An integrated approach for logistic and vendor managed inventory in supply chain

In this paper, a quaternary policy system towards integrated logistics and inventory aspect of the supply chain has been proposed. A system of multi retailers and distributors, with each distributor following a unique policy, will be analysed. The first policy is continuous time replenishment policy where the retailers’ inventory is replenished in every time interval. In the next three policies, inventory of the retailers will be replenished by some definite policy factors. The vendor managed inventory (VMI) system is used for updating the inventory of the retailers. An order-up-to policy (q, Q) is used for updating the inventory of distributors. Total erstwhile demands to the retailer will be used to determine the amount of inventory acclivity. Furthermore, the distributors will be sending the delivery vehicles to few fellow retailers who are shortlisted according to the policy, followed by the retailers and associated distributors. On the basis of random demand that the retailers are facing from end customers and the total demand that has incurred in the supply chain, products are unloaded to the selected retailers from the delivery vehicle. The path of the delivery vehicle is retrieved by dynamic ant colony optimization. In addition, a framework has been developed to measure the end-customer satisfaction level and total supply chain cost incorporating the inventory holding cost, ordering cost and the transportation cost. The framework has been numerically moulded with different settings to compare the performance of the quadruplet policies.     

Design of Stochastic Distribution Networks Using Lagrangian Relaxation

This paper addresses the design of single commodity stochastic distribution networks. The distribution network under consideration consists of a single supplier serving a set of retailers through a set of distribution centers (DCs). The number and location of DCs are decision variables and they are chosen from the set of retailer locations. To manage inventory at DCs, the economic order quantity (EOQ) policy is used by each DC, and a safety stock level is kept to ensure a given retailer service level. Each retailer faces a random demand of a single commodity and the supply lead time from the supplier to each DC is random. The goal is to minimize the total location, shipment, and inventory costs, while ensuring a given retailer service level. The introduction of inventory costs and safety stock costs leads to a nonlinear NP-hard optimization problem. A Lagrangian relaxation approach is proposed. Computational results are presented and analyzed showing the effectiveness of the proposed approach.     

The value of information sharing in a supply chain with a seasonal demand process

This paper considers a two echelon seasonal supply chain model that consists of one supplier and one retailer, with the assumption that external demand from the customer follows a seasonal autoregressive moving average (SARMA) process, including marketing actions that cannot be deduced from the other parameters of the demand process. In our model, the supplier and the retailer employ order-up-to policy to replenish their inventory. In order to evaluate the value of information sharing in a two echelon seasonal supply chain, three levels of information sharing proposed by Yu, Yan, and Cheng (2002) are used. The results for optimal inventory policies under these three levels of information sharing are derived. We show that the seasonal effect has an important impact on optimal inventory policies of the supplier under the three levels of information sharing. Our findings also demonstrate that the replenishment of lead time must be less than the seasonal period in order to benefit from information sharing. Thus, this result provides managers with managerial insights to improve supply chain performance through information sharing integration partnerships.     

Coordinating a two-level supply chain with delay in payments and profit sharing

Achieving effective coordination among suppliers and retailers has become a pertinent research issue in supply chain management. Channel coordination is a joint decision policy achieved by a supplier(s) and a retailer(s) characterized by an agreement on the order quantity and the trade credit scenario (e.g., quantity discounts, delay in payments). This paper proposes a centralized model where players in a two-level (supplier–retailer) supply chain coordinate their orders to minimize their local costs and that of the chain. In the proposed supply chain model the permissible delay in payments is considered as a decision variable and it is adopted as a trade credit scenario to coordinate the order quantity between the two-levels. Computational results indicate that with coordination, the retailer orders in larger quantities than its economic order quantity, with savings to either both players, or to one in the supply chain. Moreover, a profit-sharing scenario for the distribution of generated net savings among the players in the supply chain is presented. Analytical and experimental results are presented and discussed to demonstrate the effectiveness of the proposed model.     

