Patrick Zech, Stefan Minner, Zuo-Jun (Max) Shen
Virtual inventory sharing is an effective method to pool inventories in spare parts networks. We propose a novel location-inventory model which integrates (1) strategic facility choice, (2) tactical base-stock level setting and (3) operational sourcing decisions. The mixed integer linear program (MILP) combines a set-covering problem and a semi-Markov decision process (SMDP) which constitutes a new modeling paradigm with many potential applications for other supply chain problems. Due to the integration of the three decision stages, physical and virtual inventory pooling opportunities can be simultaneously evaluated. The model's special structure suggests Benders' decomposition (BD) as an effective method to solve the problem and several improvement techniques (like an SMDP state space reduction method or Master valid inequalities) are used to expedite convergence. Numerical experiments confirm the efficiency of BD and emphasize the value of an integrated model compared to a sequential `location first, inventory and sourcing second` approach. Integrated planning achieves average cost savings of 6.8% which are mainly driven by virtual sharing opportunities that networks offer. Furthermore, the results suggest that the integrated approach favors additional inventory build-up if virtual sharing opportunities increase.
Layla Martin (TUM): "The Competitive Pickup and Delivery Orienteering Problem for Rebalancing Carsharing Systems"
One-way and free-floating carsharing systems become unevenly distributed over time, as customer movements are in general unbalanced. Thus, operators have to rebalance their fleet periodically. In research and in practice, this is commonly modeled as either a pickup and delivery traveling salesman problem or a bipartite matching problem (mainly for autonomous repositioning). We present the pickup and delivery orienteering problem (PDOP), a bipartite profitable tour problem in which deliveries are only executed if profitable. In several cities, for example Munich, more than one operator runs a carsharing fleet. With the rise of Mobility as a Service solutions, customers have the possibility to choose the operator in real time, putting carsharing operators in direct competition. Solving the pickup and delivery orienteering problem, operators neglect the presence of other carsharing offers in the same city. We prove that ignoring competition never results in higher profits than any Nash equilibrium. We therefore present the competitive pickup and delivery orienteering problem (C-PDOP) which considers the rebalancing operations of the competitor. We prove that the C-PDOP possesses pure strategy Nash equilibria and present an Iterated Best Response (IBR) algorithm to find these. We show that the IBR terminates after at most five calculations of the PDOP. In a numerical study we compare the IBR to all Nash equilibria, showing that the IBR returns the best Nash equilibrium for the first mover and the welfare-maximizing Nash equilibrium (which is not necessarily the welfare-maximizing solution without competition) with above-average probability. The Nash equilibrium found by the IBR outperforms the solution ignoring competition by up to 88%, whilst decreasing the empty kilometers significantly. On the other hand, the merging both fleets and operating them in a monopoly can increase the profit by up to 46%, whilst outsourcing relocation operations can increase the profit by up to 35%.
Venue: Room Z 534 (City Campus)
Date: Monday, May 14h, 2018 at 14:00