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In this paper, we discuss why it is appropriate maximize the profits, instead of minimizing the costs, in an inventory system with an inventory-level-dependent demand rate. In addition, we restate Urban's viewpoint that the restriction of zero ending-inventory is not necessary in an inventory-level-dependent demand model. Consequently, we amend Giri and Chaudhuri's inventory model for deteriorating items by changing the objective to maximize the profits and relaxing the restriction of zero ending-inventory. Finally, we provide a couple of examples to show that both the order quantity and the profit obtained from our proposed model are significantly larger than those in Giri and Chaudhuri's model, in which the objective is to minimize the costs.

A model that integrates the issues of production, quality, maintenance, inspection, inflation, and time value of money is proposed in this paper. It is assumed that the production system starts in the in-control state producing items of high or perfect quality. However, the process may deteriorate with time and shifts at a random point in time to an out-of-control state and begins to produce non-conforming items. The elapsed time for the process to shift to the out-of-control state is assumed to follow a general distribution. Imperfect preventive maintenance, restoration, and inspection errors are taken into account. Also, inflation, time value of money, and shortage are considered in the proposed model. Numerical examples are presented to illustrate important aspects of the integrated model.

This work presents an optimization model to support decisions in the production planning and control of the electrofused grain industry. A case study was carried out in a Brazilian company with the aim of helping to increase productivity and improve customer service concerning meeting deadlines. A mixed integer linear programming model combining known models of process selection and single-stage lot sizing were applied to the production scheduling of electrofused grains. Optimizing this scheduling is not a simple task mainly because of the scale of the equipment setup times, the diversity of the products and the deadlines of the order due dates. A constructive heuristic is also proposed as an alternative solution method, particularly for large-sized instances. The results show that the model and the heuristic can produce better solutions than the ones currently used by the company.

We consider the extended economic production quantity (EPQ) problem when demand follows a Poisson process in a production system. A fixed lot sizing policy is implemented to minimize fluctuation of workload, and to smooth production planning and inventory control. The considered costs include setup cost, inventory carrying cost, and shortage cost when demand cannot be satisfied from stock. The main contributions of this paper are two folds. We develop and analyze the extended EPQ model. Under some mild conditions, the expected cost per unit time can be shown to be convex. Via computational experiments, we demonstrate that, in comparison with classical EPQ model, the average reduction of expected cost is significant when demand is random and the proposed model is used to determine lot sizing policy. Our computational tests have also illustrated the impact of various parameters on the expected cost model and the lot sizing policy.

In this work, we face a variant of the capacitated lot sizing problem. This is a classical problem addressing the issue of aggregating lot sizes for a finite number of discrete periodic demands that need to be satisfied, thus setting up production resources and eventually creating inventories, while minimizing the overall cost. In the proposed variant we take into account lifetime constraints, which model products with maximum fixed shelflives due to several possible reasons, including regulations or technical obsolescence. We propose four formulations, derived from the literature on the classical version of the problem and adapted to the proposed variant. An extensive experimental phase on two datasets from the literature is used to test and compare the performance of the proposed formulations.

Context. This paper deals with bilateral joint decision making in supply chains, and more specifically focuses on coordinating the decisions taken by the supplier and the producer in lot sizing. Research gap. Previous existing works in lot sizing have modeled the coordination task as a bi-level optimization problem. Unfortunately, the bi-level model causes a hierarchy between the two actors by making the leader imposing the decisions that suits his/her interests to the follower. This induces a significant conflict of interest between the two stakeholders because the leaders benefit is always greater than the follower’s one. Objective. The main goal of this work is to attenuate the conflict of interest issue between both actors by proposing a multi-objective model that alleviates the hierarchy and creates a win–win situation. Method. We propose an effective multi-objective lot sizing model, called Supplier-Producer Multi-Objective Lot Sizing (SP-MOLS); that alleviates the hierarchy between the actors’ objectives by assigning them the same importance degree and hence optimizing them simultaneously. The resolution of our SP-MOLS model using the Non-dominated Sorting Genetic Algorithm II (NSGA-II), as an effective meta-heuristic search engine, provides a set of trade-off solutions, each expressing a compromise degree between the two actors: the supplier and the producer. Results. To validate our approach, we use five test problems each containing 100 instances with a planning horizon of 10 periods and we analyze the obtained trade-off solutions using the compromise degree and the gap between costs as main consensus metrics. The obtained results reveal that a small sacrifice in the leader’s benefit could produce a significant improvement in the follower’s one. For instance, a 10% increase of the producer’s cost may generate a 42% decrease in the supplier’s one. Reciprocally, a 0.4% increase of the supplier’s cost may generate a 49% decrease in the producer’s cost. Method algorithmic improvement. As solutions of interests for both stakeholders are usually located within the extreme regions of the Pareto front, we propose NSGA-II with Focus on Extreme Regions (NSGA-II-FER) as a new variant of NSGA-II that focuses the search in the extreme regions of the Pareto front thanks to a modified crowding measure that is adaptively managed during the evolution process. This variant has shown its ability to eliminate dominance-resistant solutions and thus to come up with better extreme regions. Based on the experimental results, NSGA-II-FER is shown to have the ability to provide the decision makers with more convergent and more diversified extreme non-dominated solutions, expressing better trade-off degrees between both actors’ costs. Managerial implications. The promising results obtained by our proposal encourage decision makers’ to adopt a multi-objective approach rather than a bi-level one. From our personal perspective, we recommend running the three models (the multi-objective model and the two bi-levels ones); then analyzing the solutions of all models in terms of compromise degrees and logistic costs. This would allow both actors to observe how the hierarchy incurred by the bi-level models increases conflicts, while the multi-objective one generates solutions with much improved consensus degrees. Such observations will convince the supply chain stakeholders to adopt our multi-objective approach, while keeping an eye on the bi-level models’ solutions and the consensus degrees. Finally, we also recommend focusing on the extreme regions of the Pareto front since they contain rich solutions in terms of consensus. Such solutions are more convincing in the negotiation process and thus could lead to better win–win situations.

Network flow problems are widely studied, especially for those having convex cost functions, fixed-charge cost functions, and concave functions. However, network flow problems with general nonlinear cost functions receive little attention. The problems with step cost functions are important due to the many practical applications. In this paper, these problems are discussed and formulated as equivalent mathematical mixed 0-1 linear programming problems. Computational results on randomly generated test beds for these exact approached solution procedure are reported in the paper.