Ren-qian Zhang

Deterministic EOQ with partial backordering and correlated demand caused by cross-selling

There has been much work regarding the deterministic EOQ with partial backordering. The majority of these studies assume no correlation in sales, so independent demands across items is applied in the models. However, it is generally recognized that cross-selling effects between items often appear in real contexts. Thus, incorporating such effects in the inventory model in the form of correlated demands makes it of more practical relevance. In this paper, the authors address a two-item inventory system where the demand of a minor item is correlated to that of a major item because of cross-selling. We firstly present a two-item EOQ model with identical order cycles, where the unmet demand of the major item can be partially backordered with lost sales whereas the demand of the minor item must be met without stockouts. This model is further extended to fit a more practical case where the order cycle of the major item is an integer multiple of that of the minor item. The optimal solutions of the two models, as well as the inventory decision procedures, are also developed. Comparative analysis on these two EOQ models has been drawn in the computational study which presents some insights into the parameter effect on the optimal inventory policy.

The activity-based aggregate production planning with capacity expansion in manufacturing systems

This paper builds a mixed integer linear programming (MILP) model to mathematically characterize the problem of aggregate production planning (APP) with capacity expansion in a manufacturing system including multiple activity centers. We use the heuristic based on capacity shifting with linear relaxation to solve the model. Two linear relaxations, i.e., a complete linear relaxation (CLR) on all the integer variables and a partial linear relaxation (PLR) on part of the integer variables are investigated and compared in computational experiments. The computational results show that the heuristic based on the capacity shifting with CLR is very fast but yields low-quality solution whereas the capacity shifting with PLR provides high-quality solutions but at the cost of considerable computational time. As a result, we develop a hybrid heuristic combining beam search with capacity shifting, which is capable of producing a high-quality solution within reasonable computational time. The computational experiment on large-scale problems suggests that when solving a practical activity-based APP model with capacity expansion at the industrial level, the capacity shifting with CLR is preferable, and the beam search heuristic could be subsequently utilized as an alternative if the relaxation gap is larger than the acceptable deviation.

Non-permutation flow shop scheduling with order acceptance and weighted tardiness

Model the problem of non-permutation flow shop scheduling with order acceptance.The model is transformed to linear MIP that is optimally solved by commercial solver.Theorems that are favorable for developing algorithms are presented.An efficient two-phase genetic algorithm (TP-GA) is proposed.The heuristic yields high quality non-permutation solutions. This paper studies the non-permutation solution for the problem of flow shop scheduling with order acceptance and weighted tardiness (FSS-OAWT). We formulate the problem as a linear mixed integer programming (LMIP) model that can be optimally solved by AMPL/CPLEX for small-sized problems. In addition, a non-linear integer programming (NIP) model is presented to design heuristic algorithms. A two-phase genetic algorithm (TP-GA) is developed to solve the problem of medium and large sizes based on the NIP model. The properties of FSS-OAWT are investigated and several theorems for permutation and non-permutation optimum are provided. The performance of the TP-GA is studied through rigorous computational experiments using a large number of numeric instances. The LMIP model is used to demonstrate the differences between permutation and non-permutation solutions to the FSS-OAWT problem. The results show that a considerably large portion of the instances have only an optimal non-permutation schedule (e.g., 43.3% for small-sized), and the proposed TP-GA algorithms are effective in solving the FSS-OAWT problems of various scales (small, medium, and large) with both permutation and non-permutation solutions.

An extension of partial backordering EOQ with correlated demand caused by cross-selling considering multiple minor items

Zhang et al. (2011) proposed the partial backordering EOQ with correlated demand caused by cross-selling, where a portion of the sales of a minor item is associated with those of a major item. In this paper, we extend their model to make it more applicable to dealing with the inventory replenishment problem for multiple associated items. We formulate the model as a mixed integer nonlinear programming (MINLP) problem and develop a global optimum search procedure with the fill rate given. We further employ a one-dimensional search on the fill rate to obtain the minimum total inventory cost within a predetermined precision, which enjoys polynomial computational complexity.

