1. Managing Kanban Systems Two primary control parameters for a Kanban System. Kanban container size (n i ) Number of Kanbans (k i )

2. Managing Kanban Systems Determining Kanban container size (n i ): Based on physical size of container Based on cost function – where c 1ij – fixed material handling cost per time using technology j. c 2ij – variable cost per time D i – demand for item i h i – holding cost for item i

3. Managing Kanban Systems Determining Kanban container size (n i ): To minimize the cost function with respect to n i,

4. Managing Kanban Systems Determining Kanban container size (n i ): Ex. Consider a process with 3 distinct operations and demand of 200,000 per year and an annual holding cost of $2 per unit per year. Option Annual cost Cost per trip Max load size Manual $27,000 $.15 2 Push Cart $28,000 $.16 20 Forklift $50,000 $.90 500 Manual – n i,man * = = 300 cost = Push cart – n i,push * = = 310 cost = Forklift – n i,fork * = = 735 cost = n ij * is greater than the kanban container size for Manual, Push Cart, and Forklift, therefore use container size.

5. Managing Kanban Systems Determining Number of Kanbans (k i ): Determined by lead time(  i ) to replenish – represents the amount of inventory needed to cover the time between when a Kanban is sent from the output buffer to be refilled, until it returns filled. The number of kanban is – where l is a safety factor.

6. Managing Kanban Systems How is lead time (  i ) determined? By observation – start with “too many” kanbans in the system. Mark the time when a kanban leaves the output buffer to be replenished. Record when the kanban returns to the output buffer. Record a number of observations and find the mean and standard deviation. To build in a safety factor, the lead time should be calculated as the mean plus 2 or 3 standard deviations.

7. Managing Kanban Systems Determining Production Quantity: Although rapid setup times are necessary for a kanban system to function effectively, there may be cases where technological or cost constraints make further reduction of setup time prohibitive. Let s i = setup time for item i. D i = annual demand for item i. Q i = lot size item i. t i = time to produce item i. Find the minimum Q i that satisfies:

8. Managing Kanban Systems Determining Production Quantity: Let s i = setup time for item i. D i = annual demand for item i. Q i = lot size item i. t i = time to produce item i. Find the minimum Q i ‘ that satisfies: Then Q i = Max{n i,Q i ‘}.

9. Managing Kanban Systems Key factors which must be in place before implementing a kanban system: Demand is approximately constant over a planning period Small setup times Available, flexible capacity Disciplined workforce

10. Managing Kanban Systems Managing demand variances. Some products demand rates tend to vary by the seasons, but with some known forecast. How can a Kanban system be implemented in this type of environment? Recall the number of kanban was found using: If we can forecast D for some next time period, we can add or subtract kanbans from the system accordingly.