Supply Chain Management Simulation

1. Supply Chain Management Simulation Taufik Djatna, Dr. Eng.

2. Steady State Model

3. Basic process model with Little’s Law calculations IIT (Interval Time): IF (IIT_STDEV < = 0.0) THEN( IIT_MEAN + STEP(IIT_STEP,300)) ELSE NORMAL(IIT_MEAN,IIT_STDEV) + STEP(IIT_STEP,300) CYCLE TIME: IF (CYCLE_TIME_STDEV < = 0.0) THEN (CYCLE_TIME_MEAN + STEP(CT_STEP,300)) ELSE NORMAL(CYCLE_TIME_MEAN,CYCLE_TIME_STDEV) +STEP(CT_STEP,300) The actual equation in the LLV (Little Law Variable) converter is IF PROCESS > 0 THEN (MEASURED_TP*MEASURED_CT)/PROCESS ELSE 0 TP=ThruPut

4. Steady state behavior PROCESS = THRUPUT*CYCLE TIME Work in Process (WIP) = Thruput*Cycle Time Little’s Law:fundamental relationship for a process.

5. Graph of LITTLE’S LAWVARIABLE with step change in IIT Learning Point: Any aspect of behavior in a model may be because of a real phenomenon or it may be simply because of some attribute of the modeling environment. We should never assume that the behavior is a result of real process behavior without first trying to see if it is related to the modeling environment.

6. Queue Models • In general queuing theory, the work process a server on the units and“service”. The simplest queuing model will have only one server. • It is possibleto have multiple servers in a queuing model. • Typically, servers are assumedto be independent, so the time it takes to process a unit in one server is independentof the time in another server.

7. The M/M/1/GD/∞/∞ queuing model • The capacity of the conveyorWORK PROCESS is set to 1. LAMDA represents the average arrival rate ofitems, and MU represents the average service rate of items. • Parametersaregenerally given the symbols λ and μ respectively. This means that (1/MU) representsthe cycle time for the WORK PROCESS conveyor. The model isdriven off interarrival times and processing times, we will specify these usingrates to be consistent with the large body of literature on queuing theory and applications. • Because the conveyor capacity is set to 1, the determining factor inhow fast the work process (and hence the entire process) can serviceitems =μ. • Thus, the capacity of the process is μ. In queuing models, the ratio λ/μ is knownas the traffic intensity, usually denoted with the symbol ρ. It is considered a fundamentalparameter of the queuing system.

8. Kendall-Lee notation using the format 1/2/3/4/5/6 • Arrivalprocess. A designation of M the interarrival times =random variables with an exponential distribution.G general distribution, Ddeterministic situation with no random variation in the arrivaltimes. The mean arrival rate = λ  meaninterarrivaltime for the units is given by 1/λ. λ representsthe mean value of the thruput. • Servicetimes (the cycle time of the process).The designations are the same as for the interarrival times. The mean servicerate for the units is usually denoted by μ units per unit time. Meancycle time is given by 1/μ. • Number of parallel servers. In our model, this is thecapacity of the work process conveyor. In this chapter, we will study modelswhere this attribute is 1.

9. Queue discipline the way items are removedfrom the queue: First Come, First Served (FCFS) orequivalently, First In, First Out (FIFO). For example: arriving units may have a priority associatedwith them, and they are withdrawn from the queue based on the value ofthis priority. When the queue discipline is not important, it is referred to as GD,for general queue discipline. In this case, we do not have to worry aboutchoosing items from the queue in any particular way. • Maximum number of units allowed in the wholesystem of queue plus server: This attribute is important because there are systemsin which units are not entered into the system if the total number of unitsin the system is already too large. For example in the backlog is greater than what we think the supplier can handle andstill get our order out on time, we may give our order to another supplier.

10. Sizeof the population from which the units aredrawn: When themaintenance process has been completed on a tester unit, it is returned to service.The more units that are being maintained at any one time, the less likelythat a new unit will arrive for maintenance because fewer units are in service.

12. Equations The converters VAR IN LAMDA and VAR IN MU allow us to turn the random variation in LAMDA and MU on and off. The equations in the flows INPUT and FLOW TO WORK PROCESS are as follows: INPUT: (1-VAR_IN_LAMDA)*(1/LAMDA) + VAR_IN_LAMDA*EXPRND(1/LAMDA) FLOW TO PROCESS: (1-VAR_IN_MU)*(1/MU)+VAR_IN_MU*EXPRND(1/MU)

13. Verify the following by running the model at variousvalues of LAMDA and MU: • With LAMDA = MU (ρ = 1), the THRUPUT is 1, the MEASURED CT is 1,and LLV is 1. There is no build up in the queue. • With LAMDA>MU (ρ > 1), there is build up in the queue. No steady state exists and LLV <> 1. • With LAMDA<MU (ρ < 1), the THUPUT equals LAMDA, there is no buildupin the queue and LLV is 1. COV, the coefficient of variation = ratio of the standard deviation of a variable to its mean. Learning Point: A queuing system with random variation in the arrival and service times does not exhibit steady state behavior when the traffic intensity is equal to 1.

