Supply Chain Management Simulation

Taufik Djatna, Dr. Eng.

Steady State Model

Basic process model with Little’s Law calculations

The actual equation in the LLV (Little Law Variable) converter isIF PROCESS > 0 THEN (MEASURED_TP*MEASURED_CT)/PROCESS ELSE 0

IIT (Interval Time):

IF (IIT_STDEV < = 0.0) THEN( IIT_MEAN + STEP(IIT_STEP,300)) ELSENORMAL(IIT_MEAN,IIT_STDEV) + STEP(IIT_STEP,300)

CYCLE TIME:

IF (CYCLE_TIME_STDEV < = 0.0) THEN (CYCLE_TIME_MEAN+ STEP(CT_STEP,300)) ELSENORMAL(CYCLE_TIME_MEAN,CYCLE_TIME_STDEV)+STEP(CT_STEP,300)

TP=ThruPut

Steady state behavior

PROCESS = THRUPUT*CYCLE TIME

Work in Process (WIP) = Thruput*Cycle Time Little’s Law:fundamental relationship for a process.

Graph of LITTLE’S LAW VARIABLE with step change in IIT

Learning Point: Any aspect of behavior in a model may be because of a realphenomenon or it may be simply because of some attribute of the modelingenvironment. We should never assume that the behavior is a result of realprocess behavior without first trying to see if it is related to the modelingenvironment.

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 possible to have multiple servers in a queuing model.

• Typically, servers are assumed to be independent, so the time it takes to process a unit in one server is independent of the time in another server.

The M/M/1/GD/∞/∞ queuing model• The capacity of the conveyor WORK PROCESS is set to 1. LAMDA

represents the average arrival rate of items, and MU represents the average service rate of items.

• Parameters are generally given the symbols λ and μ respectively. This means that (1/MU) represents the cycle time for the WORK PROCESS conveyor. The model is driven off inter arrival times and processing times, we will specify these using rates 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 in how fast the work process (and hence the entire process) can service items = μ.

• Thus, the capacity of the process is μ. In queuing models, the ratio λ/μ is known as the traffic intensity, usually denoted with the symbol ρ. It is considered a fundamental parameter of the queuing system.

Kendall-Lee notation using the format 1/2/3/4/5/6

1. Arrival process. 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 arrival times. The mean arrival rate = λ mean interarrival time for the units is given by 1/λ. λ represents the mean value of the thruput.

2. Service times (the cycle time of the process). The designations are the same as for the inter arrival times. The mean service rate for the units is usually denoted by μ units per unit time. Mean cycle time is given by 1/μ.

3. Number of parallel servers. In our model, this is the capacity of the work process conveyor. In this chapter, we will study models where this attribute is 1.

4. Queue discipline the way items are removed from the queue: First Come, First Served (FCFS) or equivalently, First In, First Out (FIFO). For example: arriving units may have a priority associated with them, and they are withdrawn from the queue based on the value of this 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 about choosing items from the queue in any particular way.

5. Maximum number of units allowed in the whole system of queue plus server: This attribute is important because there are systems in which units are not entered into the system if the total number of units in the system is already too large. For example in the backlog is greater than what we think the supplier can handle and still get our order out on time, we may give our order to another supplier.

6.Size of the population from which the units are drawn: When the maintenance 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 likely that a new unit will arrive for maintenance because fewer units are in service.

Equations

The converters VAR IN LAMDA and VAR IN MU allow us to turn the randomvariation in LAMDA and MU on and off. The equations in the flows INPUT andFLOW 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)

Verify the following by running the model at various values 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 buildup in the queue and LLV is 1.

Learning Point: A queuing system with random variation in the arrival andservice times does not exhibit steady state behavior when the traffic intensityis equal to 1.

COV, the coefficient of variation = ratio of the standard deviation of a variable to its mean.

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)

Multistep Serial Workflow ProcessesType of process:1. Discrete process the product or service is

produced as separated items or units. Examples include complaints handling and tire manufacturing.

2. 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.

3. Continuous processes do not produce discrete items. An example would be the continuous production of gasoline in an oil refinery. Flow processes are really discrete processes in which the production rate is so high that it appears somewhat continuous. An example would be the packaging of beer in cans.

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 of time

that an item is being processed in the step. That is, utilization is the fraction of time a step is occupied with work.

• The thruput bottleneck of the process. The thruput bottleneck is the step that is limiting 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?

An order handling process

Five-step product development process

STEP 1 + QUEUE 1

Model fragment for tightly coupled serial processes

Learning Point: Random variation in a tightly coupled process reduces thecapacity of the process.

Learning Point: Random variation at a step in a tightly coupled processcauses blocking upstream and starving downstream.

Learning Point: For a tightly coupled balanced serial process (with exponentialrandom variation), equivalent improvements have a higher impactwhen applied to the end of the process than to the beginning of the process.

Material control systems

CONWIP Material control system

The equation in PRODUCT FLOW is thereforeIF TOTAL_PRODUCT<TOTAL_ORDERSTHEN (TOTAL_ORDERS-TOTAL_PRODUCT)/DT ELSE 0

• Learning Point: The use of a WIP cap in a pull material control system can significantly 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.

Multistep Parallel Workflow Processes

A serial process was characterized by the following properties:

1. All items follow the same path.2. All items are subject to exactly the same

operations.3. All items are processed individually.

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

Classical Example: Basic fast food restaurant parallel configuration

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 1A is this:IF (STEP_1A+STEP_1B+QUEUE_1) = 0AND 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

Model with resource constraints

Trade off Concepts

Modeling Supply Chains

Supply chain as entire set of activities of supply from start to finish. This definition covers the following:

• The physical structure from procurement of raw materials to delivery of finished products to the paying customer.

• The demand structure that covers the gathering of demand information and the creation 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 from customers, and other financial activities that support building of facilities and other operations of the supply chain.

Supply chain is a system and must be managed as a system, nodes tend 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 not know 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 that appear to sub optimize the node locally.

Simple supply chain model

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 for production and order variability to increase as we move upstream in the supply chain from the customer demand signal.

Example of Supply chain simulation

The Customer Ordering has the following equation:Initial_Demand+STEP(Demand_Increment_Variable,5)

Outflow Satisfying Customer Orders is given by the following equation: INT(Customer_Order_Backlog)/DT

Customer section of the model

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 retailerinventory level, and BR is the current retailer order backlog (which we knowis always 0). IAF (Inventory Adjustment Factor) is a factor that reflects how strongthe linkage is between order rate and the inventory difference

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 of the three components. In the model, this is all put into the equation for the inflowRetailer 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)

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 summer converter 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

Financial section of the model

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

The converter Net Revenuescontains the following equation:Total_Sales_Revenues − Total_Inventory_Cost

• Learning Point: While random variation will increase the extent of the bullwhip effect in a supply chain, we do not need to include random variation to reproduce the bullwhip behavior

Learning Point: Determining the value of IAF depends on each player’s perception 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 below because players are unlikely to be able or willing to calculate an expected order rate based on the supply line.

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 supply is critical, it is typically not a sound strategy for managing a supply chain.

Learning Point: In a supply chain, simply making information available tothe nodes is not enough to guarantee improved supply chain performance.The algorithm to process the information must also be optimized for the information supplied and the supply chain being managed.

• Modifiy the orders data by introducing a new parameter, the Demand

Information Factor (DIF), and modifying the 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

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

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

relationship exists 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 if a relationship exists between position in the chain and the impact of these parameters.

• Alternative financial models of performance for the supply chain

Main user interface to model

Model interface

THANK YOU

•QUESTION PLEASE.................•DISCUSSION ...........................