Coordination of split deliveries in one-warehouse multi-retailer distribution systems

In this paper, we consider a distribution system where a warehouse is responsible for replenishing the inventories at multiple retailers by a fleet of vehicles of limited capacity. If a distribution policy of the system involves split deliveries, that is, the inventory of at least one retailer is replenished by using multiple vehicle routes, the coordination of the deliveries can further reduce the inventory cost of the retailer. We consider the coordination where two split deliveries are realized by direct shipping and multiple-stop shipping, respectively. To the best of our knowledge, this kind of coordination was never studied in the literature but can find its application in inventory routing problems. This paper proposes and analyses a class of coordination policies for the split deliveries which can reduce the inventory costs of the retailers without increasing transportation costs. A non-linear programming model is established for formulating the class of polices. Because the optimal coordination policy corresponding to an optimal solution of the model may be hard to find and/or implement, two simple but effective coordination policies are proposed. The inventory cost savings realized by the two policies are evaluated analytically and algorithmically. Our theoretical analysis and computational experiments show that both policies are effective. Under certain conditions, they can save 50% of the inventory costs at the retailers without increasing transportation costs.     

A computational study for common network design in multi-commodity supply chains

In this paper, we study a supply chain network design problem which consists of one external supplier, a set of potential distribution centers, and a set of retailers, each of which is faced with uncertain demands for multiple commodities. The demand of each retailer is fulfilled by a single distribution center for all commodities. The goal is to minimize the system-wide cost including location, transportation, and inventory costs. We propose a general nonlinear integer programming model for the problem and present a cutting plane approach based on polymatroid inequalities to solve the model. Randomly generated instances for two special cases of our model, i.e., the single-sourcing UPL&TAP and the single-sourcing multi-commodity location-inventory model, are provided to test our algorithm. Computational results show that the proposed algorithm can solve moderate-sized problem instances efficiently.     

Bullwhip effect measure in a seasonal supply chain

In this study, the bullwhip effect in a seasonal supply chain was quantified by considering a two echelon supply chain which consists of one supplier and one retailer. The external demand occurring at the customer was assumed to follow a SARMA (1, 0) X (0, 1) _s scheme, a seasonal autoregressive-moving average process, while the retailer employed an base-stock policy to replenish their inventory. The demand forecast was performed with a SARMA (1, 0) X (0, 1) _s using the minimum mean-square error forecasting technique. In order to develop the bullwhip effect measure in a seasonal supply chain, the lead time demand forecast, forecast error, and the optimal inventory policy at the retailer were derived in sequence. The variance of order quantity based on these results was obtained. Then, various properties were derived by analyzing the bullwhip effect measure. Specifically, it was determined that the seasonal cycle plays an important role in bullwhip effect under a seasonal supply chain. The findings also point out that the replenishment lead time must be less than the seasonal cycle in order to reduce the bullwhip effect. Therefore, the lead time needs to be reduced through collaboration between the retailer and supplier.     

Fuzzy knowledge-based token-ordering policies for bullwhip effect management in supply chains

The “Bullwhip Effect” is a well-known example of supply chain inefficiencies and refers to demand amplification as moving up toward upstream echelons in a supply chain. This paper concentrates on representing a robust token-based ordering policy to facilitate information sharing in supply chains in order to manage the bullwhip effect. Takagi–Sugeno–Kang and hybrid multiple-input single-output fuzzy models are proposed to model the mechanism of token ordering in the token-based ordering policy. The main advantage of proposed fuzzy models is that they eliminate the exogenous and constant variables from the procedure of obtaining the optimal amount of tokens which should be ordered in every period. These fuzzy approaches model the mentioned mechanism through a push–pull policy. A four-echelon SC with fuzzy lead time and unlimited production capacity and inventory is considered to survey the outcomes. Numerical experiments confirm the effectiveness of proposed policies in alleviating BWE, inventory costs and variations.     

