Business Management
(a) (2+2 = 4 pts) Find the value of the objective function and verify that the constrains are satisfied when 1. x1=O,x2=1,x3=1 = 0, X2 = 0, X3 = 1 State an assignment which optimises the objective function.
Solution. Let OPT(j, R) represent the smallest capacity of the knapsack to earn a total revenue of exactly R when selecting from objects from 1 to j. Let Vj represent value of the jth object and Wj the weight of the jth object. So now let us suppose we know all answers till j-1. Now for finding answer for j,R we have two choices-Do not take the jth object. In this case answer is same as answer of j- I,R Take the jth object. Now the answer will be Wj more than the ans for R-Vj since we want R as the revenue after taking this object of value Vj. Also note that if R l Vj we cannot take this object. So here is the final recurrence So if R i= Vj OPTU, R) = min(OPT(j – I, R), OPT(j – I, R – Vj) + Wj) otherwise if R i Vj OPTa R) = OPT(j – I, R) and OPT(l, 0) = 0 for all j = 0 to n. This is beacuse 0 value requires 0 capacity. and OPT(0, R) = infinite for all R i 0. This is because without selecting any element it’s impos-sible to generate a non 0 revenue. For practical purposes we will take infinite as a very large number like INTA, AXincpp.
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(b) (2 + 2 + 2 = 6 pts) Now we formulate the TSP (covered in lecture) as a ILP problem. A salesman wishes to visit each of n — 1 other cities and return home at a minimal cost (there are n cities in total). He must visit each city exactly once and it costs cii to travel from city i to city j. You have to determine the most efficient (the least expensive) route. Assume that each city is connected to every other city. The constraints require that the salesman must enter and leave each city exactly once. To model this problem as an ILP instance, we introduce the following decision variables.
1 if the salesman goes from city i to city j and i j xid = _ 110 otherwise
i. What is being optimised in this problem? State the objective function. Solution. ii. State two constraints to enforce that the salesman enters and leaves each city exactly once. Solution. iii. Are these constraints sufficient to specify TSP as an ILP problem? Explain your answer with an example where the number of cities, n = 6. Solution.
Sample Solution
This paper pays a close look at the practice management of human resources in an organization. This will encompass the importance of the practice, functions within this office and some of the motivation techniques that can be used as well as their role in achieving organizational objectives. Furthermore, the paper will focus an attention to a reputable organization in determining the applicability of incentives and compensation in HRM. Every organization has its strategic future which is broken down into objectives that are measurable and comprehensible, so that the workforce can implement (Snell & Bohlander, 2009). The sensitivity and value placed on organizational strategic plan cannot be left in the hands its employees if they are incapable or not motivated. The organization has a responsibility not only to invest heavily in technology and detailed professional processes but also on its workforce and strategic management policies. Discussion Importance of HRM HRM as a practice significantly offers support and advice to the line management within an organization. Management of human resources must ensure an attraction, preservation, loyalty and development of highly profiled caliber of people/workforce in order to provide a competitive advantage necessary for the survival and success of the organization. The image of an organization, which develops the goodwill, is largely dependent on how well its human resources are managed (McCoy, 1999). The management of the human resources assumes the following roles. First, HRM manages the demand for human resources. Economies in which organizations are based are dynamic. There are economical shifts of growth and decline that require counteractive measures within an organizations workforce. The said measures demands both quantitative and qualitative procedures within the workforce. The practices of retrenchments, hiring, early retirements and the contract renews for the experienced are all structural adjustments that responds to economical changes affecting organizations. Second, HRM is responsible in managing social pressure in provision of the desirable environment for the workforce. The hygiene and safety of the working environment must be always maintained as it is a motivation factor in employees’ performance. The provision of appropriate protective gear while working, pollution free environment and other working conditions is a paramount concern for the HRM office Berger, 2008). Third, HRM is important in managing political pressure usually generated by calls to hire from local labor market irrespective of the resultant factors of cost and knowledge/skills. Though it is ethical to hire from the contextual economy, political pressure should not compromise the quality and quantity of organization’s production and a resulting failure in achie>
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