A heterogeneous vehicle routing problem with common carriers and time regulations: Mathematical formulation and a two-color ant colony search

•Provides a vehicle routing method that helped achieve approximately $160 M savings.•Addresses heterogeneous fleet size, layovers, outsourcing, and other complications.•Mixed integer formulations are provided for basis of branch and-cut procedures.•Proposed red-black ant colonies are helpful for many outsourcing problems.•A comparison is provided involving seven alternatives including tabu search. This paper considers a heterogeneous vehicle routing problem with common carriers and time regulations implemented at a major logistics company and contributing to an estimated $160 M in savings. In our problem, the objective is to minimize the network costs by considering heterogeneous fleet routes, outsourcing options, time windows, and drivers’ layover regulations. This variant of the vehicle routing problems has many practical applications, particularly in the design of long-haul transportation and last-mile delivery services. The problem has received limited attention in the literature likely because addressing all the needed aspects are especially challenging. To solve the large-scale problem, our work develops a meta-heuristic called Red-Black Ant Colony System (RB-ACS), which solves the two problems: dedicated fleet routing and outsourcing decisions simultaneously. The savings by supporting improved bidding and outsourcing selected deliveries. We also present a compact mixed-integer formulation for this problem and introduce strong valid inequalities to strengthen branch and cut alternatives. Further, we describe our extensive computational experiments, demonstrate the capability of the proposed RB-ACS in solving large-scale problems and show the efficiency of the formulated math models.