Tsu-Pang Hsieh

A production-inventory model incorporating the effect of preservation technology investment when demand is fluctuating with time

In most of the inventory models in the literature, the rate of deterioration of goods is viewed as an exogenous variable, which is not subject to control. In the real market, firms can reduce the rate of deterioration of products by means of effective capital investment in preservation technology. In this research, we formulate a production-inventory model for deteriorating items with time-varying demand and finite replenishment rate by allowing preservation technology cost as a decision variable in conjunction with production policy. The objective is to find the optimal production and preservation technology investment strategies while minimizing the total cost over the planning horizon. A traditional particle swarm optimization is coded and used to solve the mixed-integer nonlinear programming problem. Some numerical examples are used to illustrate the features of the proposed model.

A particle swarm optimization for solving joint pricing and lot-sizing problem with fluctuating demand and unit purchasing cost

In this paper, we extend the classical economic order quantity model to allow for not only a function of price-dependent and time-varying demand but also fluctuating unit purchasing cost. The joint replenishment problem is subject to continuous decay and a general partial backlogging rate. The objective is to find the optimal replenishment number, time scheduling and periodic selling price to maximize the discounted total profit. An effective search procedure is provided to find the optimal solution by employing the properties derived in this paper and particle swarm optimization algorithm. Several numerical examples are used to illustrate the features of the proposed model.

A particle swarm optimization for solving lot-sizing problem with fluctuating demand and preservation technology cost under trade credit

In this paper, we consider the effect of preservation technology cost investing on preservation equipment for reducing deterioration rate under two-level trade credit. The preservation technology cost is allowed for periodical upward or downward adjustments due to the time varying demand and the strategy of trade credit within the planning horizon. We establish a deterministic economic order quantity model for a retailer to determine his/her optimal preservation technology cost per replenishment cycle, the trade credit policies, the replenishment number and replenishment schedule that will maximize the present value of total profit. A particle swarm optimization with constriction factor is coded and used to solve the mixed-integer nonlinear programming problem by employing the properties derived from this paper. Some numerical examples are used to illustrate the features of the proposed model.

Deterministic ordering policy with price- and stock-dependent demand under fluctuating cost and limited capacity

In this paper, we extend the classical economic order quantity model to allow for the demand rate influenced by both selling price and displayed stock level. A finite period system is considered under inflation for deteriorating items. In addition, we impose a ceiling on the number of on-display stocks. We also allow for shortages and general partial backlogging. The objective is to maximize the discounted total profit by finding the optimal replenishment number, replenishment schedule and selling price changed periodically. An effective search procedure is provided to find the optimal solution by employing the properties derived in this paper and particle swarm optimization algorithm. Several numerical examples are used to illustrate the features of the proposed model.

Optimal dynamic pricing for deteriorating items with reference price effects when inventories stimulate demand

In this paper, we incorporate reference price effects into a deteriorating inventory problem when the demand rate depends on displayed stock level and selling price simultaneously. Reference price effects are formed empirically by customers to adjust current price perception on the basis of past purchases. The market demand is assumed to be responsive to the difference between the current selling price and the reference price, which is perceived as a loss or a gain. We consider three scenarios of market demand: loss neutrality, loss aversion, and loss seeking. An optimal dynamic pricing model is established to determine a pricing strategy maximizing the discounted total profit over an infinite time horizon. Theoretical results are derived to demonstrate the existence of the optimal solutions and to explore the relationships between optimal pricing decisions and an initial reference price based on mild assumptions. Numerical example and sensitivity analysis are presented to illustrate the theoretical results and managerial insights. Finally, concluding remarks are offered.

Determining optimal selling price and lot size with process reliability and partial backlogging considerations

In this article, we extend the classical economic production quantity (EPQ) model by proposing imperfect production processes and quality-dependent unit production cost. The demand rate is described by any convex decreasing function of the selling price. In addition, we allow for shortages and a time-proportional backlogging rate. For any given selling price, we first prove that the optimal production schedule not only exists but also is unique. Next, we show that the total profit per unit time is a concave function of price when the production schedule is given. We then provide a simple algorithm to find the optimal selling price and production schedule for the proposed model. Finally, we use a couple of numerical examples to illustrate the algorithm and conclude this article with suggestions for possible future research.

Comment on ‘An ordering policy for deteriorating items with allowable shortage and permissible delay in payment’ by Jamal, Sarker and Wang

In our original paper, we endeavoured to extend Raz et al’s (2000) off-line inspection model to consider inspection errors. But due to the neglect pointed out by Chun, our mathematical formulation went only halfway and did not allow inspection errors for the last unit in the batch. We are grateful to Chun for his insight and are happy to have derived a more general model which can be used by researchers in the future. We are also grateful to the editors for giving us the opportunity to reply to Chun’s Viewpoint.

Comment on ‘Supply chain model for a deteriorating product with time-varying demand and production rate’ by Giri and Maiti

In a recent article, Giri and Maiti (2012) developed a twoechelon supply chain model with a single buyer and a single vendor, and presented the appropriate theory for the problem. In Case (ii), as the expected number of conforming items produced by the vendor during the time interval [(i 1)Tþ tm, iT ] is less than the buyer’s order quantity, the shortage occurs. For the case considering shortages, the constraint (Equation (18)) on the joint average total cost was given by: