A Memetic Framework for Solving the Lot Sizing and Scheduling Problem in Soft Drink Plants

A genetic algorithm/mathematical programming approach to solve a two-level soft drink production problem

This paper proposes two evolutionary approaches as procedures to solve the Synchronized and Integrated Two-Level Lot-Sizing and Scheduling Problem (SITLSP). This problem can be found in some industrial settings, mainly soft drink companies, where the production process involves two interdependent levels with decisions concerning raw material storage and soft drink bottling. The first approach to solve the SITLSP is a Multi-Population Genetic Algorithm (GA) with a hierarchical ternary tree structure for populations. The second approach is a Memetic Algorithm (MA) that extends the GA approach through the inclusion of a local search procedure. The computational study reported reveals that those methods are an effective alternative to solve real-world instances of the SITLSP.

This chapter studies a two-level production planning problem where, on each level, a lot sizing and scheduling problem with parallel machines, capacity constraints and sequence-dependent setup costs and times must be solved. The problem can be found in soft drink companies where the production process involves two interdependent levels with decisions concerning raw material storage and soft drink bottling. Models and solution approaches proposed so far are surveyed and conceptually compared. Two different approaches have been selected to perform a series of computational comparisons: an evolutionary technique comprising a genetic algorithm and its memetic version, and a decomposition and relaxation approach.

Large scale batch scheduling problems with complex constraints are difficult and time-consuming to solve. Therefore, this paper addresses the green batch scheduling problem on non-identical parallel machines with time-of-use electricity prices. The objective of the problem is to minimise total electricity costs (TEC) in production. Two kinds of algorithms—single-population genetic algorithms (SPGA) and multi-population genetic algorithm (MPGA)—are proposed to solve the problem. In the algorithms, the products are allocated into batches and are then allocated to machines randomly. A greedy strategy is designed to arrange the production sequence and the starting time of the batches. Furthermore, a self-adaptive parameter adjustment strategy is proposed to enhance the adaptability of the algorithm. Computational experiments with CPLEX solver have been conducted to evaluate the performance of the algorithms. On small instances, both SPGA and MPGA can achieve approximate results compared with those obtained by CPLEX, and can also achieve smaller TEC on large instances with less computing time. In addition, the proposed MPGA implemented by parallel computing outperforms SPGA in getting better results with nearly the same computing time.

According to studies, industrial water use comprises production processes, auxiliary processes, kitchen use, and outdoor use. Reducing industrial water use is dependent on the implementation of administrative, engineering, mechanical, and human controls. The objectives of this research were to assess the water use of a Soft Drink Plant; determine the water use ratio for a two-year period; and determine the plant’s compliance with local and international regulations for wastewater discharge. We also determined the level of success of implementing a water minimisation plan, whether there was an improvement in the Water Use Ratio, and compliance of the industry with local and international discharge regulations. The sequential transformative strategy was used to collect and analyse data so as to ascertain water usage and disposal, and a semi-structured interview was conducted to validate the non-existence of heavy metals in the wastewater discharged from the soft drink plant. The Soft Drink Plant’s Water Minimisation Plan 2013-2016 achieved a high level of success overall, with 74.42% of the activities implemented by the assigned completion dates. However, three of the five measures implemented recorded low levels of success. Paired sample t-tests revealed statistically significant differences in the water use ratio obtained for the periods 2013-2014, 2014-2015, and 2013-2015, although the differences were relatively small (t (df)=2.242, p=0.047; t (df)=2.592, p=0.025; and t (df)=6.250, p=0.000) for the respective periods. Six of the eleven tested parameters were statistically different when compared to the Coca-Cola Operating Requirements and Environmental Protection Agency standards, indicating a high variation in effluent discharge.

Some physical and chemical analysis was carried out on samples collected at various distances from the effluent discharge from a soft drink plant in Ilorin into Asa River. The pH was found to range between 7.2-7.8 with a mean temperature of 25.25°C. Experimental results obtained on replicate samples showed that the standard deviation was generally below 10%. The total organic matter ranged between 21-22.9% while the nitrate concentration ranged between 5.81- 15.41 mg/l; these were high and could lead to eutrophication of the water body into which it empties. The cation and anion concentrations all fall within safe limits except for zinc and in some cases, NO3- concentrations which was higher than the standard set by regulatory bodies. A Pearson\'s correlation study showed correlations between different parameters at both 1% and 5% probability levels. Journal of Applied Sciences and Environmental Management Vol. 9(1) 2005: 187-190

This paper deals with lot sizing decisions in a flexible job shop manufacturing system considering dependencies between lot sizing decisions. A novel mathematical model is developed to optimise lot sizing and scheduling simultaneously using a product-oriented approach as opposed to the job-oriented approach which has been prevalently considered in the literature. Moreover, the proposed model considers further underlying assumptions such as assembly operations, sequence-dependent setup times, initial inventory and safety stock levels, as well as lots with unequal and variable sizes. The objective is to minimise the total production, setup, and tardiness penalty costs of the system. To solve the formulated problem, a self-adaptive Cuckoo Optimisation Algorithm (COA) embedded with three new immigration mechanisms is developed. Numerical experiments are conducted to demonstrate the validity of the model and investigate the efficiency and effectiveness of the employed optimisation algorithm.

