A two-echelon supply chain of a returnable product with fuzzy demand

This study investigates the effects of the manufacturer’s refund on retailer’s unsold products for the two-echelon decentralized and centralized supply chains of a short life and returnable product with trapezoidal fuzzy demand, in which retailer returns the unsold and the customer’s unsatisfactory products to the manufacturer. For each returnable chain, we obtain the closed-form solution of order quantity to maximize the total expected profit of the supply chain, and confirm that demand fuzziness does indeed affect the order quantity and the members’ expected profits. We provide a number of managerial insights by comparing both chains and show that each chain is more advantageous to the members depending on certain condition. Our models are appropriate for a supply chain with a returnable product that lacks information about the demand.     

Ordering and pricing decisions in a two-echelon supply chain with asymmetric demand information

This article examines coordinated decisions in a decentralized supply chain that consists of one supplier and one retailer, and faces random demand of a single product with a short life cycle. We consider a setting where the retailer has accurate demand information while the supplier does not. Such a problem with asymmetric demand information can be viewed as an extension of the newsboy problem in which both the supplier and the retailer possess the same demand information. Combining the mechanism of sharing demand information and that of quantity discount and return policy enables us to develop three coordinated models in contrast with the basic and uncoordinated model. We are able to show the ordinal relationship among the retailer’s optimal order quantities in these four models under a general form of random demand, and compare the supply chain profits and conduct sensitivity analysis analytically in four models under uniform random demand. We also provide numerical results under normal random demand that bear a resemblance to those under uniform random demand.     

Two-period pricing and decision strategies in a two-echelon supply chain under price-dependent demand

This paper presents a two-period supply chain model which is comprised of one manufacturer and one retailer who are involved in trading a single product. The demand rate in each period is dependent on the selling prices of the current period and the previous period. We assume that the manufacturer acts as the Stackelberg leader and declares wholesale price(s) to the retailer who follows the manufacturer’s decision and sets his selling prices for two consecutive periods. The manufacturer adopts one of the two pricing options: (1) setting the same wholesale price to both the selling periods (2) setting different wholesale prices to two different selling periods. Based on these pricing options, we develop four decision strategies of the manufacturer and the retailer and compare them. For a numerical example, we study the effects of these decision strategies on the optimal results of the supply chain. Further, we graphically analyze under what circumstances a particular decision strategy plays a dominant role.     

Stochastic multi-site supply chain planning in textile and apparel industry under demand and price uncertainties with risk aversion

A multi-product, multi-period, multi-site supply chain production and transportation planning problem, in the textile and apparel industry, under demand and price uncertainties is considered in this paper. The problem is formulated using a two-stage stochastic programming model taking into account the production amount, the inventory and backorder levels as well as the amounts of products to be transported between the different plants and customers in each period. Risk management is addressed by incorporating a risk measure into the stochastic programming model as a second objective function, which leads to a multi-objective optimization model. The objectives aim to simultaneously maximize the expected net profit and minimize the financial risk measured. Two risk measures are compared: the conditional-value-at-risk and the downside risk. As the considered objective functions conflict with each other’s, the problem solution is a front of Pareto optimal robust alternatives, which represents the trade-off among the different objective functions. A case study using real data from textile and apparel industry in Tunisia is presented to illustrate the effectiveness of the proposed model and the robustness of the obtained solutions.     

Integrated markdown pricing and aggregate production planning in a two echelon supply chain: A hybrid fuzzy multiple objective approach

Given high variability of demands for short life cycle products, a retailer has to decide about the products’ prices and order quantities from a manufacturer. In the meantime, the manufacturer has to determine an aggregate production plan involving for example, production, inventory and work force levels in a multi period, multi product environment. Due to imprecise and fuzzy nature of products’ parameters such as unit production and replenishment costs, a hybrid fuzzy multi-objective programming model including both quantative and qualitative constraints and objectives is proposed to determine the optimalprice markdown policy and aggregate production planning in a two echelon supply chain. The model aims to maximize the total profit of manufacturer, the total profit of retailer and improving service aspects of retailing simultaneously. After applying appropriate strategies to defuzzify the original model, the equivalent multi-objective crisp model is then solved by a fuzzy goal programming method. An illustrative example is also provided to show the applicability and usefulness of the proposed model and solution method.     

The continuous resupply policy for deteriorating items with stock-dependent observable demand in a two-warehouse and two-echelon supply chain

This paper expands previous work on stock-dependent demand for a retailer with a two-warehouse (OW/RW) situation to the case of deteriorating items and where the retailer seeks to obtain the integrated optimal distribution policy from collaboration with a supplier. Motivated by practical applications and recent literature, a policy is considered whereby products in good order from the retailer’s back-room (RW) are frequently transferred to its capacitated main store OW. Because the demand depends on the stock of good products in the OW, the aim is to keep this stock at its full capacity with products in good condition, and this can be done for as long as the RW stock of good products is positive. A firm’s objective function is the Net Present Value (NPV) of the firm’s future cash-flows. The profit functions are developed for both this continuous resupply policy and the commonly used policy in the OW/RW literature. Numerical examples are included and have been solved with grid search methods. The examples illustrate the benefits of adopting the continuous resupply policy, and also collaboration between the retailer and the wholesaler. Moreover, it is shown how these benefits can be shared by small adjustments to the product’s unit price between the firms.     

