Jen-Ming Chen

An inventory model for deteriorating items with time-proportional demand and shortages under inflation and time discounting

This paper proposes a generalized dynamic programming model for inventory items with Weibull distributed deterioration. In this model, the demand rate is assumed to be time-proportional, shortages are allowed and completely backordered, and the effects of inflation and time-value of money are taken into consideration. The solutions of the model determine the optimal replenishment schedule over a finite planning horizon so that the present worth of total cost associated with the inventory system is minimized. The proposed model permits variation in both the replenishment intervals and the service levels between order cycles. As a result, it generates a better solution than other optimization models having fixed order intervals and/or fixed service levels. The solution procedure is illustrated by two numerical examples, and comparison with an existing model is carried out.

The multi-item replenishment problem in a two-echelon supply chain: the effect of centralization versus decentralization

This paper deals with a joint replenishment arrangement with a two-echelon supply chain, having one supplier or manufacturer and one buyer or retailer, facing a deterministic demand and selling a number of products in the marketplace. We considered a situation involving a family of products sharing a common production facility, in which there is a major setup cost for each production run and an item-specific minor processing cost for each item being added into production. The retailer also has major setup costs due to economies of scale in transportation and distribution expenses and an item-specific minor setup cost for each additional item involved in the order. In such a setting, it seemed as if it would be economically beneficial for both parties to enter into a joint replenishment arrangement. We proposed both centralized and decentralized decision models to determine the best solution to minimize costs. We proved the optimal properties of the models, developed a search algorithm and numerically illustrated the benefits generated from such an arrangement. In addition, we have proposed a profit sharing mechanism through a well-known quantity discount scheme, so that potential Pareto improvements may be achieved among the participants of a coordinated supply chain.

Pricing and production lot-size/scheduling with finite capacity for a deteriorating item over a finite horizon

Although the lately evolved manufacturing technologies such as enterprise resource planning (ERP) provide a unified platform for managing and integrating core business processes within a firm, the decision-making between marketing and production planning still remains rather disjoint. It is due in large parts to the inherent weaknesses of ERP such as the fixed and static parameter settings and uncapacitated assumption. To rectify these drawbacks, we propose a decision model that solves optimally the production lot-size/scheduling problem taking into account the dynamic aspects of customers demand as well as the restriction of finite capacity in a plant. More specifically, we consider a single product that is subject to continuous decay, faces a price-dependent and time-varying demand, and time-varying deteriorating rate, production rate, and variable production cost, with the objective of maximizing the profit stream over multi-period planning horizon. We propose both coordinated and decentralized decision-making policies that drive the solution of the multivariate maximization problem. Both policies are formulated as dynamic programming models and solved by numerical search techniques. In our numerical experiments, the solution procedure is demonstrated, comparative study is conducted, and sensitivity analysis is carried out with respect to major parameters. The numerical result shows that the solution generated by the coordinated policy outperforms that by the decentralized policy in maximizing net profit and many other quantifiable measures such as minimizing inventory investment and storage capacity.

An optimal design for process quality improvement: modelling and application

Existing research works on process quality improvement focus largely on the linkages between quality improvement cost and production economics such as set-up cost and defect rate reduction. This paper deals with the optimal design problem for process improvement by balancing the sunk investment cost and revenue increments due to the process improvement. We develop an optimal model based on Taguchi cost functions. The model is validated through a real case study in automotive industry where the 6-sigma DMAIC methodology has been applied. According to this research, the management can adjust the investment on prevention and appraisal costs on quality improvement that enhances process capability, reduces product defect rate and, as a result, generates remarkable financial return.

An optimal replenishment model for inventory items with normally distributed deterioration

This paper deals with the inventory replenishment problem for deteriorating items with normally distributed shelf life, continuous time-varying demand, and shortages under the inflationary and time discounting environment. The reasons of choosing normal are twofold: it is one of the most important probability phenomena in the real world due to the classical central limit theorem, and it is also one of the most commonly used lifetime distributions in reliability contexts. The problem is formulated as a dynamic programming model and solved by numerical search techniques. The solutions of the model determine the optimal replenishment schedule over a finite planning horizon so that the present worth of the future costs associated with the system is minimized. In the extensive experiments, we validate the model, demonstrate the optimal replenishment schedule and lot-size, and carry out a comparative study to ascertain its contribution. In addition, sensitivity analysis was provided to help identify the most crucial factors that affect system performance. The experimental result shows that the deteriorating problem solved by an appropriate model (i.e. the proposed normal model) can save the total cost up to 2% approximately. It also identifies that the magnitudes of purchase cost per unit and demand rate are the most significant parameters that affect the replenishment decisions and cost.

