1/ Setup time and batch size reduction Factory Automation Laboratory Seoul National University July 23, 1999 Byun, MyungHee

2/ A workload balancing model for determining set-up time and batch size reductions in GT flow line work cells R.R.GUNG and H.J.STEUDEL Supply Chain Optimization, IBM Manufacturing Industry Solutions Lab, USA IE, University of Wisconsin-Madison, USA INT. J. PROD. RES., 1999, VOL 37, No 4,

3/ Contents Introductions Capacity constraints A workload balancing model Heuristic model to determine the MWL Performance improvement Illustrated example Conclusions

4/ Introduction The need for reduced inventory costs and shortened manufacturing lead times is prompting companies to reduce their production batch sizes. But, the batch size’s reduction means that the number of set-up operations are increased. So, Set-up time reduction has become a prerequisite for batch size reduction. However, reduction plan is not always beneficial and cost effective.

5/ Introduction- Objective of the study To present a general approach to guide the selection of set- up time and batch size reductions in order to improve the performance of a flow line work cell. Measure - average job-throughput time - WIP inventory level

6/ Capacity constraints(1/3) The total capacity constraints (the theory of constraints : Goldratt) for any production unit, T ik expected set-up + cycle time for a job of part i at workstation k N i expected number of job arrivals of part i for the year Q k total number of production hours available for the year at workstation k npt total number of unique part types nws total number of workstations in the cell

7/ Capacity constraints(2/3) The total capacity constraints in the queuing theory - the job arrival rate must be less than the service rate. - the reason for this phenomena the stochastic arrival process can occasionally cause the system to become idle, and the loss of service capacity is never gained back.

8/ Capacity constraints(3/3) For the flow line work cell, the reserved capacity constraint is expressed as follows. U k capacity cushion at workstation k

9/ A Workload Balancing Model The minimum level of set-up time reduction(SR) required at each workstation for a given level of batch size reduction. MWL maximum allowed machine workload n k number of machines at the workstation k z k number of shifts that the workstation k operates SM set-up time multiplier which is dependent on the degree of batch size reduction(BR) : SM = (1-BR) -1

10/ Example of the concept of workload balancing model

11/ Rationale explanation(1/2) When original utilization is less than MWL - utilization increases to MWL  average number of jobs(L) increases : average WIP increases batch size = 1/SM × original sizes So, If L is less than SM × original number of jobs, average WIP inventory level will decreases. Little’s law w=L/ (w : average job-throughput time) job arrival rate = SM × original arrival rate if the increased L is less than SM × original average number of jobs, the average job-throughput time will decrease.

12/ Rationale explanation(2/2) When original utilization is higher than MWL - utilization will be reduced to MWL  average number of jobs(L) decreases : average WIP will decrease, average job-throughput time will decrease.  Based on the above rationale, only workstations with low utilization tend to deteriorate performance. So, in such case, a lower level of MWL has to applied to each workstation.

13/ Heuristic model to determine the MWL(1/3) -Based on GI/G/1 queuing model STEP 1 : Determine base model’s dynamic parameters external job arrival process job arrival rate mean, square coefficient of variation(s.c.v) for the service time service time s.c.v for the inter-arrival time

14/ Heuristic model to determine the MWL(2/3) STEP 2 : Evaluate base model’s performance average number of jobs average batch size of jobs average WIP inventory level average job-throughput time

15/ Heuristic model to determine the MWL(3/3) STEP 3 : Determine new model’s dynamic parameters Calculate SR with a selected MWL alternative Follow STEP 1 to calculate the parameters STEP 4 : Evaluate new model’s performance Follow STEP 2 to calculate the parameters STEP 5 : Adjust MWL

16/ Performance improvement(1/2) Percentage improvement of cell performance Percentage improvement of average job-throughput time

17/ Performance improvement(2/2) -M/M/1 model is used

18/ Illustrated Example- simulation study Using actual data from a U-shaped flow line work cell for gear manufacturing Six workstations, production capacity = hours Maximum feasible reduction in batch sizes = 90%(1 < SM  10)

19/ Illustrated example -design setting

20/ Illustrated example- results

21/ Conclusions A model is proposed in this paper which determines the amount of set-up time reduction at each workstation for a given level of batch size reduction, in order to improve the performance of a flow line work cell. To ensure the cell performance improvement, a heuristic model is presented to determine the maximum allowed machine workload(MWL).

22/ Investment policy for multiple product setup reduction under budgetary and capacity constraints Avijit Banerjee, Vijay R.Pyreddy, Seung Lae Kim Department of Management & Organizational Sciences, College of Business & Administration, Drexel University, Philadelphia, USA Int. J. Production Economics 45 (1996)

23/ Contents Introduction Assumptions Notations and Model Heuristic procedures Numerical Illustrations Conclusions

24/ Introduction This paper examines the impact of setup reduction on the lot sizes, inventory levels and total relevant cost in a batch manufacturing process, that produces several items with similar setup reduction functions, under budget and capacity constraints. More specifically, the amount to be invested in setup reduction for each product and the resultant decreases in its batch size and relevant cost.

25/ Assumptions for this paper Simple and inexpensive methods have already been taken. A convex setup reduction function Adopting the common cycle approach to obtain schedule feasibility. Setup cost is directly proportional to the setup time Setup sequence is independent.

26/ Notations and Model(1/2) K i amortized annual investment in setup reduction for product i Q i production batch size of product i Nnumber of common cycles for all products per year L i /U i lower/upper limit of setup cost of product i S i (K i ) setup cost of product i as function of investment S i t (K i ) setup time of product i expressed in hours bproportionality constant i.e. S i (K i ) = b S i t (K i ) mtotal number of products kvector of investment K i Ttotal time available for setup and production all the products over a year

27/ Notations and Model(2/2) TRC : annual total relevant cost per year subject to

28/ Heuristic Procedures(1/2) STEP 1 : Solve the unconstrained problem about (P1) STEP 2 : Check for violation of the constraints (2)&(3) Case a : If both the constraints are satisfied, solutions are optimal. Case b : If (2) is satisfied, and (3) is violated, calculate N from (3) This value of N and K i * represent a feasible solution.

29/ Heuristic Procedures(2/2) Case c : If (3) is satisfied and (2) is violated, determine the ratio K i * /  i K i * feasible solution K i = ratio × K and recalculate N Case d : If both (2) and (3) are violated, recalculate K i and N as case c If current N satisfies (3), it is feasible. else, recalculate N as case b.

30/ A numerical illustration(1/2)

31/ Example -Results and Discussion(2/2) Without any investment in setup reduction, : cycle = 31, total relevant cost = $ per year Because this problem exceeded the solvers capabilities, it is applied in the heuristic procedures. : cycle = 101, total relevant cost = $ per year K 1 =$3869, K 2 = $3955, K 3 = $4062, K 4 = $4015, K 5 = $4100 But, setup reduction programs may not always result in improvements. If setup reduction don’t yield any benefits, K i will be zero.

32/ Concluding remarks This paper extends the current literature, not only by addressing the case of multiple products, but also by taking into account limitations on the total budget available for investing in setup reduction. Similar constraints on other resources can be readily incorporated in our suggested model. Our results of example are better than other report based on the basic period approach.

33/ References M.KUULA, A.STAM, S.LEINO, J.RANTA and J.WALLENIUS, 1999, Workload balancing in the manufacturing environment: a multi-criteria trade- off analysis, IJPR VOL. 37, No. 7 박순달, 1994, Operations Research( 경영과학 ), 민영사