On sourcing and stocking policies in a two-echelon,multiple location,repairable parts supply chain

This research develops policies to minimize spare part purchases and repair costs for maintaining a fleet of mission-critical systems that operate from multiple forward (base) locations within a two-echelon repairable supply chain with a central depot. We take a tactical planning perspective to support periodic decisions for spare part purchases and repair sourcing, where the repair capabilities of the various locations are overlapping. We consider three policy classes: a central policy, where all repairs are sourced to a central depot; a local policy, whereby failures are repaired at forward locations; and a mixed policy, where a fraction of the parts is repaired at the bases and the remainder is repaired at the depot. Parts are classified based on their repair cost and lead time. For each part class, we suggest a solution that is based on threshold policies or on the use of a heuristic solution algorithm that extends the industry standard of marginal analysis to determine spare parts positioning by including repair fraction sourcing. A validation study shows that the suggested heuristic performs well compared to an exhaustive search (an average 0.2% difference in cost). An extensive numerical study demonstrates that the algorithm achieves costs which are lower by about 7–12% on average, compared to common, rule-based sourcing policies.     

An analysis of production-inventory models with deteriorating items in a two-echelon supply chain

This paper revisits two previous studies that addressed the integrated production–inventory problem for deteriorating items in a two-echelon supply chain, where the item’s deterioration rate is a constant or follows a continuous probability distribution function. The aim of this study is to present an improved solution procedure to determine the delivery lot size and the number of deliveries per production batch cycle that minimizes the total cost of the entire supply chain. The performance of the proposed methodology is illustrated analytically and numerically.     

Comparing improvement strategies for inventory inaccuracy in a two-echelon supply chain

Classical inventory theory often assumes no discrepancies between recorded inventory and actual inventory. However, inventory records are usually inaccurate due to many reasons in practice. For example, inventory shrinkage refers to the difference between booked inventory that a company should have as a result of its sales, purchasing, and manufacturing processes and actual inventory that it has on hand. This paper concerns the impact of inventory shrinkage to a supply chain and investigates different strategies to deal with inventory shrinkage. We consider a single-period two-echelon supply chain consisting of a Stackelberg manufacturer and a retailer whose inventory is subject to shrinkage errors. Our analysis is based on a single-period newsvendor model and considers the following cases of order decisions: (a) the retailer ignores the inventory errors; (b) the retailer estimates the errors; (c) the retailer shares the inventory error information with the manufacturer; and (d) RFID technology is used to reduce or eliminate the errors. The first case is the base strategy and a common practice for many supply chains, the other two represent certain non-technological strategies of the retailer when dealing with inventory inaccuracy, and the last one represents a technology improvement strategy by the manufacturer to reduce or eliminate inventory shrinkage errors. We compare these improvement strategies and derive critical tag price for RFID implementation as a technological remedy for the inventory inaccuracy problem. Conditions for the profitability of RFID adoption are discussed.     

On explicit solutions of a two-echelon supply chain coordination game

A contracting game under asymmetric information specific to two-echelon supply chain coordination between a retailer of unknown type and a supplier is studied. When the parameter which is private information to the retailer (holding cost) is known up to an interval of uncertainty, a uniform discrete approximation for retailer types leads to closed-form solutions where the joint (coordinated) optimal order quantity for a modified holding cost plays a major role. Furthermore, the closed-form solutions result in increasing information rent for higher types under easy-to-verify conditions involving strict lower limits on the total holding costs of retailer and supplier and the difference between uncoordinated optimal costs of consecutive retailer types.     

Incorporating demand uncertainty and forecast error in supply chain planning models

This paper develops a framework for examining the effect of demand uncertainty and forecast error on unit costs and customer service levels in the supply chain, including Material Requirements Planning (MRP) type manufacturing systems. The aim is to overcome the methodological limitations and confusion that has arisen in much earlier research. To illustrate the issues, the problem of estimating the value of improving forecasting accuracy for a manufacturer was simulated. The topic is of practical importance because manufacturers spend large sums of money in purchasing and staffing forecasting support systems to achieve more accurate forecasts. In order to estimate the value a two-level MRP system with lot sizing where the product is manufactured for stock was simulated. Final product demand was generated by two commonly occurring stochastic processes and with different variances. Different levels of forecasting error were then introduced to arrive at corresponding values for improving forecasting accuracy. The quantitative estimates of improved accuracy were found to depend on both the demand generating process and the forecasting method. Within this more complete framework, the substantive results confirm earlier research that the best lot sizing rules for the deterministic situation are the worst whenever there is uncertainty in demand. However, size matters, both in the demand uncertainty and forecasting errors. The quantitative differences depend on service level and also the form of demand uncertainty. Unit costs for a given service level increase exponentially as the uncertainty in the demand data increases. The paper also estimates the effects of mis-specification of different sizes of forecast error in addition to demand uncertainty. In those manufacturing problems with high demand uncertainty and high forecast error, improved forecast accuracy should lead to substantial percentage improvements in unit costs. Methodologically, the results demonstrate the need to simulate demand uncertainty and the forecasting process separately.     

