Scheduling optimization of capacitated lot sizing problem based on immune complement algorithm

The aim of this work is to propose a solution approach for a capacitated lot sizing and scheduling real problem with parallel machines and shared buffers, arising in a packaging company producing yoghurt. The problem has been formulated as a hybrid Continuous Set-up and Capacitated Lot Sizing Problem (CSLP–CLSP). A new effective two stage optimisation heuristic based on the decomposition of the problem into a lot sizing problem and a scheduling problem has been developed. An assignment of mixture to buffers is made in the first stage, and therefore the corresponding orders are scheduled on the production lines by performing a local search. Computational tests have been performed on the real data provided by the company. The heuristic exhibits near-optimal solutions, all obtained in a very short computational time.

Capacitated lot sizing problem (CLSP) finds its applications in manufacturing, production as-well-as process industries. Typical size of the real life problems is much larger compared to the sizes that can be handled by commercial solvers, as CLSP is an NP-hard problem. Researchers have attempted different variants of CLSP in last few decades and provided many classical, exact, heuristic and metaheuristic solution approaches. In this paper, we attempt to solve the multi item capacitated dynamic lot sizing problem with backorders and setup times (CLSPBS). We apply Lagrangian relaxation on the material balance constraint, to reduce the problem into several single constraint continuous knapsack problems with upper bound on the real variables. Bounded variable linear program determines the values of real variables. For the negative or positive value of coefficients in the Lagrangian function, we fix the setup variables at zero or one respectively. Thus, the reduced problem is solved in polynomial time, as the main effort required is only sorting of numbers. We use the set up variable that are at one, to develop yet another good upper bound. Branch-and-bound procedure benefits immensely by using these bounds to make a warm start.

This paper develops a fuzzy stochastic multi-objective linear programming (FSMOLP) model for a multi-level, multi-item capacitated lot sizing problem (CLSP) in a multi assembly shop. The proposed model attempts to minimize the total cost consisting of total production variation cost, inventory cost, backlog cost and total setup cost while maximizing the resource utilization simultaneously. To cope with the uncertainty associated with the most of the input data, e.g., the demand and process-related parameters they are treated as fuzzy stochastic parameters with identical stochastic membership function during the planning horizon. To show the usefulness of the proposed solution method, a numerical example is first solved. Then, the usefulness of the proposed model is validated over a set of randomly generated test problems.

This paper addresses the capacitated lot sizing problem (CLSP) with a single stage composed of multiple plants, items and periods with setup carry-over among the periods. The CLSP is well studied and many heuristics have been proposed to solve it. Nevertheless, few researches explored the multi-plant capacitated lot sizing problem (MPCLSP), which means that few solution methods were proposed to solve it. Furthermore, to our knowledge, no study of the MPCLSP with setup carry-over was found in the literature. This paper presents a mathematical model and a GRASP (Greedy Randomized Adaptive Search Procedure) with path relinking to the MPCLSP with setup carry-over. This solution method is an extension and adaptation of a previously adopted methodology without the setup carry-over. Computational tests showed that the improvement of the setup carry-over is significant in terms of the solution value with a low increase in computational time.

We consider here the lot sizing and scheduling problem in single-level manufacturing systems. The shop floor is composed of unrelated parallel machines with sequence dependent setup times. We propose an integer programming model embedding precise capacity information due to scheduling constraints in a classical lot-sizing model. We also propose an iterative approach to generate a production plan taking into account scheduling constraints due to changeover setup times. The procedure executes two decision modules per iteration: a lot-sizing module and a scheduling module. The capacitated lot-sizing problem is solved to optimality considering estimated data and aggregate information, and the scheduling problem is solved by a GRASP heuristic. In the proposed scheme the information flow connecting the two levels is managed in each iteration. We report a set of computational experiments and discuss future work.

This study investigates the cost-effectiveness of 20 demonstration units (DUs) belonging to the "Balde Cheio" program. The units in question are from the state of Rio de Janeiro, Brazil, dating from January to December 2011, and are sorted according to the scale of production (small, medium and large). The data were analyzed using Predictive Analytical software (PASW) 18.0. The scale of production influenced the total cost of milk production, and therefore profitability and cost-effectiveness. The large-scale stratum showed the lowest total unit cost. The positive results in medium and large scales in milk production lead to optimal conditions for long-term production, with the capitalization of cowmen. The items regarding the effective operating cost (EOC) with the biggest influence on the costs of dairy activity in the small scale stratum were food, energy and miscellaneous expenses. In the medium scale, these were food, labor force, and miscellaneous expenses. Finally, in the large scale, they were food, labor force and energy. In the small and large scale, the items regarding the total cost with the biggest influence on the costs of dairy activity were food, labor force, and return on capital, while in the medium scale, they were food, return on capital, and labor force. The average break-even point of 14 of the DUs was higher than the average daily production.

This paper develops a reverse inventory model where the recoverable manufacturing process is affected by the learning theory. We propose the inclusion of the fuzzy demand rate of the serviceable products and the fuzzy collection rate of the recoverable products from customers in the total cost function of the model. Two popular defuzzification methods, namely the signed distance technique, a ranking method for fuzzy numbers, and the graded mean integration representation method are employed to find the estimate of the total cost function per unit time in the fuzzy sense. We provide a comprehensive numerical example to illustrate and compare the results obtained by the two mentioned defuzzification methods. This is one of the only few attempts in the related literature comparing the performance of these methods with the effect of the fuzziness of both of the demand and the collection rate in the presence of the learning simultaneously. The results indicate that deciding on which method could be used depends on the target strategy that could focus on the total cost, ordering lot size, or recovery lot size.

