Software Review
QMS 1.1
Software provides comprehensive collections of modules with user-friendly interfaces.
By Clarence "Red" Martin and Kenneth Cutright
Quantitative Methods Software Version 1.1 (QMS) is a comprehensive collection of software modules that covers nearly every topic that could be included in an introductory quantitative methods or operations research course. QMS was introduced in 2004 by QuantMethods (www.quantmethods.com) in response to the need for a lower cost, greater ease-of-use and deployment flexibility software package. The authors have extensive experience in academics, technology and business.
QMS is the descendant of decision support software (DSS), introduced in 1990 as a DOS-based application. Over its life, approximately 20,000 units were adopted by a number of universities, including Northwestern, Texas Wesleyan University and the University of Texas at Arlington. By the late 1990s, college coursework and personal computer systems had advanced to the point where there was a need for a graphical interface that could run in a number of computer environments and in a variety of configurations.
QMS has been through three minor revisions and a major revision. The latest version, released in May 2006, includes several popular production operations management modules. To date, it has sold subscriptions through several universities, as well as private enterprise, and several of the computational algorithms have been sub-licensed to an electronic book publisher (AtomicDog Publishers).
QMS has a variety of licensing and deployment options:
- It is available on a subscription basis from the QMS Web site (www.quantmethods.com). The standard subscription provides interactive browser access via the Internet for a period of six months at a cost of $19.95.
- It is published on a CD by Thomson Publishing. The CD can be installed on Microsoft Windows, Apple Mac and Linux workstations. See http://asp.thomsoncustom.com/products/title.asp?Isbn=0759394903.
- It can be site-licensed for a departmental server for access by students on the local school network. Site licenses are sold on a quote basis.
One of the strongest points of QMS is the excellent documentation in the form of a user's manual and help system. The manual is very well done, often with more than one example for each module and includes sample input and output screens. The help system provides immediate access to essential information regarding the module and includes context-specific online help with hyperlinked content throughout. Figure 1 shows a QMS documentation regarding the linear programming module.
Figure 1: QMS documentation for linear programming module.
Data entry is also a strong point. The user will appreciate the consistency of the easy-to-use data input schemes across the various modules. Figure 2 shows a typical input screen.
Figure 2. QMS input screen for decision analysis module.
Illustrative Problems
Basketball team selection via 0-1 programming. This problem is a goal programming formulation of a problem of selecting a starting basketball team with multiple goals based on players characteristics including statistics from regular season play (obviously a classroom example rather than a real-world application). The starting team is to be selected from 12 players and there are eight goals which are treated as "meet or fail" to meet (binary) variables (close only counts in horseshoes and hand grenades). The 0-1 programming models has 20 binary variables (12 players plus eight goals) and 12 constraints (four hard constraints and eight goals constraints). As such it represents about as large a problem as one would expect to encounter in an introductory OR/MS course.
Figure 3 shows a portion of the input screen for this problem. Solution of the problem requires about 5 seconds and Figure 4 and Figure 5 show portions of the output screen.
Figure 3. QMS input screen for basketball team selection problem.
Figure 4. QMS output screen for basketball team selection problem.
Figure 5. QMS output screen for basketball team selection problem.
Markov Chain Problem
Figure 6 provides a graphical illustration of a Markov chain consisting of three transient states (A, B and D) and two absorbing states (C and E).
Figure 6. State diagram for Markov chain problem.
This simple Markov chain was selected so that the behavior is intuitively obvious. Figure 7 displays a portion of the QMS output screen which show the initial state probabilities were 1.0 for A and 0 for the remaining states. Figure 8 shows the remainder of the output screen displaying the steady-state solution and a graphical display of the state probabilities versus the number of periods.
Figure 7. QMS output screen for Markov chain problem.
Figure 8. QMS output screen for Markov chain problem.
Mathematical Programming Models
The following are brief descriptions of the modules available in QMS.
Linear programming. The linear programming module uses the tableau version of the simplex method. It has four output options, each of which includes full sensitivity analysis. They are: 1) solution only, 2) first and last tableaus, 3) all tableau summaries, and 4) all full tableaus. Sensitivity analysis includes both constraints and variables with range analysis. Upper and lower bounds (other than zero) are handled as regular constraints. If the LP has two variables, a graphical display of the feasible region, objective function level lines and the optimum solution are provided as illustrated in Figure 9.
