Replenishing routing under vendor managed inventory systems

This study is inspired by an empty container allocation problem that is related to the management of importing or exporting empty containers in anticipation of future requirements or in response to reduce the redundancy at the port, respectively. We consider the problem to be a non-standard inventory problem with positive and negative demands at the same time. Under a general holding-penalty cost function and one-time period delay for the availability of full containers just arriving at the port, we show that there exists an optimal pair (U,D) of critical policies when only one port is discussed, which is to import empty containers up to U units when the number of empty containers at the port is less than U, or export down to D units when the number is more than D, and do nothing otherwise. When multi-ports are considered, a modified (u, d) policy for each port is introduced to direct the allocation. In the previous case, the replenishment of empty containers at each port is controlled by a decision-maker and the containers are kept at independent servicing ports. Such an instance can be considered as a Vendor managed inventory (VMI) problem. In a VMI system, the supplier decides which retailer should be replenished at what time, and with what quantities of items. Then, an interesting problem is, whether the suppler can replenish all the retailers? We consider a replenishment problem where the supplier has only one vehicle and can replenish only one retailer per period using the vehicle, while different retailers need different periodical replenishments. We model this problem as a single item inventory replenishment routing problem between a single supplier and multiple retailers with direct delivery…


1 Introduction
1.1 Background
1.2 Methodology
1.2.1 Problem description
1.2.2 Stochastic and dynamic modeling approach
1.2.3 Preliminary problem formulation
1.3 Contributions
2 Empty container management
2.1 Introduction
2.2 Literature review
2.3 Problem description
2.4 The case when only one port is considered
2.4.1 Optimal policy for finite horizon problems
2.4.2 The infinite horizon problem
2.4.3 Properties of the (u,d) policy
2.5 The case when multi-ports are considered
i2.5.1 The heuristic algorithm
2.6 Numerical examples
2.6.1 When only one port is considered
2.6.2 When multi-ports are considered
2.7 Conclusion
3 Replenishment routing problems between single supplier and multiple retailers with direct delivery
3.1 Introduction
3.2 Literature review
3.3 Preliminary knowledge of number theory
3.4 Model analysi
3.5 The example
3.6 Conclusion
4 Routing design for multi-location inventory problems
4.1 Introduction
4.2 Model analysis
4.3 Two specific cases
4.3.1 Case 1
4.3.2 Case 2
4.4 The example
4.5 Conclusion
5 Conclusion and Future Work

Author: Li, Jing An

Source: City University of Hong Kong

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