Optimal lot sizing in a non-cooperative material manager–controller game

Production lot sizing in failure prone two-stage serial systems

The datasets presented here were partially used in “Formulation and MIP-heuristics for the lot sizing and scheduling problem with temporal cleanings” (Toscano, A., Ferreira, D., Morabito, R., Computers & Chemical Engineering) [1], in “A decomposition heuristic to solve the two-stage lot sizing and scheduling problem with temporal cleaning” (Toscano, A., Ferreira, D., Morabito, R., Flexible Services and Manufacturing Journal) [2], and in “A heuristic approach to optimize the production scheduling of fruit-based beverages” (Toscano et al., Gestão & Produção, 2020) [3]. In fruit-based production processes, there are two production stages: preparation tanks and production lines. This production process has some process-specific characteristics, such as temporal cleanings and synchrony between the two production stages, which make optimized production planning and scheduling even more difficult. Thus, some papers in the literature have proposed different methods to solve this problem. To the best of our knowledge, there are no standard datasets used by researchers in the literature to verify the accuracy and performance of proposed methods or to be a benchmark for other researchers considering this problem. The authors have been using small data sets that do not satisfactorily represent different scenarios of production. Since the demand in the beverage sector is seasonal, a wide range of scenarios enables us to evaluate the effectiveness of the proposed methods in the scientific literature in solving real scenarios of the problem. The datasets presented here include data based on real data collected from five beverage companies. We presented four datasets that are specifically constructed assuming a scenario of restricted capacity and balanced costs.

The determination of lot sizes and production schedules of multiple products in multiple periods is difficult when sequence-dependent set-up costs are present. By using an initial set-up cost estimator (ISCE) the joint problem can be divided and solved sequentially. A search of the literature reveals that, while there is considerable research on the individual problems of lot sizing and scheduling, there is a dearth of study on either the joint problem or on the effect of ISCE selection on the total cost solution. Using a variety of data sets, this paper evaluates the sensitivity of ISCE selection on the solution to the joint problem. Results of the study demonstrate that the choice of an ISCE can have a significant effect on the final lot sizes and schedules. Additionally, the research shows that ‘common sense’ a priori assumptions about ISCE performance may lead to the selection of an inappropriate ISCE.

We propose a decision support approach, called DESMILS, to solve multi-item lot sizing problems with a large number of items by using single-item multiobjective lot sizing models. This approach for making lot sizing decisions considers multiple conflicting objective functions and incorporates a decision maker’s preferences to find the most preferred Pareto optimal solutions. DESMILS applies clustering, and items in one cluster are treated utilizing preferences that the decision maker has provided for a representative item of the cluster. Thus, the decision maker provides preferences to solve the single-item lot sizing problem for few items only and not for every item. The lot sizes are obtained by solving a multiobjective optimization problem with an interactive method, which iteratively incorporates preference information and supports the decision maker in learning about the trade-offs involved. As a proof of concept to demonstrate the behavior of DESMILS, we solve a multi-item lot sizing problem of a manufacturing company utilizing their real data. We describe how the supply chain manager as the decision maker found Pareto optimal lot sizes for 94 items by solving the single-item multiobjective lot sizing problem for only ten representative items. He found the solutions acceptable and the solution process convenient saving a significant amount of his time.

Um dos vários desafios de qualquer organização é a realização do planejamento da produção que, se incorreto, pode resultar na ociosidade de máquinas no processo produtivo. Em trabalhos anteriores, nos quais se investigaram o efeito do dimensionamento do lote no MRP, não se considerou o sequenciamento de itens. Neste estudo, investigaram-se os efeitos de variações no tamanho do lote no MRP e seus reflexos na ociosidade de máquinas no processo produtivo de uma empresa no ramo de PVC. Com a mudança da regra de lote por lote (L4L) para quantidade fixa (EOQ) foi possível obter redução significativa na ociosidade das máquinas. Os resultados apontam a importância de considerar o sequenciamento de componentes no estudo da sistemática de gerenciamento do MRP e seu impacto na ociosidade das máquinas. Concluiu-se que a sequência dos itens no processo produtivo deve ser considerada quando da decisão de dimensionamento do lote no MRP.

Common replenishment cycle order policies for multiple products with capacity expansion opportunities and quantity discounts

Today's industrial activities are increasing with sophisticated technology, all applied to satisfy consumers in various services. One of the important parts of an industry is the inventory of goods. This is related to the continuity of the resulting production. In meeting the needs of consumers, a plan is needed in production so that there is no shortage of raw materials and the production process does not stop. Grain is an agricultural commodity whose demand and production levels occasionally increase. We can see that until now, our country, Indonesia, still imports rice from other countries, where rice is the main production product produced from grain. The problem can be solved with the Lot sizing method used in this study, which is used to determine the size of the order quantity. In the rice mill itself, grain storage has a limited capacity, so it cannot be directly stored with a large capacity when the price of grain is down. Applying this method as an application will make it easier to manage grain inventory at the rice mill and estimate inventory costs for the next 1 () year. The results of the lot sizing calculation (silver meal) show that for the next year, the smallest cost of procurement of dry milled grain (MDG) demand is obtained from the procurement of demand every month. In other words, procurement is more appropriate every month or period so that the costs incurred for grain inventory are smaller. The following data are the results of the silver meal lot sizing calculation: (1) 39015.4 kg, (2) 35871.2 kg, (3) 39536 kg, (4) 33894.8 kg, (5) 31402 kg, (6) 27982.5 kg, (7) 41461.9 kg, (8) 35336.7 kg, (9) 41305.6 kg, (10) 45717.5 kg, (11) 42007.9 kg, (12) 50828 kg. The cost incurred per order is Rp. 6,000,000