Systemsby 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.

3. 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.

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

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

6. 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

7. 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.

8. Sequencing Mixed Models • Let qj → Proportion of product type j, j=1,…,P tij→ Time to perform task I on product type j Sk → Set of tasks assigned to workstation k • An average feasibility is

9. Sequencing Mixed Models • For each item ‘j’, Qj items to be produced • ‘r’ be the greatest common denominator of all Qj. Cycle repeats for r times to satisfy demand. • Repeated cycle consists of Nj = Qj / r • Bottleneck station kb is the station with maximum total work. kb = argmaxkCk • Xjn be 1 if item j is placed in nth position & 0 otherwise • j(n) denotes the type of item placed nth

10. Sequencing Mixed Models • Selecting the nth item to be entered in the line is to optimize the following problem Subject to j = 1,.., p ……… 1 n = 1,.., N & j = 1 ,…, P ... 2 n = 1,.., N & k = 1 ,…, K … 3 0 or 1

11. Sequencing Heuristics 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 Bof 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.

12. 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.

13. Example – Solution • 1 Red, 1 Blue, 2 Black, 2RWB per cycle. • Set s1 = s2 = 0.9

14. 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.

15. Exercise – Solution • Repeating Cycle : NA = 2, NB = 1, NC = 1, N = 4 • Let Max Inventory(±) < 1 * Assume A undesirable due to inventory accumulation

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

17. Unpaced Lines • Let us divide the line into 2 lines as 1 to kb & kb+1 to K • Station 1 to k-1 work faster than kb • Each item has to spend skb 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

18. Unpaced Line - Illustration • Let S1 = 2, S2 = 4, S3 = 3

19. Assignment Find a repeating cycle for entering product onto the mixed model line. Demand and the bottleneck process times are shown below.

20. 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.