A variable neighborhood search with an effective local search for uncapacitated multilevel lot-sizing problems

In this study, we improved the variable neighborhood search (VNS) algorithm for solving uncapacitated multilevel lot-sizing (MLLS) problems. The improvement is twofold. First, we developed an effective local search method known as the Ancestors Depth-first Traversal Search (ADTS), which can be embedded in the VNS to significantly improve the solution quality. Second, we proposed a common and efficient approach for the rapid calculation of the cost change for the VNS and other generate-and-test algorithms. The new VNS algorithm was tested against 176 benchmark problems of different scales (small, medium, and large). The experimental results show that the new VNS algorithm outperforms all of the existing algorithms in the literature for solving uncapacitated MLLS problems because it was able to find all optimal solutions (100%) for 96 small-sized problems and new best-known solutions for 5 of 40 medium-sized problems and for 30 of 40 large-sized problems.

Neighborhood search techniques for solving uncapacitated multilevel lot-sizing problems

In this paper, several neighborhood search techniques for solving uncapacitated multilevel lot-sizing problems are investigated. We introduce three indexes: distance, changing range, and changing level that have great influence on the searching efficacy of neighborhood search techniques. These insights can help develop more efficient heuristic algorithms. As a result, we have developed an iterated neighborhood search (INS) algorithm that is very simple but that demonstrates good performance when tested against 176 benchmark instances under different scales (small, medium, and large), with 25 instances having been updated with new best known solutions in the computing experiments.

The multi-item newsvendor model with cross-selling and the solution when demand is jointly normally distributed

Products are often demanded in tandem because of the cross-selling effect. The demand for an item can increase if sales of its cross-selling-associated items are achieved or decrease when the associated items are out of stock, resulting in lost sales. Therefore, a joint inventory policy should be pursued in a cross-selling system. This paper introduces customer-driven cross-selling into centralized and competitive newsvendor (NV) models by representing an item’s effective demand as a function of other items’ order quantities. We derive first-order optimality conditions for the centralized model in addition to pure-strategy Nash equilibrium conditions and uniqueness conditions of the equilibria for the competitive model. We further develop gradient-based (GB) and iteration-based (IB) algorithms to solve the centralized and competitive models, respectively. A computational study verifies the effectiveness of the proposed algorithms. The computational results show that a larger cross-selling effect leads to a larger order quantity in a centralized NV model but a smaller order quantity in a competitive NV model, and a larger positive correlation between items’ demands leads to higher profits with smaller order quantities in both models. Moreover, NVs will order more items if the demand variance is greater, however resulting in lower profits. In a competitive situation, one will prefer smaller order quantities than in a centralized decision situation.

Non-linear optimal control of manufacturing system based on modified differential evolution

This study considers the non-linear optimal control of the complex manufacturing system. We construct a mathematical model, which decomposes the complex manufacturing system into many correlated working centers, where the number of inventory and production evolves dynamically. It aims to minimize the cost of production control. We can utilize MDE algorithm to solve this model. The model can be easily used in multi-product, multi-center, multi-period manufacturing system.

Association Rules Based Research On Man-Made Mistakes In Aviation Maintenance: A Case Study

Its an important problem for aviation maintenance enterprise to assure quality of maintenance activity. Thinking over human factors and organization management, the paper produces a production system continuous improvement model for aviation maintenance quality. First, the model gathers characteristics of human factors and man-made maintenance mistakes. Based on association rules, relationships between human factors and the man-made mistakes are found. So, measures for improving organization and management could be produced, which is more pertinent. And, these measures will be used for production system continuous improvement. In an aviation maintenance firm, we made a case study in maintenance management of a type of military aero-transporter and reach to the anticipative effects

Scenario-based Stochastic Capacity Planning Model and Decision Risk Analysis

Abstract To study the capacity planning problem under uncertainty in which market demand and product price are stochastic, multi period capacity planning model based on scenario was investigated in this paper. Two models were proposed: one is a prearranged planning model in which the capacity investment plan do not change with the stochastic market demand, and the other is an adaptive planning model in which capacity investment plan could trace the evolution progress of the stochastic market demand. The computational study compared the decision results of both models, which reveals that the adaptive planning model could suggest better decision. Moreover, based on downside risk analysis, the investment risk of stochastic capacity planning has been investigated, and a prearranged capacity planning model considering the expected downside risk of the objective revenue was proposed. In the model, a constraint of expected downside risk is added to the initial stochastic model to reflect the decision-makers risk preference. Whether to consider the risk or not will result in different decisions, which, in the computational study, were compared.