Figure 9. Graphical illustration in linear programming module.
Integer linear programming. The integer linear programming module uses a standard branch and bound approach built upon the linear programming module. Variables can be declared as real, binary or integer, so both mixed integer and zero-one options are treated. Problem size will, in most cases, be limited by the amount of computation time and computer memory available. The one display option is solution only.
Assignment problem. The assignment problem module uses the Hungarian algorithm to solve either minimization or maximization problems. Output options are solution only or the default, which shows all tables generated during the solution process.
Transportation problem. The module for solving the transportation problem uses the standard stepping-stone, tableau method for either minimization or maximization problems. Initial solution options are northwest-corner, best-cell and Vogel's method. Display options are solution only or the complete set of tableaus encountered during the solution process.
Network Models
(The system permits networks input in any of the network modules to be transferred to the other modules, saving the effort of re-entering the network.)
CPM/Pert Network. Uses the activity-on-arc representation of projects. The PERT method asks for the standard optimistic, pessimistic and most-likely estimates for activity duration.
Minimum spanning tree. An effective approach for this easy to formulate and solve problem.
Shortest path. Solves for the minimum time or distance from a single start node to a single end node.
Maximum flow/minimum cut. Solves the maximum flow/minimum cut problem by the classical labeling procedure of Ford and Fulkerson. Display options are solution only or the sequencing of steps in the solution process. The arcs belonging to the minimum cut are not specified in the solution. Alternate optimal solutions are common.
Traveling sales representative module. Utilizes an inconvenient data input approach which is arc-by-arc data entry rather than a matrix style. The module works well, with the solution showing the forward and reverse passes. Problem size is limited by the computational requirements. The "box canyon" problem is identified and solved.
Forecasting Models
Averaging. The methods used here are moving average, weighted moving and exponential smoothing. Graphical displays of actual values and averages are included in the solution display.
Linear regression. A standard regression module whose solution display includes all the values one would produce in a manual calculation, r, r-squared, standard error, MAD and a graphical display of X-Y values.
Inventory and Production Models
(The system permits common inputs in one module to be transferred to the other modules, saving the effort of re-entering the data.)
Economic order quantity with discounts. Provides for a single price break along with the usual EOQ. The reorder level based on a specified lead time is calculated. Demand is assumed to be deterministic, so safety stock is zero. Holding, ordering, purchasing and total annual costs are computed. Output includes a graphical display of inventory level over time.
Economic order quantity with stockouts. Adapts EOQ to deal with stockouts. Output includes a graphical display of inventory level over time.
Economic production lot size. Looks at EOQ from the point of view of production lot size. Output includes a graphical display of inventory level and cumulative production over time.
Dynamic Programming Models
Knapsack. Solves the knapsack problem where weight, value and availability of each item are accepted as inputs. Although no limits are specified, the algorithm will break down if too large availabilities are specified. Output includes a pie graph of the optimum composition of the knapsack.
Stagecoach. Implements the classical stagecoach model (i.e., multi-stage, shortest path problem) which has been used to introduce dynamic programming to untold numbers of students.
Production planning. Solves single-product, multi-period production planning problems in which demand, minimum production, maximum production, storage limit, setup cost, unit cost and holding cost are specified by period. Although no limits are specified, the algorithm will break down if too large production quantities are allowed.
Decision Theory Models
Decision analysis. Applies a number of different criteria to decision situations that are typically characterized in a payoff matrix in which options are selected and subsequent events occur (with experiments possibly intervening). Criteria under uncertainty are maxi max, maxi min, mini max regret (Savage) and Hurwicz. Criteria for decisions under risk are Laplace, maximum expected payoff and minimum expected regret. Bayesian decision methods address scenarios in which experimentation is possible and utilize a contingency table approach to Bayesian revision of probabilities.
