Supply Chain Models Jayendran Venkateswaran IEOR @ IIT Bombay
Inventory model with supply line Quantity in Inventory Transit DELIVERY Rate Order Rate Sales Rate + + Supply Delay - Inventory Gap Desired Order Rate + + - + Desired Inventory Time to Adjust Inventory • But Supply Line information is Expected Sales Rate Change in Sales not used in decision making Fraction Adjusted IEOR, IIT Bombay IE 604: System Dynamics Modelling & Analysis Jayendran Venkateswaran
Accounting Supply line in Decisions • How do we consider the supply line (i.e., past and pending orders in transit) when we make new ordering decisions? • Adjust In-transit inventory in reference to a Desired In-transit – Similar to how we adjusted inventory levels • Update Desired Order Rate to include this adjustment IEOR, IIT Bombay IE 604: System Dynamics Modelling & Analysis Jayendran Venkateswaran
Model with Supply Line Adjusted Quantity in Inventory Transit DELIVERY Rate Order Rate Sales Rate + + - Supply Delay Adjustment for intransit - + - Adjustment for Desired Intransit inventory Time to adjust quantity + Desired Inventory intransit + - Desired Order Rate Time to Adjust Inventory + Expected Sales + Desired Delivery Rate Change in Sales • Underlying equations Fraction Adjusted • Update your model, simulate and observe the results. – Save model as InventorySL.mdl IEOR, IIT Bombay IE 604: System Dynamics Modelling & Analysis Jayendran Venkateswaran
Model with Supply Line Adjusted (2) • Observe the results • Does system reach equilibrium? • What are the equilibrium values of the stocks? Comment. IEOR, IIT Bombay IE 604: System Dynamics Modelling & Analysis Jayendran Venkateswaran
How much should be in Supply Line • Typically, how much In-transit do we need to maintain? • How to determine the Desired Intransit quantity ? • Desired In-transit quantity = Desired Delivery*Supply Delay • Update your model, simulate and observe the results. • Save model as Retailer.mdl IEOR, IIT Bombay IE 604: System Dynamics Modelling & Analysis Jayendran Venkateswaran
How much Desired Inventory? • How can we set the Desired Inventory? • Typically based on the number of weeks of inventory coverage desired. • Note: – Desired Inventory will be based on the management’s decision – Desired In-transit Quantity to be determined as per Little’s Law IEOR, IIT Bombay IE 604: System Dynamics Modelling & Analysis Jayendran Venkateswaran
Simultaneous Initial Conditions • The model to start in dynamic equilibrium. • What should be the initial values of the stocks? – When initial Sales is 0 kg/day – When initial Sales is 10 kg/day IEOR, IIT Bombay IE 604: System Dynamics Modelling & Analysis Jayendran Venkateswaran
Your Retailer Model to look like this Quantity in Inventory Transit DELIVERY Rate Order Rate Sales Rate + + - Supply Delay Inventory Adjustment for intransit - Coverage + - + + Adjustment for Desired Intransit inventory Time to adjust quantity + Desired Inventory intransit + + - + Desired Order Rate Time to Adjust Inventory + Expected Sales + Desired Delivery Rate Change in Sales Fraction Adjusted • In Model >> Settings, set smaller TimeStep until no significant change in dynamics – Choose time step to be about one-eighth the value of the smallest time constant in the model IEOR, IIT Bombay IE 604: System Dynamics Modelling & Analysis Jayendran Venkateswaran
Fulfilling Customer Orders • The customer orders can be fulfilled only when we have required inventory. Typically, inventory is a non-negative quantity, representing the physical availability of goods. – Orders not immediately filled are lost forever. • Create new variable, Customer Orders (kg/Day) • Sales Rate = ? • Anything else to be changed? • Change in Sales = Customer orders - Expected Sales IEOR, IIT Bombay IE 604: System Dynamics Modelling & Analysis Jayendran Venkateswaran
Complete Retailer Model Quantity in Inventory Transit DELIVERY Rate Order Rate Sales Rate + + + - Max Sales Rate Supply Delay - Adjustment for intransit - Min Order + - + Processing Delay Adjustment for Desired Intransit Customer Order Rate inventory Time to adjust quantity intransit + + + - Desired Inventory + Desired Order Rate + Time to Adjust Inventory Inventory Coverage + Expected Sales + Desired Delivery Rate Change in Sales + - Fraction Adjusted IEOR, IIT Bombay IE 604: System Dynamics Modelling & Analysis Jayendran Venkateswaran
Supply chain: Model Distributor • Till now, we have a model of the Retailer. • Let’s suppose the Distributor has exactly the same decision structure as Retailer. • Replicate Retailer structure for Distributor – Copy your Retailer.mdl as Retailer-Distributor.mdl – Open Retailer-Distributor.mdl file. – Set Zoom to 50% – Click in the white area, Click Crtl+A and Crtl+C – Click Crtl+V – Press on any black area and Drag the black area to right of the model area. – Let all the variables with ‘0’ in them denote Retailer IEOR, IIT Bombay IE 604: System Dynamics Modelling & Analysis Jayendran Venkateswaran
Link Retailer and Distributor • The Customer Orders of Distributor is the Desired Order rate 0 of Retailer • The Order rate 0 of Retailer is determined by the Sales Rate of the Distributor • Simulate and observe the results. Note: It is good modeling practice to give proper names to variables. Avoid subscripts. Can you think of appropriate names for Distributor echelon? IEOR, IIT Bombay IE 604: System Dynamics Modelling & Analysis Jayendran Venkateswaran
Customizing Model • For Retailer: – Supply Delay = 2 days – Inventory Coverage = 4 days – Time to adjust inventory = 3 days – Time to adjust inTransit = 3 days Suppose End Customer Order – Min Order Processing Delay = 1 day Rate = 10 • For Distributor: Kg/Day, – Supply Delay = 4 days Simulate the – Inventory Coverage = 8 days model in dynamic – Time to adjust inventory = 3 days equilibrium – Time to adjust inTransit = 3 days – Min Order Processing Delay = 1 day IEOR, IIT Bombay IE 604: System Dynamics Modelling & Analysis Jayendran Venkateswaran
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