BUSOBA 2321 Final Exam | Verified with 100% Correct Answers

BUSOBA 2321 Final Exam | Verified with 100% Correct Answers What question are we trying to answer when performing sensitivity analysis? How sensitive is our solution to changes in the assumptions that we made? T or F: The optimal solution will not always be at a corner point False - it always will be since this is where two constraints are maxed out - more resources = more production = more optimal T or F: The assumptions made in our linear program formulation (i.e. how much profit we will be able to make per unit of a particular product) may change based on market conditions - which we do not have control over. True Define shadow price The change in the OBJ FN value if we increase one constraint by one unit. By solving for the shadow price of a constrained resource, what question are we answering? If we have a additional unit of the constrained resource available, how much could our OBJ FN value increase by? How do we know if the addition of a constraing will result in the OBJ FN value increases, staying the same, or decreasing? An additional constraint will never increase the OBJ FN VAL. If the constraint is redundant (i.e. it is already being adhered too; there is another constraint that is more restrictive than this new constraint), our OBJ FN val wiull remain the same - the feasible region will not change. If it is not redundant (is not already being adhered to - the addition of this constraint decreases our feasible region), our OBJ FN val will decrease What are the two sections of a sensitivity report? 1. adjustable cells 2. constraints For what type of constraint (what sign) might slack exist? maximums; < For what type of constraint (what sign) might surplus exist? Minimums > Why might the allowable increase of a constraint be infinite? If slack already exists - if we already aren't using up all of what we currently have available, we will never gain anything by increasing the availability of the resource. Why might the allowable decrease of a constraint be infinite? if a surplus already exists - no matter how much the RHS of the constraint decreased, no additional value would be added because we are already above the current minimum - making the minimum lower would not help us. If surplus exists, what is the allowable increase for the constraint? the amount of the surplus if the minimum increases to our current amount of production, the constraint will then be binding and thus the shadow price will become a non-zero value If surplus exists, what is the allowable decrease for the constraint? Infinity If slack exists, what is the allowable increase for the constraint? Infinity If slack exists, what is the allowable decrease for the constraint? the amount of the slack decreasing by this amount will mean that we would be using all of the resource - it would then be binding and the shadow price would change When a constraint is binding, the shadow price is a non-zero value When a constraint is not binding, the shadow price is Zero For what reasons might the optimal solution omit one of the decision variable (i.e. produce zero) 1. there is no constraint that requires the production of that product 2. it has the lowest profit margin Provide two definitions of reduced cost 1. The minimum amount by which the OFC of a DV needs to change to cause that DV to have a nonzero value (AKA to include it in the optimal solution) 2. The amount by which the OBJ FN val would change if we were forced to include one unit of that DV in our optimal solution rather than zero T or F: the reduced cost is a value associated with a constraint. False - The reduced cost is a value associated with a decision variable. How is the reduced cost calculated? marginal Cont. to OBJ FN Val - marginal value of resources used What is the marginal value of the resources used by a DV? Sum of the products of the # of units of the resource used in production of 1 unit of the DV and the shadow price of that resource In general, under what circumstance would a DV not be included in the optimal soluton? if it has a nonzero reduced cost i.e. if what is gained by producing this product is less than the value of the resources that would be used up in producing this product - resources that could go towards producing a different product which contributes more heavily to the OBJ FN Val What rule do we used to determine whether our sensitivity report is still valid after changing multiple values (I.e. multible OFCs -OR- multiple RHS's)? 100% Rule If the Sum of change/allowable change values is less than 100%, then the shadow prices in our sensitivity report are still valid. If changing multiple values at once while performing sensitivity analysis, how do we calculate the net effect on the OBJ FN value? (Change in units 1)(Shadow Price 1) + (Change in units 2)(Shadow Price 2) How would you go about answering the following question?: a new government regulation that product Z requires an additional unit of raw material C. Is the solution still optimal multiply the current number of product Z that we are producing by the increase in material per unit. See if that lies within allowable increase for raw material C. If it does, the shadow price is still valid and thus the solution is still optimal (Reduced costs remain unchanged). How would you go about answering the following question?: What would be the maximum price you would pay for an additional unit of Labor Hours A? How many units would you acquire at this price? You would not pay any more than the shadow price of the resource (AKA the value gained through having additional units of the resource). You would acquire max increase - after this value there is no way to ensure if the new shadow price would stil exceed the price that we are paying for additional umits of the material. T or F: When we have a binary constraint (i.e. in an assignment problem) we do not need to include a non-negativity constraint True T or F: in a balanced assignment problem, all resource and all project constraints could technically be formulated as = 1 True When an assignmeny problem has less resources than projects, what should be the signs on the resource constraints? What should be the sign on the project constraints? Resource : ? Project: = 1 T or F: in an assignment problem, if one resources can be assigned to a project more than once, we no longer need the binary constraint. True - but do need integer >= 0 constraint List two common applications of Binary integer variables Selection (group members. new facility locations, etc.) Set coverage (locations of police precintcs, hospitals etc.) Under what circumstances might we use goal program rather than linear programming? -when we have multiple objectives -when an LP results in an infeasible solution What is the objective of a goal program? Minimize total undesirable deviation T or F: Every goal has one deviation variable. False - every goal has two deviation variables - one for overachieving and one for underachieving Both the underachieving deviation variable and the overachieving deviation variable must always have a ___________ value non-negative In a soft constraint, the overacheiving variable always has a coefficient of _________, and the underachieving variable always has a coefficient of __________. -1, +1 T or False: In soft constraints, the sign can be <=, >=, or =. False - In soft constraints, the sign will always be =. The LHS will include the actual amount used, from which the overachievement is deducted or the underachievement is added, so that the LHS as a whole will always equate to the actual value of the goal on the RHS If the original constraint (before being converted to a soft constraint) was <=, the deviation variable that we want to minimize (and therefore include in the OBJ FN) is _____________ d+ If the original constraint (before being converted to a soft constraint) was >=, the deviation variable that we want to minimize (and therefore include in the OBJ FN) is _____________ d- If the original constraint (before being converted to a soft constraint) was =, the deviation variable that we want to minimize (and therefore include in the OBJ FN) is _____________ d+ and d- T or F: Budget constraints (as hard constraints) will always be <=. False - If we have a goal of spending the entire budget, the sign of the original constraint before converting to soft should be =. Thus, we will want to minimize both the d- and the d+ associated with this goal A pure goal program is one in which the coefficents are not adjusted - all deviation variables are associated with constraints which all of the same units ad weights What are the OBJ FN coefficients in a % GP? 1/RHS What are the OBJ FN coefficients in a weighted GP? respective weights What are the OBJ coefficients in a weighted % GP? weight/RHS T or F: The least important goal will not have an increased weight - its coeff will be 1. True