The Economics of a Closed-Loop Supply Chain with Remanufacturing

This study deals with joint decisions on pricing and production lot-sizing in a closed-loop supply chain consisting of manufacturing and remanufacturing operations. This study emphasizes the economic analysis of this hybrid system with substitution between the new and the remanufactured versions of the same product. We develop analytical models under a newsvendor framework bearing the following questions in mind. Can a hybrid system operate cost-effectively? Can it outperform the manufacturing-only system? If yes, to what extent and under what conditions? If not, what are the key factors that cause underperformance? This study formulates a multi-variable optimization problem and performs mathematical and numerical analysis. Results show that the hybrid system does not outperform the manufacturing-only system under a generic setting, but achieves better performance under conditions with a higher degree of substitution and/or a lower remanufacturing cost. In this scenario, participating in remanufacturing is not only an issue of environmental responsibility, but a profit-boosting option.

OPTIMAL ORDERING POLICY FOR A DETERIORATING ITEM WITH IMPERFECT QUALITY AND PARTIAL BACKORDERING

ABSTRACT This study develops a production-inventory model considering a deteriorating item with imperfect quality and partial backordering. Such implicit assumptions are reasonable in view of the fact that poor-quality items do exist during production. Defective items are usually picked up during the screening process. Shortages are partially backordered since not all customers are willing to wait for new replenishments of stocks. The impatient customer will result in lost sale. The analysis shows that our model is a generalization of the models in current literatures. Also, a lower bound on the back-ordered ratio is obtained to ensure concave of the net expected profit function. An algorithm and numerical analysis are used to illustrate the solution procedure. Computational results indicate that our model leads to more realistic results.

Pricing and lot-sizing for a deteriorating item in a periodic review inventory system with shortages

We consider a single product that is, subject to continuous decay, a multivariate demand function of price and time, shortages allowed and completely backlogged in a periodic review inventory system in which the selling price is allowed to adjust upward or downward periodically. The objective of this paper is to determine the periodic selling price and lot-size over multiperiod planning horizon so that the total discount profit is maximized. The proposed model can be used as an add-in optimizer like an advanced planning system in an enterprise resource planning system that coordinates distinct functions within a firm. Particular attention is placed on investigating the effect of periodic pricing jointly with shortages on the total discount profit. The problem is formulated as a bivariate optimization model solved by dynamic programming techniques coupled with an iterative search process. An intensive numerical study shows that the periodic pricing is superior to the fixed pricing in profit maximization. It also clarifies that shortages strategy can be an effective cost control mechanism for managing deterioration inventory.

On Channel Coordination Under Price-Dependent Revenue-Sharing: Can Ebay's Fee Structure Coordinate the Channel?

This article deals with the problem of coordinating a vertically separated channel under consignment contracts with a price-dependent revenue-sharing (R-S) function. We consider the retailer being a channel leader who offers the vendor a leave-it-or-take-it contract, and the vendor being a price-setting firm who sells the one-of-a-kind goods through the exclusive channel. Under such a setting, the retailer decides on the term of R-S contract, and the vendor determines the retail price of the product. For each item sold, the retailer deducts an agreed-upon percentage from the price and remits the balance to the vendor. We model the decision-making of the two firms as a Stackelberg game, and carry out equilibrium analysis for both the centralized and decentralized regimes of the channel with consideration of three kinds of contracts: the fixed, the price-increasing, and the price-decreasing R-S percentage. Our analysis reveals that the contract with a price-decreasing R-S function, for example, the fee structure adopted by eBay.com, performs worse than the others. It persists in a consistent bias: the price-decreasing R-S induces the vendor to choose a higher price, and the retailer tends to receive a lower R-S percentage, which leads to less demand quantity, less profit, and channel inefficiency.

The impact of inspection errors, imperfect maintenance and minimal repairs on an imperfect production system

This paper develops an integrated model of production lot-sizing, maintenance and quality for considering the possibilities of inspection errors, preventive maintenance (PM) errors and minimal repairs for an imperfect production system with increasing hazard rates. In this study, a PM activity is imperfect in that a production system cannot be recovered as good as new and might cause the production system to shift to the out-of-control state with a certain probability. Numerical analyses are used to simulate the effect of changes in various parameters on the optimal solution for which the time that the process remains in the in-control state is assumed to follow a Weibull distribution. In addition, we investigate the effects of inspection errors and PM errors on the minimum total cost of the optimal inspection interval, inspection frequency and production quantity.