“Batching Policy in Kanban Systems” IE 561 Paper Presentation “Batching Policy in Kanban Systems” Uday S. Karmakar Sham Kekre

Kanban Developed at Toyota car plants, To smooth the flow of products throughout the production process. Aim is to Improve system productivity, Secure operator involvement. Later, developed as a means of production activity control to achieve goals of JIT. Serves as an information system to control production quantities at every stage of manufacturing.

Kanban A Kanban System is a control mechanism used in a manufacturing cell. A manufacturing cell consists of: A production process, An inventory storage location.

Properties of the Kanban Scheme 1.Produce in multiples of a minimum quantity or batch. A batch has a card (container). 2.The number of cards (containers) in the system is fixed. Inventory in process is fixed. 3.Production is only initiated if a free card (container) is available. A card is a “work order”. It triggers the system.

Kanban Scheme It controls: Production inside a manufacturing cell, Transportation between cells. Two types of cards exist: Withdrawal kanban, Production kanban.

Examples for withdrawal kanban and production kanban.

Effect of batch sizing on production lead times. The paper studies: Effects of: Batch sizing, Card count. on the expected costs of : Inventory holding, Backorder. Effect of batch sizing on production lead times.

The paper examines 3 different configurations of a Kanban system: Single Card - items within the production cell are controlled by the Kanban scheme. - production kanban is used. Dual Card - transportation out of cells are also controlled. - withdrawal kanban, production kanban used. 3. Two-Stage Kanban System - Two manufacturing cells in series, one feeding the other.

Assumptions on the model: - Demand to facility follows Poisson, - Free cards queue for production, - Cell is processing single item class, - As batch sizes change, average demand arrival and production rates per batch change.

State of the system is represented in terms of: The number of cards on order, The number of cards in finished inventory, The number of batches on backorder.

A Single Card Kanban System A cell producing a single item in batches, Each batch corresponds to a card. Number of batches in process is fixed. Demand arrive according to Poisson, Production time for a batch is exponentially distributed.

Notation for single card model

Semi-infinite birth death process for single card kanban

Conclusions: for large q, cost is asymptotically linear Lot sizing is very critical when u is high more containers For small q, cost diverges

A Dual Card Kanban System Transportation of finished items is controlled by kanban system. M: number of withdrawal kanbans that are needed to draw from finished inventory of the cell.

Two-Stage Kanban System

Conclusions: Larger the Q, inventory holding costs at both stages grow ~ linearly. Smaller the Q, shortage costs rise for any choice of the card numbers.

CASE: Changing number of containers at each stage; No general analytical results at hand, The approach is making conclusions by numerically studying specific cases.

Variation of costs with number of containers at each stage

CASE: Changing number of containers as well as batch size; No general analytical results at hand, The approach is - Fix number of containers at a stage, - Search for optimal number of containers for other stage, - Search for optimal batch size.

With fixed number of stage 2 containers; Optimal cost and batch sizes with varying cards for stage 1

With fixed number of stage 1 containers; Optimal cost and batch sizes with varying cards for stage 2

Concluding Remarks Batch size for each card has significant effect on the performance of Kanban System. Effect of number of cards is significant. There’s an interaction between card numbers and batch size. For multi-stage Kanban; parameters at one stage affects performance at other stages. Kanban systems can be optimized through the control of its parameters.