The berth allocation problem (BAP) involves decisions on how to allocate the berth space and to sequence maritime vessels that are to be loaded and unloaded at a container terminal involved in the maritime logistics. As the berth is a critical resource in a container terminal, an effective use of it is highly essential tohave efficient berthing and servicing of vessels, and to optimize the associated costs. This study focuses on the minimum cost berth allocation problem (MCBAP) at a container terminal where the maritime vessels arrive dynamically. The objective comprises the waiting time penalty, tardiness penalty, handling cost and benefit of early service completion of vessels. This paper proposes three computationally efficient mixed integer linear programming (MILP) models for the MCBAP. Through numerical experiments, the proposed MILP models arecompared to an existing model in the literature to evaluate their computational performance. The computational study with problem instances of various problem characteristics demonstrates the computational efficiency of the proposed models.

The management of inventory in a divergent supply chain involves inventory allocation/rationing in addition to the determination of order policy parameters. In the case of a stock point feeding product(s) to several downstream members, rationing mechanism can be viewed as a special case of the allocation mechanism. In a supply chain with multi-period ordering cycles, a rationing decision ensures that the entire inventory available with the feeder stock point is rationed to downstream members, whereas an allocation decision neednot allocate the entire inventory available, and it is at the discretion of the decision maker at the feeder stock point to retain inventory for possible high priority demands in future periods. In any supply chain permitting backordering of demands from downstream members, the clearing of backorders is a matter of concern. This study addresses the said issue by ensuring that the feeder stock point considers the current period demand for fulfilment only after clearing the backorders with respect to the downstream members. Through this study, anattempt is made to develop mathematical models for supply chains operating with installation-specific costs (holding and shortage) and ordering policy (base stock) over a finite time horizon with and without clearing backorders in the case of rationing as well as allocating inventory to downstream members. Specifically, thiswork appears to be the first comparative study on allocation and rationing mechanisms in association with/ without backorder clearing mechanisms in divergent supply chains, and their impact on the total supply chaincost.