Shruti Speak's

Inventory theory is concerned with the design of inventory systems to minimize costs. Observation of almost any company balance sheet reveals that a very significant part of its assets comprise inventories of raw materials, products within the production process, or finished products. How do companies use operations research to improve their inventory policy for when and how much to replenish their inventory? They use scientific inventory management comprising of the following steps: 1. Formulate a mathematical model describing the behavior of the inventory system. 2. Seek an optimal inventory policy with respect to this model. 3. Use a computerized information processing system to maintain a record of the current inventory levels. 4. Using this record of current inventory levels, apply the optimal inventory policy to signal when and how much to replenish inventory. The mathematical inventory models used with this approach can be divided into two broad categories—

Dynamic programming  (referred to as  DP  ) is a very powerful technique to solve a particular class of problems. It demands elegant formulation of the approach and simple thinking. The idea is very simple, If you have solved a problem with the given input, then save the result for future reference, so as to avoid solving the same problem again. If the given problem can be broken up into smaller sub-problems and these smaller sub-problems are in turn divided into smaller ones, and in this process, if you observe some over-lapping sub-problems, then its a big hint for DP. Also, the optimal solutions to the sub-problems contribute to the optimal solution of the given problem. There are two ways of doing this. 1.) Top-Down :  Start solving the given problem by breaking it down. If you see that the problem has been solved already, then just return the saved answer. If it has not been solved, solve it and save the answer. This is usually easy to think of and very intuitive. This is

The graphical method is applicable to solve the LPP involving two decision variables x 1 , and x 2 , we usually take these decision variables as x, y instead of x 1 , x 2 . To solve an LPP, the graphical method includes two major steps: a)   The determination of the solution space that defines the feasible solution.  Note that the set of values of the variable x 1 , x 2 , x 3 ,....x n which satisfy all the constraints and also the non-negative conditions are called the feasible solutions of the LPP. b)   Finding the optimal solution from the feasible region. a)To determine the feasible solutions of an LPP, we have the following steps: Step 1: Consider only the first quadrant of xy-coordinate plane(because both the variables x 1 and x 2 are non-negative). Step 2: Each equation is of the form ax+by≤c or ax+by≥c. Draw the line ax+by=0. For each equation, the line divides the first quadrant into two regions say R 1 and

Big-M Method The Big-M method of handling instances with artificial  variables is the “commonsense approach”. Essentially, the notion is to make the artificial variables, through their coefficients in the objective function, so costly or unprofitable that any feasible solution to the real problem would be preferred, unless the original instance possessed no feasible solutions at all. But this means that we need to assign, in the objective function, coefficients to the artificial variables that are either very small (maximization problem) or very large (minimization problem); whatever this value,let us call it Big M . In fact, this notion is an old trick in optimization in general; we  simply associate a penalty value with variables that we do not want to be part of an ultimate solution(unless such an outcome is unavoidable). Indeed, the penalty is so costly that unless any of the  respective variables' inclusion is warranted algorithmically, such variables will never be p