运筹学与供应链管理-第5讲(编辑修改稿)

运筹学与供应链管理-第5讲(编辑修改稿)内容摘要：

an be assigned to any of the 4 plants. 2. Once F is assigned, M can be assigned to any of the remaining 3 plants. 3. Now O can be assigned to any of the remaining 2 plants. 4. P must be assigned to the only remaining plant. There are 4 x 3 x 2 x 1 = 24 possible solutions. In general, if there are n rows and n columns, then there would be n(n1)(n2)(n3)…(2)(1) = n! (n factorial) solutions. As n increases, n! increases rapidly. Therefore, this may not be the best method. Assignment Model For this model, let xij = number of ’s of type i assigned to plant j where i = F, M, O, P j = 1, 2, 3, 4 The LP Formulation and Solution Notice that this model is balanced since the total number of .’s is equal to the total number of plants. Remember, only one . (supply) is needed at each plant (demand). Assignment Model As a result, the optimal assignment is: 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 Total Cost ($000’s) = 10 + 10 + 15 + 13 = 48 Assignment Model The Assignment model is similar to the Transportation model with the exception that supply cannot be distributed to more than one destination. Relation to the Transportation Model In the Assignment model, all supplies and demands are one, and hence integers. As a result, each decision variable cell will either contain a 0 (no assignment) or a 1 (assignment made). In general, the assignment model can be formulated as a transportation model in which the supply at each origin and the demand at each destination = 1. Assignment Model Case 1: Supply Exceeds Demand Unequal Supply and Demand: In the example, suppose the pany President decides not to audit the plant in Tilburg. Now there are 4 .’s to assign to 3 plants. Here is the cost (in $000s) matrix for this scenario: PLANT NUMBER OF . 1 2 3 AVAILABLE F 24 10 21 1 M 14 22 10 1 O 15 17 20 1 P 11 19 14 1 No. of 4 Required 1 1 1 3 Assignment Model To formulate this model, simply drop the constraint that required a . at plant 4 and solve it. Assignment Model Unequal Supply and Demand: Case 2: Demand Exceeds Supply Unequal Supply and Demand: In this example, assume that the . of Personnel is unable to participate in the European audit. Now the cost matrix is as follows: PLANT NUMBER OF . 1 2 3 4 AVAILABLE F 24 10 21 11 1 M 14 22 10 15 1 O 15 17 20 19 1 No. of 3 Required 1 1 1 1 4 Assignment Model 1. Modify the inequalities in the constraints (similar to the Transportation example) 2. Add a dummy . as a placeholder to the cost matrix (shown below). PLANT NUMBER OF . 1 2 3 4 AVAILABLE F 24 10 21 11 1 M 14 22 10 15 1 O 15 17 20 19 1 Dummy 0 0 0 0 1 No. of 4 Required 1 1 1 1 4 Zero cost to assign the dummy Dummy supply。 now supply = demand Assignment Model In the solution, the dummy . would be assigned to a plant. In reality, this plant would not be audited. Assignment Model Unequal Supply and Demand: In this Assignment model, the response from each assignment is a profit rather than a cost. Maximization Models For example, AutoPower must now assign four new salespeople to three territories in order to maximize profit. The effect of assigning any salesperson to a territory is measured by the anticipated marginal increase in profit contribution due to the assignment. Assignment Model Here is the profit matrix for this model. NUMBER OF TERRITORY SALESPEOPLE SALESPERSON 1 2 3 AVAILABLE A 40 30 20 1 B 18 28 22 1 C 12 16 20 1 D 25 24 27 1 No. of 4 Salespeople 1 1 1 3 Required This value represents the profit contribution if A is assigned to Territory 3. Assignment Model The Assignment Model Certain assignments in the model may be unacceptable for various reasons. Situat。