A new heuristic to solve the one-warehouse N-retailer problem

We deal with a multi-echelon inventory system in which one warehouse supplies an item to multiple retailers. Customer demand arrives at each retailer at a constant rate. The retailers replenish their inventories from the warehouse that in turn orders from an outside supplier. It is assumed that shortages are not allowed and lead times are negligible. The goal is to determine replenishment policies that minimize the overall cost in the system. We develop a heuristic to compute efficient policies, which also can easily be used in a spreadsheet application. The main idea consists of finding a balance between the replenishment and the inventory holding costs at each installation. This new heuristic we compare with two other approaches proposed in the literature; the computational studies show that in most of the instances generated the new method provides lower costs.     

A study on inventory replenishment policies in a two-echelon supply chain system

Inventory control plays an important role in supply chain management. Properly controlled inventory can satisfy customers’ demands, smooth the production plans, and reduce the operation costs; yet failing to budget the inventory expenses may lead to serious consequences. The bullwhip effect, observed in many supply chain management cases, causes excessive inventory due to information distortion, i.e. the order amount is exaggerated while a minor demand variation occurs, and the information amplified dramatically as the supply chain moves to the upstream. In this paper, one of the main causes of bullwhip effect, order batching, is considered. A simplified two-echelon supply chain system, with one supplier and one retailer that can choose different replenishment policies, is used as a demonstration. Two types of inventory replenishment methods are considered: the traditional methods (the event-triggered and the time-triggered ordering policies), and the statistical process control (SPC) based replenishment method. The results show that the latter outperforms the traditional method in the categories of inventory variation, and in the number of backlog when the fill-rate of the prior model is set to be 99%. This research provides a different approach to inventory cost-down other than the common methods like: information sharing, order batch cutting, and lead time reduction. By choosing a suitable replenishment policy, the number of backorder and the cost of inventory can be reduced.     

Coordinating the ordering and advertising policies for a single-period commodity in a two-level supply chain

This study deals with the news-vendor problem to the case of a two-level supply chain consisting of one manufacturer and one retailer, and investigates the combined effects of the cooperative advertising mechanism, the return policy and the channel coordination. The manufacturer and the retailer could maintain the potential market size by making some marketing expenditures on some national brand names and invest in local advertising, but with diminishing returns. The decision problem facing the profit-oriented entities in the supply chain is to determine the optimal advertising and inventory policies for maximizing their own profit. Both the non-cooperative policy and the cooperative policy are formulated to offer structural and quantitative insights into the interplay between upstream and downstream entities of the supply chain. In addition, the implications of a profit-sharing mechanism based on achieving a win–win relationship of the channel members was also proposed.     

The impact of information sharing on ordering policies to improve supply chain performances

Bullwhip effect represents the amplification and distortion of demand variability as moving upstream in a supply chain, causing excessive inventories, insufficient capacities and high operational costs. A growing body of literature recognizes ordering policies and the lack of coordination as two main causes of the bullwhip effect, suggesting different techniques of intervention. This paper investigates the impact of information sharing on ordering policies through a comparison between a traditional (R, S) policy and a coordination mechanism based on ordering policy (a combination of (R, D) and (R, S) policies). This policy relies on a slow, easy to implement, information sharing to overcome drawbacks of the effect, in which replenishment orders are divided into two parts; the first is to inform the upstream echelons about the actual customer demand and the second is to inform about the adjustment of the inventory position, smoothing at the same time the orders of the different levels of the supply chain. A simulation model for a multi-echelon supply chain quantifies the supply chain dynamics under these different policies, identifying how information sharing succeeds to achieve an acceptable performance in terms of both bullwhip effect and inventory variance.     

Rationing mechanisms and inventory control-policy parameters for a divergent supply chain operating with lost sales and costs of review

We consider a static divergent two-stage supply chain with one distributor and many retailers. The unsatisfied demands at the retailers’ end are treated as lost sales, whereas the unsatisfied demand is assumed to be backlogged at the distributor. The distributor uses an inventory rationing mechanism to distribute the available on-hand inventory among the retailers, when the sum of demands from the retailers is greater than the on-hand inventory at the distributor. The present study aims at determining the best installation inventory control-policy or order-policy parameters such as the base-stock levels and review periods, and inventory rationing quantities, with the objective of minimizing the total supply chain costs (TSCC) consisting of holding costs, shortage costs and review costs in the supply chain over a finite planning horizon. An exact solution procedure involving a mathematical programming model is developed to determine the optimum TSCC, base-stock levels, review periods and inventory rationing quantities (in the class of periodic review, order-up-to S policy) for the supply chain model under study. On account of the computational complexity involved in optimally solving problems over a large finite time horizon, a genetic algorithm (GA) based heuristic methodology is presented.     

