An Integrated Problem of Production Scheduling and Transportation in a Two-Stage Supply Chain with Carbon Emission Consideration
This study considers a scheduling model for a supply chain system that can choose a set of subcontractors from the available subcontractors (non-identical manufacturing facilities) to fulfill a part of its orders/jobs in order to maximize the supply chain profitability. Further, this study aims to reduce carbon emissions from transportation activities in the supply chain. The orders/jobs to be processed have different processing times on different manufacturing facilities and due dates. All the completed jobs at the outsourced centers (sub-contractors) need to be transported back to the central manufacturing facility. The present study integrates three issues: (1) selection of subcontractors; (2) scheduling of jobs, and (3) logistic scheduling with carbon emission consideration; all these decisions in a supply chain have not been considered together in the existing literature. We present this problem with the objective of minimizing the total costs associated with production and logistic decisions, and propose a mixed-integer linear programming model.
A Study on Mathematical Models for Transforming the Job-Shop Layout Into Flow-Shop Layout
In this paper, we study the problem of transforming a job-shop layout into a flow-shop layout by introducing additional machines, so that all job-related operations can be processed in a flow-shop layout. The objective is to find the shortest sequence of machines, so that the overhead of introducing additional machines can be reduced. This transformation of job-shop layout into flow-shop layout has the advantage of automating the flow-line, which is an important step in digital manufacturing. The study first focuses on a special case (which is studied generally in the literature) where all the jobs would have the same and equal number of operations to be performed in a job-shop, but each job has a different machine routing when compared to other jobs. We propose a Mixed Integer Liner Programming (MILP) model for solving this special case. Further, in order to evaluate the performance of the proposed MILP model, we compare the same with an existing model in literature. From the results, we confirm that the proposed model is superior in terms of the CPU time, in solving the problem instances considered for the study. The study also extends this special case, and considers the generalized case where jobs could have different number of operations, and the study proposes a comprehensive MILP model for solving the generalized case.
Priority fractional rationing (PFR) policy and a hybrid metaheuristic for managing stock in divergent supply chains
A distributor catering to demands of multiple retailers is considered in this paper and stock-management in this divergent supply chain is achieved through the deployment of periodic review base-stock (i.e. (R, S) policy) policy at every member. In the model of the supply chain considered in this study, in every time-period, an attempt is made by the distributor to first transport backlogged-demands from the downstream members till the distributor’s previous instance-of-review even before considering demands from downstream members in recent time-periods. This practice of the distributor attempting first to satisfy backlogged-demands till its last instance of review will ensure that the shipment will reach the retailer, contemplating whom the order was made by the distributor. A Mixed Integer Linear Programming (MILP)-based mathematical formulation of the supply chain (with the objective of minimizing the Total Supply Chain Cost (TSCC)), to obtain optimum policy (R, S) parameters at each member of the supply chain, and inherently performing the allocation and rationing of stock over a finite planning horizon, is proposed through this paper. A new heuristic allocation and rationing mechanism for the distributor to distribute stock among retailers during the occurrence of shortage named as Priority Fractional Rationing (PFR) policy is also introduced in this study. A heuristic methodology which is a hybrid of Genetic Algorithm and Particle Swarm Optimization algorithm (HGA-PSO) combined with PFR policy is proposed through this study after analyzing the computational difficulty encountered and lack of tractability of stock-allocation and stock-rationing mechanism while the MILP-based mathematical formulation is solved to optimality. A local search technique as part of the Particle Swarm Optimization (PSO) algorithm, similar to mutation operation in Genetic Algorithm (GA) is introduced due to the observation of inferior results during pilot studies. The performance evaluation studies of the HGA-PSO with that of stand-alone GA, stand-alone PSO with new local search and the exact solution obtained by solving the MILP-based mathematical formulation is presented. The results indicate the superior performance of the hybrid algorithm in comparison with stand-alone GA and PSO.