# problem narration # define gurobi model # sets and their explanations # parameters / data and their description # decision variables and their explanations # objective function and explanation # constraints and their explanation # Run optimization and explanation # print the results and explanations

14.1 Assigning personnel to machines An operator needs to be assigned to each of the six machines in a workshop. Six workers have been pre-selected. Everyone has undergone a test of her productivity on every machine. Table 14.1 lists the productivities in pieces per hour. The machines run in parallel, that is, the total productivity of the workshop is the sum of the productivities of the people assigned to the machines. Table 14.1: Productivity in pieces per hour Machines Workers 1 2 3 4 5 6 1 13 24 31 19 40 29 2. 18 25 30 15 43 22 3 20 20 27 25 34 33 4 23 26 28 18 37 30 5 28 33 34 17 38 20 6 19 36 25 27 45 24 The objective is to determine an assignment of workers to machines the maximizes the total productivity. We may start by calculating a (non-optimal ) heuristic solution using the following fairly natural method: choose the assignment pm with the highest productivity, cross out the line p and the column m (since the person has been placed and the machine has an operator), and restart this process until we have assigned all persons. The problem should then be solved to optimality using Mathematical Programming. And finally, solve the same problem to optimality, but for machines working in series