Incorporating lateral transfers of vehicles and inventory into an integrated replenishment and routing plan for a three-echelon supply chain

This paper focuses on developing an integrated replenishment and routing plan that takes into account lateral transfers of both vehicles and inventory for a three-echelon supply chain system including a single plant, multiple distribution centers and multiple retailers. A mixed integer programming model to the overall system is formulated first, and then an optimization-based heuristic consisting of three major components is proposed. The purpose of the first component is to assign retailers to distribution centers, and determine routing schedules for each distribution center. And the remaining two components are corresponding to two smaller optimization models – a variant of the classical transportation problem modeled for determining vehicle transfer between distribution centers, and a variant of the conventional minimum cost network flow problem modeled for determining inventory replenishment and transfer. Experimental results reveal that the proposed algorithm is rather computational effectiveness, and the pooling strategy that considers both vehicles and inventory transfers is a worthy option in designing supply chain operations.     

On ordering adjustment policy under rolling forecast in supply chain planning

Rolling forecast is a useful tool for lowering total cost with regard to practical inventory management. The details regarding a rolling forecast are obtained from a customer’s projected ordering data. The customer estimation of a rolling forecast may deviate from actual orders because of unstable conditions or customer’s deliberation. This study investigates what measures a customer might apply in responding to a situation where the rolling forecast deviates from the actual order. In addition, an appropriate ordering adjustment policy is proposed for better monitoring the supply chain performance with regard to a variant level of error concerning rolling forecast data. This study also considers the influence of lead time and inventory cost structure. We adopted a simulation approach, employing a model developed and examined in several different settings. The proposed ordering adjustment policies are determined by AVG, SD, and RMSE calculated from differences existing between historical forecasts and realized data. Levels of estimate error and estimate bias in a rolling forecast are included in the experimental procedure. Results reveal that the RMSE ordering adjustment policy is the most effective in situations of normal and downside estimation bias, whereas the AVG policy is more appropriate in the case of upside estimation bias. The level of estimation error is irrelevant to the selection of ordering adjustment policies, but it is positively associated with inventory costs. Stock-out costs and lead time are positively associated with inventory costs. Accuracy of the rolling forecast is therefore deemed to be essential in a situation involving a long lead time with high stock-out costs.     

A heuristic method for the inventory routing and pricing problem in a supply chain

The inventory routing problem (IRP) in a supply chain (SC) is to determine delivery routes from suppliers to some geographically dispersed retailers and inventory policy for retailers. In the past, the pricing and demand decisions seem ignored and assumed known in most IRP researches. Since the pricing decision affects the demand decision and then both inventory and routing decisions, it should be considered in the IRP simultaneously to achieve the objective of maximal profit in the supply chain. In this paper, a mathematical model for the inventory routing and pricing problem (IRPP) is proposed. Since the solution for this model is an NP (non-polynomial) problem, a heuristic method, tabu search adopting different neighborhood search approaches, is used to obtain the optimal solution. The proposed heuristic method was compared with two other methods considering the IRPP separately. The experimental results indicate that the proposed method is better than the two other methods in terms of average profit.     

Performance evaluation of a two‐echelon supply chain with stochastic demand,lost sales,and Coxian‐2 phase replenishment times

This paper deals with a two‐echelon supply chain comprising a retailer and manufacturer. The retailer faces Poisson demand and follows a (S, s) continuous review inventory policy. The manufacturer produces and ships the retailer's orders with random delay that follows the Coxian‐2 distribution. Assuming lost sales at the retailer and infinite capacity at the manufacturer, we try to explore the performance of the supply chain system. The system is modeled as a continuous‐time Markov process with discrete space. The structure of the transition matrices of these specific systems is categorized as block‐partitioned, and a computational algorithm generates the matrices for different values of system characteristics. The proposed algorithm allows the calculation of performance measures—fill rate, cycle times, average inventory (work in progress [WIP])—from the derivation of the steady‐state probabilities. Moreover, expressions for the holding costs and shortage costs are derived.     

