CHAPTER 1
INTRODUCTION
1.1 0-1 Knapsack problem
The 0-1 Knapsack Problem is an example of a combinatorial optimization problem, which seeks for a best solution from among many other solutions. It is concerned with a knapsack that has positive integer volume (or capacity) V. There are n distinct items that may potentially be placed in the knapsack. An item i have a positive integer, volume Vi and positive integer benefit Bi. In addition, there are Qi copies of the item i available, where quantity Qi is a positive integer satisfying 1 ≤ Qi ≤∞.
Let Xi determines how many copies of item i are to be placed into the knapsack. The goal is to:
Maximize
N
∑ Bi Xi i = 1
Subject to the constraints
N
∑ Vi Xi ≤V i = 1
And
0 ≤ Xi ≤ Qi
If one or more
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• Cutting stock: In industrial application of cutting stock, optimization methods are carefully programmed for each new task. ATLBO algorithm could be used to give better suggestions.
• Budget control: For large scale budget management it is difficult to handle lots of computerized data and need rapidly of optimization, there is ATLBO algorithm able to play a very important part in managing the budget of long time.
• Financial management: Financial management is the basic need for all types of organization so there is various technologies for monitoring and maintaining money, proposed ATLBO algorithm could be suggest better management results.
1.6 Structure of the Thesis
This dissertation consists of seven chapters. The first chapter provides a general introduction and overview of the area of research, including a general introduction of 0-1 knapsack problem, Teaching learning based optimization (TLBO) and problem definition. The motivation is discussed along with the scope of the study and
Budget management analysis is used by mangers as a tool and helps determine that all resources available are being used efficiently. The budgets are determined yearly and are based upon the previous year’s budget and variances. This paper will discuss specific strategies to manage budgets within forecast, compare five to seven expense results with budget expectations, describe possible reasons for variances, give strategies to keep results aligned with expectations, recommend three benchmarking techniques, and identify those that might improve budget accuracy, and justify the choices made.
into a portfolio with the weight in asset A ranging between 0 and 1 in increments of 0.10.
This research paper is a brief discussion of budget management analysis. Budgeting is the key to financial management, and is the key to translates an organization goals or plan into money. Budgeting is a rough estimate of how much a company will need to get their work done, and provides the basis for evaluating performance, a source of motivation, coordinating business activities, a tool for management communication and instructions to employees. Without a budget an organization would be like a driver, driving blinded without instructions or any sense of direction, that’s how important a budget is to every organization and individual likewise (Clark, 2005).
The dynamic programming within RACT Algorithm can find the optimal solution for the 0/1 knapsack problem (12). Therefore, we need to show the optimal solution of the 0/1 knapsack problem with quantized real-valued weights.
The following linear programming problem has been written to plan the production of two products. The company wants to maximize its
Methods and apparatuses are provided that employ an improved greedy algorithm for addressing NP-Hard problems and others like them. The improved greedy algorithm considers possible local savings while also remaining significantly fast.
Z multi = 0.5 × [1.49155 – 0.0000938× X(1) distance preferences – 0.049155 × X(2) arrival demand time + 0.0006566 × X(3) no. of carts + 0.0005628 × X(4) velocity of carts] – 0.5 × [1.4642 – 0.0005717×X(1) distance preferences – 0.049406 × X(2) arrival demand time + 19 × X(3) no. of carts + 0.0006390 × X(4) velocity of carts]
In a transportation problem, a demand constraint (the amount of product demanded at a given destination) is a less-than-or equal-to
The following linear programming problem has been written to plan the production of two products. The company wants to maximize its profits.
Problem #2.” (To make your life easier, optimal stocking quantity, Q, is computed by the
Most entities and organization create budgets as a guide for controlling its spending, prediction of profit, and it expenditure as they progress toward a set goal. Budget involves pulling resources together to achieve a specific goal. According to Gapenski (2006), budgeting is an offshoot in a planning process. A basic managerial accounting tool use in holding planning and control functions together is referred to as set of budgets (p. 255). One major setback manager or budget developer encounter is trying to design a future, a process that cannot be created with the precision just right. This article highlights some financial management
Q3. Suppose you want to add commodities into your investment opportunity set in addition to cash, domestic equity, and domestic bonds. What is your optimal asset allocation decision in this case, i.e., how should you allocate your fund across cash, domestic equity, domestic bonds, and commodities? What is the Sharpe ratio of your optimal complete portfolio?
Budgetary control is part of overall organisation control and is concerned primarily with the control of performance. The use of budgetary control in performance management has of late taken on greater importance especially as a more integrative control mechanism for the organisation. Discuss.
Exact optimisation method is the optimisation method that can guarantee to find all optimal solutions. In principle, the optimality of generated solution can be proofed mathematically. Therefore, exact optimisation is also termed as mathematical optimisation. However, exact optimisation approach is impractical usually. The effort of solving an optimisation problem by exact optimisation grows polynomially with the problem size. For example, to solve a problem by brute force approach, the execution time increases exponentially respect to the dimensions of the problem.
Along with the development of globalization, companies must have an efficient system to keep the competitive advantage. The broad application of new technology gives a basis to the advent of ABB. Nowadays, more and more companies start to use ABB in the budgeting process. Referring to ABB, companies do well in their budgeting period. This shows that ABB itself has many outstanding characters. In this article we will compare it with traditional budget method, so that it could give us a general survey about the characters and benefits ABB has.