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Generally, the transportation of cargo plays a vital role in effective supply chain management. For the safe transportation of the goods, the Returnable Containers (RCs) are provided by the container management organization to the consignee as rental basis. Unfortunately, some of the RCs are returned as delay in time for some situations. This study explores a situation of container management organization that unexpected delay of empty containers and then suggests a restoring strategy for shortfall units. As a strategy of restoring the shortfall units, this research considers the leasing option instead of buying the new RCs. This paper examines the container inventory model with the consideration of the delayed return of containers under the fuzzy arena. Because the container's return rate is unpredictable and uncertain, the container inventory model is formulating under fuzzy environment. This research describes a container inventory model with price-sensitive demand. In this model, the container return rate as well as the proportion of repairable from received RCs as Triangular Fuzzy Numbers (TFNs). The optimal duration of inspection of the container and the optimal duration of the lease of an RC are obtained. The expected total cost using the fuzzy return rate and the fuzzy proportion of repairable RCs is computed. The container inventory model under fuzzy arena is proposed to attain the approximate outcome for the unpredictable and uncertain parameters. The impact of the fuzzy proportion of retuned RCs, fuzzy reparable from received RCs, and the changes in some parameters on optimal solutions are performed in the sensitivity analysis. [ABSTRACT FROM AUTHOR]

Estimating market demand for a product is essential to business growth; yet, it is exceedingly difficult. This article considers various demand patterns for a single product in a three-echelon supply chain where a single supplier, a single manufacturer and a single retailer are involved. A robust inspection process is considered at the manufacturer's end to deliver a high-quality product to the retailer. The backorder strategy is incorporated to enhance the company's trust and reputation among consumers. The major idea of this research is to analyze the nature of the product's demand in three distinct situations, as well as the benefits of implementing the backorder technique. Three cases are analyzed on the basis of different demand patterns, in which the demand rate is assumed to be constant (i.e., deterministic), price-dependent and fuzzy in the first, second and third cases, respectively. To verify this model, numerical examples are tested independently with identical information for each case and owing to the complexity of the objective function; a genetic algorithm is employed to obtain the best solution. Finally, sensitivity analysis, managerial insights and conclusions, including the future directions, are provided. [ABSTRACT FROM AUTHOR]

This study renders a location-inventory problem for a closed-loop supply chain network under the circumstance of price-dependent demands, in which there are suppliers/recovering centers, stores and consumer areas. In this respect, the demand is supposed to be correlated, and the inventory of new and returned products are controlled via a continuous review system (Q, r) in the stores. What is more, the shortage is allowed and could be emerged as back-ordered and lost sales. A nonlinear programming model is offered to formulate the problem, which maximizes the total profit of the supply chain. In this regard, miscellaneous decisions are determined, such as location-allocation facilities, inventory levels and prices of products. So as to solve the proposed model, two well-known meta-heuristic algorithms with particular encoding and decoding procedures, including a genetic algorithm (GA) and an imperialist competitive algorithm (ICA), are employed due to the Np-hard nature of the model. Finally, with the intention of illustrating the validation and applicability of the model, a real case study of a wireless network is investigated. [ABSTRACT FROM AUTHOR]

The process of deterioration may not start immediately after the consignment reaches the go down; there generally occurs a delay. In certain cases, deterioration might begin after a certain period which may further prolong due to the introduction of better methods of inventory management. To take into cognizance of these situations, in contrast to the ordinary assumption in the existing models, we have considered that the decay in owned warehouse begins earlier than that in case of rented warehouse as the latter always provides for better inventory management and facilities. Applying these phenomena, a two-storage inventory model has been formulated with advance payment under three different situations according to different possibilities of starting times of deterioration in both warehouses. In this model, demand depends upon the selling price wherein shortages are considered partially with fixed backlogging rate. Analyzing and investigating the proposed problem, three different optimization problems are formulated and the optimality of these problems is proved theoretically. To solve the model, an algorithm is proposed. Then, to illustrate the model numerically, an example is considered and solved. Finally, post optimality is performed in order to investigate the effects of changes of different system parameters. [ABSTRACT FROM AUTHOR]

In this article, we establish an inventory model for deteriorating items with a return period and price-dependent demand for the retailer who offers two-phase advance sales to his/her customers. The replenishment cycle is divided into two sales periods: one is the two-phase advance sales period, and the other is the spot sales period. Before customers with reservations receive their orders, they may cancel the order. On the other hand, when the customers receive the order, they can make a request to return products for any reason during the return period. We provide an easy-to-use method to obtain the optimal selling price and the optimal sales period to achieve the retailer's maximum total profit. Finally, we give numerical examples to illustrate the solution procedure. We perform a sensitivity analysis to investigate the effect of changes of some main parameter values on the optimal solution and provide an economic interpretation. [ABSTRACT FROM AUTHOR]

If an exporter or a wholesaler sells goods at a fixed price to be paid in the currency of the seller's country, then the purchase price of the importer depends upon the prevailing exchange rate of their respective currencies. Ideally, in a floating exchange rate system, the purchase price has to change according to shifts in the exchange rate. In such a scenario the entire exchange rate risk is borne by the importer/buyer. However, in international trade, it is customary for the parties to enter into a risk-sharing agreement, under which the buyer does not pay the seller on the basis of the prevailing exchange rate, but pays a mutually agreed upon price that falls within a range of fluctuating exchange rates. In this manner, the profit or loss due to fluctuations in the exchange rate would be shared by both the parties. These stochastic variations in purchase prices are modeled through a Markov chain. In this article, the resulting purchase and inventory problem is analyzed by identifying a regenerative cycle. An optimal selling price that maximizes the expected profit per unit time is also discussed. Further, optimal ordering policies under no stock-out conditions are derived with an optimal uniform demand corresponding to the optimal selling price. Through sensitivity analyses, differences in profit function with respect to carrying cost fraction, setup costs, and purchase prices are also shown. An investigation into the possible loss if this model solution is not implemented is also made through numerical illustrations. A discussion of a special case of two-purchase price scenario gives additional insight into the problem. [ABSTRACT FROM AUTHOR]

