【正文】 ng this problem: 1. Rewrite the supply constraints to be equalities and rewrite the demand constraints to be . Unfulfilled demand will appear as slack on each of the demand constraints when one optimizes the model. When demand is greater than supply: Variations on the Transportation Model 全國(guó)領(lǐng)先的工作效率提升平臺(tái) 2. Revise the model to append a placeholder origin, called a dummy origin, with supply equal to the difference between total demand and total supply. The purpose of the dummy origin is to make the problem balanced (total supply = total demand) so that one can solve it. The cost of supplying any destination from this origin is zero. Once solved, any supply allocated from this origin to a destination is interpreted as unfilled demand. Variations on the Transportation Model 全國(guó)領(lǐng)先的工作效率提升平臺(tái) Certain routes in a transportation model may be unacceptable due to regional restrictions, delivery time, etc. In this case, you can assign an arbitrarily large unit cost number (identified as M) to that route. This will force one to eliminate the use of that route since the cost of using it would be much larger than that of any other feasible alternative. Eliminating Unacceptable Routes Choose M such that it will be larger than any other unit cost number in the model. Variations on the Transportation Model 全國(guó)領(lǐng)先的工作效率提升平臺(tái) Generally, LP models do not produce integer solutions. The exception to this is the Transportation model. In general: Integer Valued Solutions If all of the supplies and demands in a transportation model have integer values, the optimal values of the decision variables will also have integer values. Variations on the Transportation Model 全國(guó)領(lǐng)先的工作效率提升平臺(tái) Assignment Model In general, the Assignment model is the problem of determining the optimal assignment of n “indivisible” agents or objects to n tasks. For example, you might want to assign Salespeople to sales territories Computers to works Consultants to clients Service representatives to service calls Commercial artists to advertising copy The important constraint is that each person or machine be assigned to one and only one task. 全國(guó)領(lǐng)先的工作效率提升平臺(tái) We will use the AutoPower example to illustrate Assignment problems. AutoPower Europe’s Auditing Problem AutoPower’s European headquarters is in Brussels. This year, each of the four corporate vicepresidents will visit and audit one of the assembly plants in June. The plants are located in: Leipzig, Germany Liege, Belgium Nancy, France Tilburg, the Netherlands Assignment Model 全國(guó)領(lǐng)先的工作效率提升平臺(tái) The issues to consider in assigning the different vicepresidents to the plants are: 1. Matching the vicepresidents’ areas of expertise with the importance of specific problem areas in a plant. 2. The time the management audit will require and the other demands on each vice president during the twoweek interval. 3. Matching the language ability of a vice president with the plant’s dominant language. Keeping these issues in mind, first estimate the (opportunity) cost to AutoPower of sending each vicepresident to each plant. Assignment Model 全國(guó)領(lǐng)先的工作效率提升平臺(tái) The following table lists the assignment costs in $000s for every vicepresident/plant bination. PLANT Leipzig Nancy Liege Tilburg . (1) (2) (3) (4) Finance (F) 24 10 21 11 Marketing (M) 14 22 10 15 Operations (O) 15 17 20 19 Person el (P) 11 19 14 13 Assignment Model 全國(guó)領(lǐng)先的工作效率提升平臺(tái) PLANT Leipzig Nancy Liege Tilburg . (1) (2) (3) (4) Finance (F) 24 10 21 11 Marketing (M) 14 22 10 15 Operations (O) 15 17 20 19 Personnel (P) 11 19 14 13 Consider the following assignment: Total cost = 24 + 22 + 20 + 13 = 79 The question is, is this the least cost assignment? Assignment Model 全國(guó)領(lǐng)先的工作效率提升平臺(tái) Complete enumeration is the calculation of the total cost of each feasible assignment pattern in order to pick the assignment with the lowest total cost. Solving by Complete Enumeration This is not a problem when there are only a few rows and columns (., vicepresidents and plants). However, plete enumeration can quickly bee burdensome as the model grows large. Assignment Model 全國(guó)領(lǐng)先的工