14. Profiles with random variation included (traffic intensity, ρ = 1) (1-VAR_IN_LAMDA)*(1/LAMDA_MEAN)+ VAR_IN_LAMDA*NORMAL(1/LAMDA_MEAN,LAMDA_STDEV) (1-VAR_IN_MU)*(1/MU_MEAN)+ VAR_IN_MU*NORMAL(1/MU_MEAN,MU_STDEV)

15. Multistep Serial Workflow Processes Type of process: • Discrete process the product or service is produced asseparated items or units. Examples include complaints handling and tire manufacturing. • Batch process items are processed together as a lot. For example,a machine might be able to handle 30 parts at a time, so the parts are grouped in batches of 30. Service processes tend to be modeled as discrete/batch processes. • Continuous processesdo not produce discrete items. An examplewould be the continuous production of gasoline in an oil refinery. Flow processesare really discrete processes in which the production rate is so high that it appearssomewhat continuous. An example would be the packaging of beer in cans.

16. Serial process represented as a series of conveyors The main variables we want to predict include: • The capacity of the process—that is, the maximum thruput we are able to flow through the process. • The overall cycle time of the process. • The utilization of each process step. The utilization of a step is the fraction oftime that an item is being processed in the step. That is, utilization is the fractionof time a step is occupied with work. • The thruput bottleneck of the process. The thruput bottleneck is the step that islimiting the overall rate at which items can be processed. • The critical cycle time step—this step has the greatest impact on the overall process cycle time. Which steps should we focus on to create the most improvement for the least effort?

17. An order handling process Five-step product development process STEP 1 + QUEUE 1

19. Model fragment for tightly coupled serial processes Learning Point: For a tightly coupled balanced serial process (with exponential random variation), equivalent improvements have a higher impact when applied to the end of the process than to the beginning of the process. Learning Point: Random variation in a tightly coupled process reduces the capacity of the process. Learning Point: Random variation at a step in a tightly coupled process causes blocking upstream and starving downstream.

20. Material control systems

21. CONWIP Material control system The equation in PRODUCT FLOW is therefore IF TOTAL_PRODUCT<TOTAL_ORDERS THEN (TOTAL_ORDERS-TOTAL_PRODUCT)/DT ELSE 0

22. Learning Point: The use of a WIP cap in a pull material control system cansignificantly reduce the variation in WIP (and cycle time) over the equivalent push system. • For a pull system, the risk that an item will be required on the supply side and will not be available. • For a push system, the risk that an item will be required by a customer and will not be available.

23. Multistep Parallel Workflow Processes A serial process was characterized by the following properties: • All items follow the same path. • All items are subject to exactly the same operations. • All items are processed individually.

24. Learning Point: Replacing serial process configurations with parallel configurations can lead to significantly improved performance.

25. Classical Example: Basic fast food restaurant parallel configuration The equation for FLOW TO 1A is this: IF (STEP_1A+STEP_1B+QUEUE_1) = 0 AND STEP_2A = 0 THEN 1/DT ELSE 0 The equation for FLOW TO 1A is this: IF (STEP_1A+STEP_1B) = 0 AND STEP_2A = 0 THEN 1/DT ELSE 0 The equation for FLOW TO 1B is this: IF STEP_2B = 0 THEN 1/DT ELSE 0

26. Model with resource constraints

27. Trade off Concepts

28. Modeling Supply Chains Supply chain as entire set of activities of supply from start tofinish. This definition covers the following: • The physical structure from procurement of raw materials to delivery of finishedproducts to the paying customer. • The demand structure that covers the gathering of demand information and thecreation of orders from that information. • The logical structure that covers information flow and decision making throughout the supply chain. • The financial structure that covers paying suppliers, gathering revenue fromcustomers, and other financial activities that support building of facilities andother operations of the supply chain.

29. Supply chain is a system and must be managed as a system, nodestend to operate in a somewhat independent way.This shows up in many ways: • Node-to-node communication is often poor. • Even when information is available from outside the node, the node may notknow how best to use it. • Performance metrics are node focused. • Decision making works well at the node level but is poor at the supply chain level. • Generally, no one has authority for decision making at the supply chain level.We try to foster “team decisions” and any node will tend to resist decisions thatappear to sub optimize the node locally.