Complexity of the multi-product capacitated lot sizing problem(CLSP) with pricing(<Special Issue>Variational Inequality and Combinatorial Problems)

Multiple-method analysis of logistics costs

We consider the problem of setting appropriate safety leadtimes in an assembly system where all components are purchased and the only manufacturing operation is final assembly. First, we describe two formulations of this problem: (1) minimize total inventory carrying and tardiness costs and (2) minimize inventory carrying costs subject to a service constraint. Second, we discuss how these formulations sometimes fail to adequately provide a decision maker with sufficient information to establish leadtimes when applied independently but how they can be used together to provide a useful decision support system. Finally, we describe a procedure similar to ABC analysis that allows us to solve a much smaller related problem whose solution provides a good approximation to the solution of the original problem. We conclude the paper with numerical examples and a discussion of an actual implementation.

In the capacitated version of the Divide and Conquer algorithm for lot sizing in multi-stage production/inventory problems, feasibility is often lost when the reorder intervals are rounded off to powers of two. We propose a new algorithm for rounding off the reorder intervals which always produces a feasible policy. We have shown that the relative increase in cost that occurs when the intervals are rounded off using this algorithm cannot exceed 44%, and that for systems with a single capacity machine (including the ELSP), the cost increase cannot exceed 6%. Computational experience with industrial data sets indicates that the algorithm performs very well.

PurposeDairy farms, along with livestock and specialty crop farms, face a tight labor supply and increasing labor costs. To overcome the challenging labor market, farm managers can increase labor-use efficiency through both human resource and capital investments. However, little is known about the relationship between such investments and farm profitability. The purpose of this paper is to examine the relationship between dairy farm financial performance and labor-use efficiency, as measured by labor productivity (milk sold per worker equivalent); labor costs (hired labor cost per unit of milk sold and hired labor cost per worker); and investment in labor-saving equipment.Design/methodology/approachCluster analysis is applied to partition dairy farms into three performance categories (high/middle/low), based on farms’ rate of return on equity, asset turnover ratios and net dairy income per hundredweight of milk. Next, the annual financial rank is fitted into both random- and farm-level fixed-effects ordered logit and linear models to estimate the relationship between dairy farms’ financial performance and labor-use efficiency. This study also investigates the implications of using a single financial indicator as a measure of financial performance, which is the dominant approach in literature.FindingsThe study finds that greater labor productivity and cost efficiency (as measured by hired labor cost per unit of milk sold) are associated with better farm financial performance. No statistically significant relationship is found between farm financial performance and both hired labor cost per worker and advance milking systems (a proxy of capital investment in labor-saving technology). Future studies would benefit from better measurements of labor-saving technology. This study also demonstrates inconsistency in regression results when individual financial variables are used as a measure of financial performance. The greater labor-use efficiency on high-performing farms may be a combination of hiring more-skilled workers and managerial strategies of reducing unnecessary labor activities. The results emphasize the importance of managerial strategies that improve overall labor-use efficiency, instead of simply minimizing total labor expenses or labor cost per worker.Originality/valueThis study examines the importance of labor productivity and labor cost efficiency for dairy farm management. It also develops a novel approach which brings a more comprehensive financial performance evaluation into regression models. Furthermore, this study explicitly demonstrates the potential for inconsistent results when using individual financial variable as a measure of financial performance, which is the dominant measurement of financial performance in farm management studies.

The study examined the economics of small-scale maize production in Toto Local Government Area of Nasarawa State, Nigeria. A two-stage sampling technique was adopted for the data collection. Descriptive statistics, regression and gross margin analyses were used to analyse the data collected. The study revealed that majority of the respondents were within the active working age and most of them (83%) were male. The majority of the respondents were married and had a household size of five persons and farm size of 1-2ha. Results of the regression analysis revealed that the output of small-scale maize farmers was influenced by farm size, marital status and annual income at 1% and 5% respectively. A gross margin of N170,594.50 was earned from one hectare of maize farm with a return per naira invested of 2.40. The cost of labour constituted a greater proportion of the costs of production, accounting for about 58.38% and 39.52% of the total variable cost and the total cost respectively, the total cost. The problems militating against maize production in the study area were high cost of labour, pests and diseases, inadequate storage facilities, inadequate capital, marketing problems, transportation, poor access to credit facilities and high cost of inputs. The study, therefore, recommends that farmers should be properly educated by the extension agents on pest and disease control measures. Moreover, inputs should be made available to farmers at subsidized rates by relevant stakeholders.Keywords: Maize, costs, returns, problems, small-scale, production

SYNOPTIC ABSTRACTThis paper deals with the effect on the {optimal lot sizes, cycle length, and cost} of the system for several products produced on several machines with repetitive common cycle length when the solution is constrained by limited storage space or capital. In order to solve the constrained production lot size problem it is necessary to determine the maximum volume or value of the inventory (MV) required for a given production plan. One simple measure of the storage space or capital required is the sum of the peak values of the individual product inventory levels (SMV). Since the peak inventory levels for all products do not occur simultaneously, SMV is usually much larger than the exact MV and, therefore, would be expected to yield a higher cost solution.In this paper efficient computational procedures are developed to find the exact MV and the corresponding constrained optimal lot sizes and cycle length when the products are made on a single machine. Techniques to determine the MV are explo...

This paper presents a method for computing the lot size to be produced each time each product is scheduled for production when all products are produced on a single machine. The method also computes the distribution of lot size for each product. The demand for each product is a stochastic variable with known distribution, distributed independently for nonoverlapping time periods and identically for equal time periods.