The Simplex Solution Method

The simplex method is a general mathematical solution technique for solving linear programming problems. In the simplex method, the model is put into the form of a table, and then a number of mathematical steps are performed on the table. These mathematical steps in effect replicate the process in graphical analysis of moving from one extreme point on the solution boundary to another. However, unlike the graphical method, in which we could simply search through all the solution points to find the best one, the simplex method moves from one better solution to another until the best one is found, and then it stops. The manual solution of a linear programming model using the simplex method can be a lengthy…

Capacity Planning Model

Abstract: Capacity planning decisions affect a signiﬁcant portion of future revenue. In equipment intensive industries, these decisions usually need to be made in the presence of both highly volatile demand and long capacity installation lead times. For a multiple product case, we present a continuous-time capacity planning model that addresses problems of realistic size and complexity found in current practice. Each product requires speciﬁc operations that can be performed by one or more tool groups. We consider a number of capacity allocation policies. We allow tool retirements in addition to purchases because the stochastic demand forecast for each product can be decreasing. We present a cluster-based heuristic algorithm that can incorporate both variance reduction techniques from the simulation literature and…

Optimization of portfolio risk

This paper is a critique one the article entitled “Post-Modern Portfolio Theory” by Swisher and Kasten (2005). The framework for this critique is to determine whether there ground to agree or disagree on the claims of the authors as against the evidence they presented. Swisher and Kasten asserted about the unreliability of Modern portfolio theory (MPT) and its mean-variance optimization (MVO) model for asset allocation in the financial services industry particularly on building portfolios. They instead suggested the use of post-modern portfolio theory (PMPT) which presents a new method of asset location that optimizes a portfolio based on return versus downside risk (down side optimization, or DRO) instead of MVO. What makes PMPT different from PMT as explained by the…

Variable Cost and Following Table

EM 505 – Decision Models, Fall 2012 Homework 3 – December 10-11, 2012 1. The diagram below depicts a system of aqueducts that originate at three rivers (nodes R1, R2 and R3) and terminate at a major city (node T) where the other nodes are junction points in the system. Using units of thousands of acre feet, the tables below show the maximum amount of water that can be pumped through each aqueduct per day and the following diagram shows the network of the system. The city water manager wants to determine a flow plan that will maximize the flow of water of the city. Formulate this problem as a max flow problem by identifying a source, a sink and…

Operation Research

INTRODUCTION & HISTORY OF OPERATIONAL RESEARCH Operational research came into existence in 1885 when Frederick W. Taylor emphasised the application of scientific analysis to methods of production. The name (OR) probably came from a programme under taken by Great Britain during world war2, “research in military operations”. After the success of OR in military operations, it quickly spread to all phases of Industry and Government. By 1951, OR had take place as a distinct science in the United States. Hence it is said that Or is “the art of winning war without actually fighting it”. OPERATIONAL RESEARCH IN INDIA: In India OR society founded in 1959, also became a member of International Federation of OR Societies in 1959. Now OR…

Recommending a Low-Cost Customer Service

Executive Summary Acme De Mexico’s Manager has requested assistance in developing a minimum cost daily assignment schedule for the customer service employees in their newly built store. Specifically, he wants to know the minimum total cost per day, which is the decision variable. He also wants to know the exact amount of part time and full time employees which will determine the total cost. The objective function is to minimize costs. Acme specified a minimum number of employees required for each shift, a maximum number of employees per shift, specific shifts for full time and part time workers, and a maximum percentage of 50% of the total hours for part time employees. These constraints were input into Microsoft solver, which…

Quain Lawn and Garden, Inc. Case Analysis

After a false retirement Bill and Jeanne Quain realized their destined action in the plant and shrub business. The need for a high-quality commercial fertilizer prompted the innovation of a blended fertilizer called “Quain-Grow”. Working with chemists at Rutgers University, a mixture was constructed from four compounds, C-30, C-92, D-21 and E-11. Specifications (i.e constraints) for the mixture demanded that Chemical E-11 must constitute for at least 15% of the blend, C-92 and C-30 must together constitute at least 45% of the blend, and D-21 and C-92 can together constitute no more than 30% of the blend. Lastly, Quain-Grow is packaged and sold in 50-pound bags. The objective of this analysis is to determine what blend of the four chemicals…

Merton Truck

Keeping 3000$ and 5000$ as unit contributions respectively for Model 101 and Model 102 trucks, formulate the Merton’s product mix decision problem using LP. Present the LP problem in the standard form including all the details and units. Using solver, find the optimal product mix of these two trucks? What is the optimum total contribution that Merton can obtain? Tabulate, the optimality range for the decision variable coefficients and comment what will happen if the current unit contribution moves outside the range? Tabulate, the feasibility range for each constraint’s capacity and comment what will happen if the current capacity moves outside the range? Due to increase in Engine component’s material cost, the unit contribution for Model 101 came down to…

BDM midterm

Ralph Edmund loves steak and potatoes. Therefore, he has decided to go on a steady diet of only these two foods for all his meals. Ralph realizes that this is not the healthiest diet, so he wants to make sure that he eats the right quantities of the two foods to satisfy some key nutritional requirements. He has obtained the following nutritional and costs data. The Oak Works is a family owned business that makes hand crafted dining room tables and chairs. They obtain the oak from a local tree farm, which ships them 2500 pounds of oak each month. Each table uses 50 pounds of oak while each chair uses 25 pounds of oak. The family builds all the…

Girl Power

Sensitivity analysis helps to test the sensitivity of the optimum solution with respect to changes of the coefficients in the objective function, coefficients in the constraints inequalities, or the constant terms in the constraints. For Example in the case study discussed: The actual selling prices (or market values) of the two products may vary from time to time. Over what ranges can these prices change without affecting the optimality of the present solution? Will the present solution remain the optimum solution if the amount of raw materials, production time, or storage space is suddenly changed because of shortages, machine failures, or other events? The amount of each type of resources needed to produce one unit of each type of product…