Mathematical Programming Applications in Logistics Planning

The talk presents two applications of mathematical programming arising in logistics planning. The first one is a simultaneous fleet deployment and vessel speed optimization problem of a container liner shipping company considering cargo routing, transshipment and empty container repositioning under transit time constraints. This problem is referred as the simultaneous Service type Assignment and container Routing Problem (SARP) in the sequel. A path-flow based mixed-integer linear programming formulation (MILP) is suggested for the SARP. A Branch and Bound (BB) algorithm is used to solve the SARP exactly. A Column Generation (CG) procedure, embedded within the BB framework, is devised where the resulting subproblems are constrained SPP which is NP-hard and solved by a label correcting algorithm. The methodology is examined on randomly generated instances from real life service networks.

The second one is an online e-commerce logistics planning problem faced with many retailers in fashion industry. The retailer operates a set of stores, not all of which carry the items requested. The items of an order are dispatched from a single store at which all items must first be consolidated before sending to the customer. A third-party logistics (TPL) company handles the transportation of goods between the stores and the customer. The TPL company uses a concave pricing policy based on the distance between the origin and the destination, as well as the weight of the items. The resulting problem is non-convex yet can be reduced to a MILP formulation that is then efficiently solved using a matheuristic that combines the solution of a set covering model with local search. Lastly, additional research directions based on the experience of the speaker are mentioned.