Most of today's production systems are working with parallel production resources to increase throughput rate due to the increase in high variability in demand and product mix. Effective control and performance evaluation of such systems is of paramount importance to minimize production and inventory-related costs. We examine a production-inventory system featuring parallel production resources capable of producing various products. In many industries such as automotive, white goods, electronics, and paint, multiple/parallel production resources are widely used to produce the ideal amount and satisfy incoming demands for distinct products. In this study, shortage cost is not restricted to only one type and both lost sales and backordering cases are analyzed. In order to analyze the optimal production policies' behavior, we initially formulate dynamic programming models for both lost sales and backordering systems, treating them as Markov Decision Processes. Subsequently, we solve these models using the value iteration algorithm. Given the challenges posed by the curse of dimensionality in the value iteration algorithm, we suggest alternative heuristic production policies. These policies extend the existing ones described for multi-item single-resource make-to-stock (MTS) systems to accommodate multiple resources. We construct simulation models to assess the efficacy of the heuristic policies, conducting comparisons of their performance against both the optimal policy and among one another. To the best of our knowledge, there has been no exploration of scenarios involving multiple production resources concurrently manufacturing distinct products in a MTS environment. Hence, this study serves as an extension to the examination of multi-item, multi-production resource MTS systems.

This research deals with a multi-job Integer batch scheduling problem on a single machine with different due dates. Every job demanded one or more parts, and the single machine processed the job into a number of batches. The objective is to minimize total actual flow time, defined as the total flow time of all jobs starting from the arrival to the common due date. The decisions are to determine the sequence of jobs, the number of batches, batch size, and sequence of all batches on a single machine. This research proposes three algorithms, developed based on the longest due date rule (The P1-LDD Algorithm), the adjacent pairwise interchange method (The P2-API Algorithm), and the permutation method (The P3-PM Algorithm). The numerical experience shows that the three algorithms produce an outstanding solution. The P1-LDD Algorithm fits to solve a simple problem. The P2-API Algorithm has superior to solve a big complicated problem. The P3-PM Algorithm has the best performance to solve small complicated problems.

This study aims to investigate the multi-item inventory model in a production/rework system with multiple production setups. Rework can be depicted as the transformation of production rejects, failed, or non-conforming items into re-usable products of the same or lower quality during or after inspection. Rework is very valuable and profitable, especially if materials are limited in availability and also pricey. Moreover, rework can be a good contribution to a ‘green image environment’. In this paper, we establish a multi-item inventory model to determine the optimal inventory replenishment policy for the economic production quantity (EPQ) model for imperfect, deteriorating items with multiple productions and rework under inflation and learning environment. In inventory modelling, Inflation plays a very important role. In one cycle, production system produces items in n production setups and one rework setup, i.e. system follows (n, 1) policy. To reduce the deterioration of products preservation technology investment is also considered in this model. Holding cost is taken as time dependent. We develop expressions for the average profit per time unit, including procurement of input materials, costs for production, rework, deterioration cost and storage of serviceable and reworkable lots. Using those expressions, the proposed model is demonstrated numerically and the sensitivity analysis is also performed to study the behaviour of the model.