Inventory

Introduction

Whether in manufacturing, wholesale or retailing, business enterprises are almost always doing battle with a tricky dynamic phenomenon: oscillations in inventory. This simple model illustrates some of the causes of (and suggests solutions to) oscillation in inventory control.

One way to test the stability of a model is to observe its reaction to stimulus. Here, certain time functions in Powersim are used to stimulate a simple inventory model--with interesting results. Specifically, generating external disturbances by means of the time functions STEP, RAMP, PULSE, and SINWAVE produces varying degrees of oscillations in an otherwise stable-state (equilibrium) structure.

To make the model a bit easier to experiment with, we've provided interactive elements to control some of the variables in the system. Powersim's Button and Slider input objects make it easy to vary parameters and observe changes in the model behavior from run to run, without having to type new values in to redefine variables.

Model

Causal Loop Diagram

The causal loop diagram shows the feedback processes that control inventory accumulation. The diagram comprises two reinforcing and two balancing feedback loops.

B1 is a balancing (or negative) feedback loop depicting the causal relationship between the orders received and the level of inventory. An increase in the level of inventory will reduce the inventory adjustment required to meet the desired level of inventory. A reduction in inventory adjustment, on the other hand, decreases the actual orders made and subsequently the orders received (all things being equal).

B2 is another balancing loop depicting the relationship between the level of inventory and shipments made. An increase in shipment depletes the level of inventory, while an increase in the stock of inventory leads to an effort to ship more.

R1 is a reinforcing (positive) feedback loop depicting the causal relationships among shipment, desired inventory, inventory adjustment and the orders placed. An increase in the shipment made leads to an increase in desired inventory to make up for the shortfall. The higher the desired inventory, the greater the inventory adjustment which, in turn, increases orders.

R2 is another reinforcing loop depicting the direct causal relationships among shipment, average shipment and orders. An increase in daily shipment leads to an increase in the average shipment over time; higher average shipment requires that more orders be made to cover an increased daily shipment.

Flow Diagram

Some important assumptions of the model include:

•	Shipment to customers is made from the stock of inventory.

•	Desired inventory is determined by a fixed normal shipments multiplied by the desired inventory coverage, which equals three weeks' worth of anticipated shipments.

•	Orders are determined by averaging prior shipments and correcting the discrepancy between the desired and actual inventory.

•	Orders received is a "third-order" material delay of orders placed.

Features

Button

Powersim's Button object is extremely useful for providing multiple-choice inputs to a model. We've set up the first set of buttons to allow choosing from among different predefined stimulation scenarios:

The four scenarios all affect the shipment rate. In order, they are:

STEP(10,10) results in a 10 unit step increase in the shipment rate at time 10

RAMP(20,10) increases the shipments by 20 units each time unit starting at time 10

PULSE(10,10,200) pulses the shipment rate by 10 units at time 10

STEP(SINWAVE(10,25),15) starts a sinewave at time 15

Depicted graphically, they look like this:

Our second use of the Button is simply as a switch to determine whether there is any "noise" in the shipment rate (in this case, a Random function that varies shipments over a range, a bit more realistic than keeping them constant):

Slider

Powersim's Slider provides an easy means of varying a model's parameters over a range. The input portion of the Slider/Bar object--the companion Bar, as the name implies, provides a bar-graph output to display the value of a variable during a simulation--the Slider thus allows you to interact with the model during the simulation by changing one of its predefined constants.

The Sliders give you control over three important elements in the system. They are:

TimeDelay Number of weeks it takes to receive materials for which orders are placed.

TimeToAverageShipment Number of weeks it takes to average shipment.

DesiredInventoryCoverage Number of weeks that the inventory could cover shipments.

The default settings of the Sliders and Buttons are set at:

•	The Time Delay is 3 months.

•	The Time to Average Shipment is 2 months.

•	Desired Inventory Coverage is equal to 3.

•	The test Input is set at STEP.

•	Noise is turned On.

Running the simulations produces, as indicated above, some interesting results. Note that, using the sliders, you can vary the delays while the simulation is running.