## 6 Designing, Balancing and Scheduling Assembly Lines with Uncertain Parameters
### A Robust Approach to the ALBP with Uncertain Parameters
Two mixed-integer programming settings were proposed for this uncertain ALBP-1 and explain how these settings can be adapted to handle the special case, where one must integrate a particular set of workers in the assembly line. A construction heuristic was developed that yields high-quality solutions in a fraction of the CPU time needed to solve the uncertain ALBP-1 to optimality in the robust sense. Computational results showed the benefits of solving this robust optimization problem instead of its deterministic counterpart. The problem of placing the inventory over a network, which is used for assembling a final product, is a challenging issue in supply chain designs because the manufacturer wants to reduce inventory over the supply chain. The process of designing a supply chain and placing inventory, to offer a higher service level at the lowest possible cost, is not an easy choice for a decision-maker. In the paper [117], the authors used the supply chain representation, where a supply chain was divided into supplying, manufacturing and delivering stages. The main problem was to select a resource option in order to perform each above stage based on the selected options and to place an amount of inventory at each stage in order to offer satisfactory customer service with a low total supply chain cost. A resource option represents suppliers, manufacturing plants (production lines) and transport modes in the supplying, manufacturing or delivering stage. The assembly algorithm based on an ant colony optimization was developed to minimize the total supply chain cost and the lead time of the products to ensure all product deliveries without delays. The concerns of most companies related to economic savings, optimal utilization of resources along with increasing environmental protection regulations prompt the manufacturer to be focused on recycling the products that are at the end of their life. In [118], a job-shop scheduling problem is considered with reverse flows under uncertainty. Since most parameters of the model (e.g., operation durations) were tainted with uncertainty in real-world applications, a robust programming was used. Due to the complexity of solving the job-shop scheduling problem, an exact algorithm for small-sized instances and simulated annealing with a discrete harmony search for large-sized instances were developed. The model performance was evaluated by comparing the computational results available from the OR literature. The performance of the proposed meta-heuristic algorithms was evaluated by comparing the obtained schedules with the exact algorithm for small-sized instances and with three meta-heuristics (the discrete particle swarm optimization, the invasive weed optimization and the greedy algorithm) for medium-sized and large-sized instances. The satisfying results showed that the presented model and proposed algorithms ensure a good solution quality within a reasonable CPU time for the tested instances. Assembly operation duration variations in a manufacturing production line can result in a longer duration to complete operations than a predetermined cycle time, leading to a production line stoppage and loss of production time. In practice, a portion of the predetermined cycle time may be allocated as a predefined fixed-size buffer time, which is determined based on the experience, to account for such uncertain duration variations for a paced assembly line without storage-buffers between workstations. The size of the required buffer time in each workstation depends on the variation levels of operation durations and the desired conservatism level for preventing cycle time violations. Moreover, there are uncertainties in other nonviable activity durations in the workstations, which are known as inter-task times. Although many studies on the stochastic manufacturingassembly line design focused on minimizing the cost incurred when the predetermined cycle time is exceeded due to operation duration variations, they mostly disregarded the inter-task times.