A new approach for solving capacitated lot sizing and scheduling problem with sequence and period-dependent setup costs

Purpose: We aim to examine the capacitated multi-item lot sizing problem which is a typical example of a large bucket model, where many different items can be produced on the same machine in one time period. We propose a new approach to determine the production sequence and lot sizes that minimize the sum of start up and setup costs, inventory and production costs over all periods. Design/methodology/approach: The approach is composed of three steps. First, we compute a lower bound on total cost. Then we propose a three sub-steps iteration procedure. We solve optimally the lot sizing problem without considering products sequencing and their cost. Then, we determine products quantities to produce each period while minimizing the storage and variable production costs. Given the products to manufacture each period, we determine its correspondent optimal products sequencing, by using a Branch and Bound algorithm. Given the sequences of products within each period, we evaluate the total start up and setup cost. We compare then the total cost obtained to the lower bound of the total cost. If this value riches a prefixed value, we stop. Otherwise, we modify the results of lot sizing problem. Findings and Originality/value: We show using an illustrative example, that the difference between the total cost and its lower bound is only 10%. This gap depends on the significance of the inventory and production costs and the machine's capacity. Comparing the approach we develop with a traditional one, we show that we manage to reduce the total cost by 30%. Research limitations/implications: Our model fits better to real-world situations where production systems run continuously. This model is applied for limited number of part types and periods. Practical implications: Our approach determines the products to manufacture each time period, their economic amounts, and their scheduling within each period. This outcome should help decision makers bearing expensive start up and setup costs, to reduce their Inventory and Production costs and Start up and setup cots. Originality/value: The main idea of the proposed approach is to intelligibly reduce the number of products to manufacture within each period in order to decrease the setup cost; since in case of limited machine's capacity, we show that setup costs could increase when reducing the total number of parts manufactured over the entire planning horizon. In fact, the triangular inequality in setup costs is proved to be not usually available.