30. Simple supply chain model

31. In real supply chains, three elements of complexity can be present: • Dead time—it takes time for material at any node to reach a node downstream.Also, it can take time for orders to move from a node to a node upstream. • Feedback—performance at any node will be impacted by other nodes. For example,node 3 cannot supply node 4 if it has not been supplied by node 2. • Variability—production rates at nodes can fluctuate, demands can change, and so on. Learning Point: The bullwhip effect in supply chains is the tendency forproduction and order variability to increase as we move upstream in thesupply chain from the customer demand signal.

32. Example of Supply chain simulation The Customer Ordering has the following equation: Initial_Demand+STEP(Demand_Increment_Variable,5) Outflow Satisfying Customer Orders isgiven by the following equation: INT(Customer_Order_Backlog)/DT

33. Customer section of the model

34. Retailer section of the model O = IAF * (ITR − IR + BR) where O is the order rate, ITR is the retailer inventory target, IR is the current retailer inventory level, and BR is the current retailer order backlog (which we know is always 0). IAF (Inventory Adjustment Factor) is a factor that reflects how strong the linkage is between order rate and the inventory difference

35. For component 3, we use the following equation: O = SLF * (SLTR − SLR) Little’s Law (inventory = thruput*cycle time) SLTR = Retailer Orders Data * Supply Transit Time The total order rate is thus the sum ofthe three components. In the model, this is all put into the equation for the inflow Retailer Ordering, which has the following equation: INT(Retailer_Orders_Data + (Inventory_Adjustment_Factor*(Inventory_Target-Retailer_Inventory)/DT) + (Supply_Line_Factor*(Retailer_Supply_Line_Target-In_ Transit_to_Retailer))/DT)

36. The production rate equation is given by the following: MIN(Max_Rate, INT(Brewery_Orders_Data + (Inventory_Adjustment_Factor * (Inventory_Target - Brewery_Inventory + Production_Order_Backlog)/DT) + Supply_Line_Factor * (Brewery_Supply_Line_Target- In_Production_at_Brewery)/DT)) Calculate the total inventory in the system using the converter Total Inventory, which is a summerconverter with the following equation: Brewery_Inventory + In_Production_at_Brewery + Distributor_Inventory + In_Transit_to_Distributor + Wholesaler_Inventory + In_Transit_to_ Wholesaler + Retailer_Inventory + In_Transit_to_Retailer

37. Financial section of the model The converter Net Revenues contains the following equation: Total_Sales_Revenues − Total_Inventory_Cost The equation for the inflow Inventory Costing is the following equation: Total_Inventory*Cost_of_Capital*Beer_Standard_Cost/DT The equation for the inflow Sales Revenue is the following equation: (Sales_Price-Beer_Standard_Cost)*Selling_To_Customer

38. Learning Point: While random variation will increase the extent of the bullwhipeffect in a supply chain, we do not need to include random variationto reproduce the bullwhip behavior Learning Point: Determining the value of IAF depends on each player’sperception of the relative costs of high inventory versus the cost of stockouts. Learning Point: In practical situations, the value of the SLF will tend to be low because players are unlikely to be able or willing to calculate an expectedorder rate based on the supply line.

39. O = IAF * (ITR − IR + BR) • If BR < N1, IAF = IAF1 • If BR < N2, IAF = IAF2 • If BR < N3, IAF = IAF3, . . . . . . where IAF1 < IAF2 <IAF3 < . Learning Point: Even though increasing the Inventory Adjustment Factor,IAF, value ensures that we react faster to inventory fluctuations when supplyis critical, it is typically not a sound strategy for managing a supply chain. Learning Point: In a supply chain, simply making information available to the nodes is not enough to guarantee improved supply chain performance. The algorithm to process the information must also be optimized for the informationsupplied and the supply chain being managed.

40. Modifiy the orders data byintroducing a new parameter, the Demand Information Factor (DIF), and modifyingthe orders equations to the following: Wholesaler: Customer_Ordering*Demand_Information_Factor + (1 - Demand_Information_Factor)*Retailer_Orders_Arriving Distributor: Customer_Ordering*Demand_Information_Factor + (1-Demand_Information_Factor) * Wholesaler_Orders_Arriving Brewery: Customer_Ordering*Demand_Information_Factor + (1-Demand_Information_Factor)*Distributor_Orders_Arriving

41. Distributor ordering profile for DIF = 0 and 1 Variation of net revenues with demand information factor, DIF

42. Modifications to the basic model • Adding random variation to the order delay times and supply transit times. • Adding random variation to the customer demand signal • Using the nonlinear response equation • Using different values of IAF, SLF, and DIF at each node to see if a relationshipexists between position in the chain and the impact of these parameters. • Using different order delay times and supply transit times at each node to see ifa relationship exists between position in the chain and the impact of these parameters. • Alternative financial models of performance for the supply chain

43. Main user interface to model

44. Model interface

45. THANK YOU • QUESTION PLEASE................. • DISCUSSION ...........................