In this paper, we study a two-echelon supply chain inventory system with a single manufacturer and a single buyer, considering price-dependent demand and variable lead time. Lead time can be reduced by added crashing cost. We first assume that the lead time demand follows a normal probability distribution and then consider the case where it is distribution free. We develop both the centralized and decentralized models and derive the optimal solutions by using profit maximization criterion. Feasibility and efficiency of the proposed models are justified through two numerical examples. We numerically investigate how the optimal decisions are affected by changes in various model-parameters. From numerical study, we observe that even though the lead time reduction diminishes the retailer's selling price, it enhances the system profit significantly. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the simultaneous coordination of price and capacity building decisions in a dyadic supply chain. This problem is a combination of capacity reservation problem and pricing problem. While the coordination of supply chain with stochastic demand and fixed prices has received much attention in the literature, price-dependent and stochastic demand has been less considered. We study the latter case where a price-setting retailer faces a linear decreasing demand with respect to price. To capture the uncertainty of the demand, we add a stochastic variable to the demand function. In addition, we incorporate production rate and inventory cost on the supplier side. We propose Revenue Sharing Reservation Contract with Penalty (RSRP) as a coordination mechanism to align the price and capacity decisions. We then extend the model to include multiple retailers which are geographically dispersed. We next conduct a comprehensive numerical example with an extensive sensitivity analysis to understand the behavior and robustness of the supply chain under a RSRP, and finally, we draw some managerial implications. [ABSTRACT FROM AUTHOR]

The saliency of returns in today's business world is unquestionable, in such items as toys, Christmas decorations, books, seasonal/fashion items and the like. This is largely due to the high economic benefits prevalent in some industries today and to the increasing opportunities for resale in secondary and global markets. This paper attempts to model the profitability of returns policy in presence of a secondary market, to a profit-maximizing manufacturer in a newsvendor framework. The returns policy applies both for the unsold merchandise left at the end of the selling season and the items returned by the unsatisfied customers within the specified time period. With a returns policy, the manufacturer shares the risks of demand uncertainty, in turn assuaged by the availability of secondary market. The manufacturer's decision is to arrive at an optimal wholesale price and the returns policy, based on the retailer's reaction on that offer. The retailer in turn optimizes the retail price and the order quantity to meet a price-dependent uncertain demand. This set of optimal policies has then been contrasted to that obtained from maximizing the combined profit of the manufacturer and of the retailer. The key question in the comparison has been clearly answered. The total combined profit that coordinates the policies of both channels exceeds that of the sum of the profits obtained independently. [ABSTRACT FROM AUTHOR]

This paper discusses the optimal pricing and replenishment policies of an economic order quantity model for non-instantaneous deteriorating items with partial backlogging over an infinite time horizon. The model is studied under the replenishment policy starting with no shortages. The backlogging rate is any non-increasing function of the waiting time up to the next replenishment. The objective of this model is to maximize the total profit which includes the sales revenue, purchasing cost, set up cost, holding cost, shortage cost, and opportunity cost due to lost sales. Here, the selling price, replenishment quantity, replenishment cycle length, and the time duration of the positive inventory level are taken as decision variables to maximize the profit of the inventory system. The existence and the uniqueness of the solution of the proposed inventory system are examined. We suggest a solution procedure to find the optimal solution of the described model. Numerical examples are presented to determine the developed model and the solution procedure. Sensitivity analysis of the optimal solution with respect to major parameters is carried out and some useful managerial results are obtained. [ABSTRACT FROM AUTHOR]

This paper investigates the duality relationships between Marshallian and compensated price-dependent consumer demands. We associate the compensated price-dependent demand with Luenberger’s benefit function, which has nice aggregation properties and provides a general basis for conducting welfare analysis. As an analog to the well-known “Slutsky equation,” we derive a “Luenberger equation” establishing the general relationships between Marshallian and compensated price-dependent slopes. Our duality results strengthen the conceptual linkages between positive economic analysis and welfare analysis. [ABSTRACT FROM AUTHOR]

In developing the best strategy for real-world applications, the vendor must have some knowledge of the buyers’ behavior such as response to shortages and price increases. Using this knowledge, he can develop a policy that will ensure the largest net profit. Considering the fact, a two-warehousing inventory model has been developed where the demand is price-sensitive under the bulk release rule. Stockouts are allowed and are fully backlogged. Moreover, the transportation cost is taken to be dependent on the transported units. The model jointly optimizes the selling price and the order quantity by maximizing the system profit. Results have been validated with the help of a numerical example. [ABSTRACT FROM AUTHOR]

This paper studies the decision-making and coordination of supply chain (SC) considering the effect of price-dependent demand. By assuming demand decreases as the price increases, we analyse the impacts of the dependence on the SC in three different models: decentralized without coordination, centralized coordination and decentralized with coordination by revenue sharing contract. The existence of the best solution in the different models is proved, and the performance of revenue sharing coordination SC is similar to the centralized one. We find that the more evidently the price affects the demand, the more revenue sharing contract improves the performance of SC. The dependence affects the decision-making and the parameter setting of revenue sharing contract is also found. [ABSTRACT FROM AUTHOR]