A production-inventory model with probabilistic deterioration in two-echelon supply chain management

In this study, a production-inventory model is developed for a deteriorating item in a two-echelon supply chain management (SCM). An algebraical approach is applied to find the minimum cost related to this entire SCM. We consider three types of continuous probabilistic deterioration function to find the associated cost. The purpose of this study is to obtain the minimum cost with integer number of deliveries and optimum lotsize for the three different models. Some numerical examples, sensitivity analysis and graphical representation are given to illustrate the model. A numerical comparison between the three models is also given.     

The impact of partial information sharing in a two-echelon supply chain

We consider a simple two-echelon supply chain composed of a manufacturer and a retailer in which the demand process of the retailer is an AR(1) where the random component is a function of both sides’ information. We focus on partial information sharing under which each side informs the other of an interval in which the exact value of its own component of demand lies. These various levels of information sharing can reduce the supply chain costs.     

Integrated inventory management and supplier base reduction in a supply chain with multiple uncertainties

This paper considers a manufacturing supply chain with multiple suppliers in the presence of multiple uncertainties such as uncertain material supplies, stochastic production times, and random customer demands. The system is subject to supply and production capacity constraints. We formulate the integrated inventory management policy for raw material procurement and production control using the stochastic dynamic programming approach. We then investigate the supplier base reduction strategies and the supplier differentiation issue under the integrated inventory management policy. The qualitative relationships between the supplier base size, the supplier capabilities and the total expected cost are established. Insights into differentiating the procurement decisions to different suppliers are provided. The model further enables us to quantitatively achieve the trade-off between the supplier base reduction and the supplier capability improvement, and quantify the supplier differentiation in terms of procurement decisions. Numerical examples are given to illustrate the results.     

Hybrid algorithm for a vendor managed inventory system in a two-echelon supply chain

In this paper we address the issue of vendor managed inventory (VMI) by considering a two-echelon single vendor/multiple buyer supply chain network. We try to find the optimal sales quantity by maximizing profit, given as a nonlinear and non-convex objective function. For such complicated combinatorial optimization problems, exact algorithms and optimization commercial software such as LINGO are inefficient, especially on practical-size problems. In this paper we develop a hybrid genetic/simulated annealing algorithm to deal with this nonlinear problem. Our results demonstrate that the proposed hybrid algorithm outperforms previous methodologies and achieves more robust solutions.     

Collaborative production planning of supply chain under price and demand uncertainty

This research is motivated by an automobile manufacturing supply chain network. It involves a multi-echelon production system with material supply, component fabrication, manufacturing, and final product distribution activities. We address the production planning issue by considering bill of materials and the trade-offs between inventories, production costs and customer service level. Due to its complexity, an integrated solution framework which combines scatter evolutionary algorithm, fuzzy programming and stochastic chance-constrained programming are combined to jointly take up the issue. We conduct a computational study to evaluate the model. Numerical results using the proposed algorithm confirm the advantage of the integrated planning approach. Compared with other solution methodologies, the supply chain profits from the proposed approach consistently outperform, in some cases up to 13% better. The impacts of uncertainty in demand, material price, and other parameters on the performance of the supply chain are studied through sensitivity analysis. We found the proposed model is effective in developing robust production plans under various market conditions.     

Analysis of supply chain coordination under fuzzy demand in a two-stage supply chain

This paper considers a two-stage supply chain coordination problem and focuses on the fuzziness aspect of demand uncertainty. We use fuzzy numbers to depict customer demand, and investigate the optimization of the vertically integrated two-stage supply chain under perfect coordination and contrast with the non-coordination case. As in the traditional probabilistic analysis, we prove that the maximum expected supply chain profit in a coordination situation is greater than the total profit in a non-coordination situation.     

A periodic-review inventory control policy for a two-level supply chain with multiple retailers and stochastic demand

We consider a time-based inventory control policy for a two-level supply chain with one warehouse and multiple retailers in this paper. Let the warehouse order in a fixed base replenishment interval. The retailers are required to order in intervals that are integer-ratio multiples of the base replenishment interval at the warehouse. The warehouse and the retailers each adopt an order-up-to policy, i.e. order the needed stock at a review point to raise the inventory position to a fixed order-up-to level. It is assumed that the retailers face independent Poisson demand processes and no transshipments between them are allowed. The contribution of the study is threefold. First, we assume that when facing a shortage the warehouse allocates the remaining stock to the retailers optimally to minimize system cost in the last minute before delivery and provide an approach to evaluate the exact system cost. Second, we characterize the structural properties and develop an exact optimal solution for the inventory control system. Finally, we demonstrate that the last minute optimal warehouse stock allocation rule we adopt dominates the virtual allocation rule in which warehouse stock is allocated to meet retailer demand on a first-come first-served basis with significant cost benefits. Moreover, the proposed time-based inventory control policy can perform equally well or better than the commonly used stock-based batch-ordering policy for distribution systems with multiple retailers.