Modeling in-house vs contract maintenance with fixed costs and learning effects

Most companies perform a mix of in-house repair and contract repair. Some operations that need to be performed regularly are done by plant personnel as a part of routine preventive maintenance. Other operations require equipment or skills that the plant personnel do not possess, and these are routinely handled by contracts. A third category is made up of those repairs or maintenance actions which could be done either in-house or by contract. Such a situation arises in many vehicle fleet maintenance shops, in a manufacturing environment where both contractors and skilled technicians are available, and in a wartime environment where repairs are either performed by highly skilled enlisted personnel or by vendors. In addition to assisting in such problems, a good analytical structure for solving such problems has potential value in determining the number of employees with each skill level that the manufacturer has to keep in the work force. In situations where a maintenance operation can be done either in-house or by contract to an outside firm, it is natural to ask how many units of the operation should be done in-house (or by contract) so as to minimize the total maintenance cost. One formulation of this problem assumes that the time per unit is a constant for each craft and for each repair type. This leads to a linear programming model which is easily formulated and solved. In a real maintenance environment, however, learning takes place, and the per unit times decreases as the number of units repaired increases. Including this learning in the problem formulation gives a nonlinear objective function and nonlinear constraints. The objective function is further complicated by including a fixed cost (for diagnostic equipment and one-time training) for each maintenance operation performed in-house. The resulting problem with all these nonlinearities can be solved using a Monte Carlo improvement technique. The problem and its formulation together with the solution algorithm are described.