Single machine scheduling to minimize a modified total late work function with multiple due dates

Abstract

In this paper, the problem of scheduling n jobs on a single machine is evaluated. We introduce a Modified Total Late Work function that allows a declining piecewise linear penalty over time. Multiple due dates for each job are identified and at each due date, the penalty is reassessed. Many instances occur when delivery urgency leads to progress metrics or dates being added to a contract. Over the life of the contract, a loss of incentives or a price decrease can occur at each of the negotiated due dates. After the final due date, the product is valueless and the penalty ceases to accrue. The number and placement of contract due dates are part of the initial negotiations. Two metaheuristics, Simulated Annealing and the Noising Method, are empirically evaluated to determine their performance when measured by this new loss function.