Queueing System Models
Queues. Determines queue performance for the M/M/s queuing model with Poisson arrivals, exponential service-time distribution, multiple servers and infinite population and waiting space. Output includes mean time in queue and system, mean number of customers in queue and system, probability of waiting, and tabular and graphical display of individual system occupancy probabilities.
Finite Markov Chain Models
Markov chains. This module is cast as a Markov chain representation of a market share scenario. For example, the initial state probabilities are referred to as "initial market share." However, different scenarios could still be modeled with this module. The module simply updates the initial state probability vector by multiplying by the transition probability matrix until convergence to steady state is observed. Output includes tabular and graphical displays of these intermediate state probability vectors as well as the steady state solution.
Learning Curve Models
Learning curves. Calculates the unit processing times associated with learning curve behavior. The learning rate can either be specified as input or determined from a set of sample data. Output includes tabular and graphical displays of both predicted and historical data in linear or log format.
Simulation inventory model. Allows the user to specify one of six probability distributions for the daily sales volume and for the lead time. It also permits selection of the reorder stock level and the number of inventory cycles to be simulated.
Output shows the lead time (in days), the demand during lead time for each cycle, and the resulting number on hand or backordered. The ending inventory for each cycle is presented in graphical form. Changing the reorder quantity permits the user to determine a value that keeps stockouts at an acceptable level. A very useful tool for investigating the reorder level and demand-during-leadtime relationship in stochastic inventory problems
Queuing. This simulation of a queuing system allows the user to specify one of six potential probability distributions for arrivals and services: constant, uniform, normal, Poisson, negative exponential and discrete (allows custom specification of distribution). Outputs include tabular display of arrivals, departures and number in system along with a graphical display of number in the system.
Production/Operations Management Models
Site location model. The user supplies the X & Y coordinates and the demands (weights) for each of the destinations to be served by a proposed distribution center (warehouse or manufacturing site). The model computes the weighted centroid as well as the straight line distance from the centroid to each of the destination sites.
Breakeven analysis. Takes the fixed and variable costs and the selling price and computes the breakeven cost and volume. A profit function is generated, and the total cost, total revenue and profit functions are displayed graphically and in tabular form.
Make-or-buy. The fixed and variable costs and the buy cost are required inputs. The breakeven cost and volume are computed, and a graphical display is provided, showing the optimal decision as a function of the projected quantity.
Cost-volume analysis. The user specifies the fixed and variable costs for two or more alternatives, and the breakeven cost and volume are computed and displayed in tabular and graphical formats.
Multicriteria decision-making. The decision-maker specifies the decision criteria and whether each is a maximization or minimization measure, along with the weight assigned to each criterion. The user supplies the values for each alternative (bidder) under each of the selected criteria. Inputs can be in any metric (square feet, dollars, acres, miles, etc.) or in rank (1st, 2nd, etc.). Inputs are converted to ordinal data, weighted, and the preferred alternative(s) is/are identified.
Conclusions
QMS 1.1 is an easy-to-start MS/OR software package well suited for use in an introductory course in management science and/or decision science. There is no need to have understanding of any programming languages or the ability to write programs. It extensively covers the important topics in decision science or management science. The interfaces are user-friendly for both inputting the data as well as the graphical outputs that are easy to understand. One of the strong attributes of the software is the built-in ability to generate intermediate outputs for how-to analysis. Online help is available for each individual module that facilitates quick responses to student inquiries and questions. Each module is accompanied by demo examples that walk the user through the steps to use the module. Furthermore, context-sensitive help to explain the operations of the models and to help with inputs and interpretation of results is included with the software.
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Clarence "Red" Martin holds a Ph. D. in operations research from the Graduate School of Industrial Administration at Carnegie-Mellon University. He served on the faculty of the Department of Industrial & Systems Engineering at Ohio State University before coming to Ohio University in 1985. He has served as a consultant to several companies in the areas of production planning, scheduling, forecasting and facility configuration.
Ken Cutright has been at Ohio University since 1984. He spent five years teaching in the Russ College of Engineering and Technology before moving to the College of Business. He received a Ph.D. in industrial engineering from West Virginia University. He is chair of the Management Systems Department in the College of Business at Ohio University and teaches in the area of operations management and quantitative business analysis.
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