Analysis of the maximum level policy in a production-distribution system

We consider a production-distribution system, where a facility produces one commodity which is distributed to a set of retailers by a fleet of vehicles. Each retailer defines a maximum level of the inventory. The production policy, the retailers replenishment policies and the transportation policy have to be determined so as to minimize the total system cost. The overall cost is composed by fixed and variable production costs at the facility, inventory costs at both facility and retailers and routing costs. We study two different types of replenishment policies. The well-known order-up to level (OU) policy, where the quantity shipped to each retailer is such that the level of its inventory reaches the maximum level, and the maximum level (ML) policy, where the quantity shipped to each retailer is such that the inventory is not greater than the maximum level. We first show that when the transportation is outsourced, the problem with OU policy is NP-hard, whereas there exists a class of instances where the problem with ML policy can be solved in polynomial time. We also show the worst-case performance of the OU policy with respect to the more flexible ML policy. Then, we focus on the ML policy and the design of a hybrid heuristic. We also present an exact algorithm for the solution of the problem with one vehicle. Results of computational experiments carried out on small size instances show that the heuristic can produce high quality solutions in a very short amount of time. Results obtained on a large set of randomly generated problem instances are also shown, aimed at comparing the two policies.     

Newsvendor problems with demand forecast updating and supply constraints

This study investigates an extension of the newsvendor model with demand forecast updating under supply constraints. A retailer can postpone order placement to obtain a better demand forecast with a shorter supply lead time. However, the manufacturer would charge the retailer a higher cost for a shorter lead time and set restrictions on the ordering times and quantities. This prevents retailers from taking full advantage of demand forecast updating to improve profits. In studying the manufacturer-related effects, two supply modes are investigated: supply mode A, which has a limited ordering time scale, and supply mode B, which has a decreasing maximum ordering quantity. For supply mode A, it is proven under justifiable assumptions that a retailer should order either as early or as late as possible. For supply mode B, an algorithm is proposed to simplify the ordering policy by appropriately relaxing the ordering quantity restrictions. Numerical analysis is conducted to investigate the influence of product and demand parameters on the value of demand forecast updating in the two supply modes. A comparison of the different supply scenarios demonstrates the negative effects of increased purchasing cost and ordering time and quantity restrictions when demand forecast updating is implemented.     

Coordinating a three-level supply chain with delay in payments and a discounted interest rate

Both researchers and practitioners recognize the importance of the interactions between financial and inventory decisions in the development of cost effective supply chains. Moreover, achieving effective coordination among the supply chain players has become a pertinent research issue. This paper considers a three-level supply chain, consisting of a capital-constrained supplier, a retailer, and a financial intermediary (bank), coordinating their decisions to minimize the total supply chain costs. Specifically, we consider a retailer managing its cash through the supplier’s bank, in return for permissible delay in payments from the supplier. The bank, benefiting from increasing its cash holdings with the retailer’s cash deposits, offers the supplier a discount on its borrowing rate. We show that the proposed coordination mechanism achieves significant cost reduction, by up to 26.2%, when compared to the non-coordinated model. We also find that, with coordination, the retailer orders in larger quantities than its economic order quantity, and that a higher return on cash for the retailer leads to a higher order quantity. Furthermore, we empirically validate our proposed coordination mechanism, by showing that banks, retailers, and suppliers have much to gain through collaboration. Thus, using COMPUSTAT datasets for the years 1950 through 2012, we determine the most important factors that affect the behavior of the retailers and suppliers in granting and receiving trade credit. Our results indicate that engaging into such a coordination mechanism is a win–win situation to all parties involved.