Computation Section
Subunit Inventory Game
 - Policies

The stochastic inventory problem is an example of decision making under uncertainty. The problem is simply stated and the model of the game is well known. Still finding a good sequence of ordering decisions is not easy. Although it is not too hard to obtain a solution for a specific instance, we need a policy that describes a set of rules that specifies when an order should be placed and how much should be ordered. The policy should be a function of the current and past data concerning the inventory system. The most general policy would also be a function of the parameters of the system. Inventory theory provides insights to this question, but how do we implement a policy on our worksheet model?

The simplest way to do this is to enter formulas in the control (green) areas of the solution table. The formulas can address any cells on the worksheet, but to be realistic, they should only use information from the current or previous periods. To enter a formula, the worksheet must be Unprotected. The commands for Protection are found on the Tools menu of Excel. Once the formulas are entered, the simulation button can test the quality of the policy with repeated simulations. When testing a policy do not click the Restart button. That button erases the contents of the control column.

The method we have just described is hindered because many of the rows and columns of the worksheet have been hidden to make the game easier to play. Also many details of computation are hidden, rather than confuse the user. For full access to the contents of the worksheet. Select the Relink command from the Simulation add-in menu.

The command reveals all the hidden rows and columns and replaces the buttons with those directly linked to the Simulate add-in. This is indicated by the red color for the buttons in the figure below. To understand the workings of this worksheet refer to the instructions for the Simulation add-in. The worksheet is unprotected and provides much more detailed information about the situation. Policies can easily be described by formulas in the control column and tested with the Simulate button. The backorder model is illustrated, but a similar worksheet underlies the lost sales game.


The worksheet will be returned to its original hidden form by clicking the Start button on the Start_BO worksheet. The red buttons of the Simulate add-in are replaced by the blue buttons of the Inventory Game.

The subject of Inventory Theory provides guidance about policies for operating the simple systems reflected in these games. Policies for deterministic systems are described in the Inventory Theory section of the OM/IE Operations section. The Inventory add-in of the OM/IE Computations section provides optimal solutions for (r, q) policies for the backorder and lost sales models.

Changing the Game

The teacher or student can easily change features of the game. The easiest changes are the parameters of the model presented in the initial dialog. The strategy of play and the appropriate policy certainly depends on the lead time and the various cost parameters.

A more interesting game would have demand governed by seasonal effects or driven by a time series with steps and trends. It is not difficult to create a time series model with the Simulation add-in. The formula for the demand on the game worksheet can be directed to the demand created by the time series.

The Simulation add-in together with Excel equations and functions provide unlimited possibilities for changing features of this game or for creating new games. If you create something useful and interesting, this author would be glad to hear about it. Use the Contacts link to send a message.

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tree roots

Operations Management / Industrial Engineering
by Paul A. Jensen
Copyright 2004 - All rights reserved

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