In this work, we consider the Vehicle Routing Problem with Simultaneous Delivery and Pickup, and constrained by time windows, to improve the performance and responsiveness of the supply chain by transporting goods from one location to another location in an efficient manner. In this class of problem, each customer demands a quantity to be delivered as a part of the forward supply service and another quantity to be picked up as a part of the reverse recycling service, and the complete service has to be done simultaneously in a single visit of a vehicle, and the objective is to minimize the total cost, which includes the traveling cost anddispatching cost for operating vehicles. We propose a Mixed Integer Linear Programming (MILP) model for solving this class of problem. In order to evaluate the performance of the proposed MILP model, a comparison study is made between the proposed MILP model and an existing MILP model available in the literature, with the consideration of heterogeneous vehicles. Our study indicates that the proposed MILP model gives tighter lower bound and also performs better in terms of the execution time to solve each of the randomly generatedproblem instances, in comparison with the existing MILP model. In addition, we also compare the proposed MILP model (assuming homogeneous vehicles) with the existing MILP model that also considers homogeneous vehicles. The results of the computational evaluation indicate that the proposed MILP model gives much tighter lower bound, and it is competitive to the existing MILP model in terms of the execution time to solve each of the randomly generated problem instances.

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.

In this paper, we develop branch-and-bound algorithms for objectives such as sum of weighted flowtime, weighted tardiness and weighted earliness of jobs, for an m-machine no-wait (continuous) flowshop. We believe that there has been no prior work on exact algorithms for this problem setup with a variety of objective functions. For the interest of space, we confine our discussion to a subset of certain combination of these objectives and the extension to other objective combinations is quite straight-forward. We explore the active nodes of a branch-and-bound tree by deriving an assignment-matrix based lower bound, that ensures oneto-one correspondence of a job with its due date and weight. This idea is based on our earlier paper on general m-machine permutation flowshop (Madhushini et al. in J Oper Res Soc 60(7):991–1004, 2009) and here weexploit the intricate features of a no-wait flowshop to develop efficient lower bounds. Finally, we conclude our paper with the numerical evaluation of our branch-and-bound algorithms.

This paper focuses on developing the optimal solution or a lower bound for N-job, M-machine Permutation Flowshop Scheduling (PFS) problem in a manufacturing system with the objective of minimizing the makespan using Lagrangian Relaxation (LR) technique. Even though LR technique is considered, in general,as a good method to obtain a lower bound, research in this direction with respect to our problem under study appears scarce. We address this gap by developing two MILP based Lagrangian Relaxation models, namely, Lagrangian Relaxation Method 1 (called Proposed Lagrangian Lower Bound Program (PLLBP)) and Alternate Lagrangian Relaxation Method 1 (called ALR) to find the optimal solution or a lower bound on the makespan. Basically, we develop these LR methods to overcome the possible limitation of the general LR procedureinvolving the sub-gradient approach. Benchmark PFS problem instances are used to evaluate the performance of these methods. It is observed that the PLLBP outperforms the ALR, and it provides better lower bounds than thelower bounds (in most instances) reported in the literature. Even though the PLLBP is superior in terms of solution quality, it has a limitation in that it cannot execute problem instances beyond 500 jobs due to the associated computational effort.