Collaborative shipping: an analysis of can-order replenishment policies, cost-sharing agreements, and information distortion.

This dissertation analyzes the stochastic multi-item inventory problem from the horizontal collaboration point of view. In Chapter 2 of this dissertation, we cover the general features of the Joint replenishment problem (JRP), and we classify the existing JRP models according to the demand characteristics. The resulting categorizations provide a useful overview for researchers studying inventory replenishment problems, by providing detailed information on the inventory system characteristics and the employed solution approaches, highlighting articles that involve stochastic variables (e.g., demand arrivals or lead times) and present exact solution approaches. Further, a description of the most commonly used allocation mechanisms is presented together with their formulation.

In Chapter 3, we present a Continuous-Time Markov Chain (CTMC) model to compute the steady-state distribution of the possible state transitions of the two-company setting when orders are synchronized using the can-order policy. The CTMC model allows us to quantify the exact inventory and transportation cost performance of each company in the collaboration, and to optimize the optimal control parameters of the can-order policy that maximizes the coalition gains, i.e., minimizes the total joint logistics costs. Once the collaboration costs are calculated, two decisions have to be made: (i) which set of costs will be redistributed, and (ii) how those costs will be allocated.  We consider different agreements to distribute the costs (or gains) of the collaboration, ranging from no cost redistribution at all, sharing the transportation costs (or its gains) only, to sharing the total logistics costs (or its gains) that are impacted by the collaboration. Also, we study four different allocation mechanisms to redistribute the collaboration costs/gains. Each of these allocation mechanisms can be applied to each of the four sets of costs. We quantify the individual cost performance of transportation and inventory holdings, and we investigate which cost-sharing agreement enables a long-term partnership where each company obtains individual gains when they set up a collaborative shipping agreement.

While Chapter 3 studies the performance of the collaboration under the can-order policy and the long-term stability per type of cost-sharing agreement, Chapter 4 focusses on the non-cooperative framework of the information game. We investigate the incentives for information distortion and whether/when this may pose a threat to the stability (and thus the long-term viability) of the collaboration. Specifically, we investigate the best reporting strategy for each company, assuming that each company works out by reasoning. That is, a company may misreport its demand in order to maximize its realized individual gains on the assumption that the other company behaves in equal manner. Of course, the resulting realized individual gains depend on the specific set of costs to be redistributed and on the allocation mechanism selected. Further, we investigate two types of contract to allocate the costs among the companies. We employ the concept of dominance, i.e., by iteratively eliminating dominated strategies, to find the best reporting strategy under each cost-sharing agreement and to analyze under which settings truth-telling reporting may be an equilibrium.

In the inventory management literature, the lot size of the replenishment orders is usually determined by the retailer to balance the fixed cost per order against the holding costs, whereby the transportation utilization rate or the CO2 implications are not considered. In Chapter 5 we revise the stand-alone and collaborative inventory models taking sustainability concerns into account. We thus reformulate for both models the classical single objective optimization approach as a multi-objective inventory problem. Conceptually, we investigate the individual costs and the total carbon emissions generated as the result of the storage of each inventory item, and the frequencies of individual (and joint) orders placed. We make use of a non-dominated sorting procedure to eliminate all possible dominated combinations of control parameters of the can-order policy, i.e., combinations that result in a higher carbon emission for a given cost, in order to identify the set of efficient solutions (Pareto optimal solutions). These results are used to provide some insights about the effectiveness of different ordering policies to control carbon emissions. The results of the multi-criteria decision analysis indicates that a slight percentage cost increase results in a significant reduction of carbon emissions. Finally, Chapter 6 summarizes the conclusions, addresses the limitations of this dissertation, and suggests avenues for further research by highlighting both trends and gaps in the research field.