Who wants to break the hockey-stick sales pattern in the supply chain?

The hockey-stick pattern faced by suppliers consists of sales spikes at the end of each period. One of its causes is the information asymmetry that favors the retailer, who has better knowledge about the stochastic consumer demand. Because of delayed purchases, the supplier is induced to offer promotions, allowing the retailer to forward-buy at low prices. We model this situation as an infinitely repeated game, where each stage-game is subject to imperfect information. Drawing from the Nash equilibrium, we express sales and inventories in terms of demand, cost and the strategies players may adopt, and derive the conditions for a cooperative equilibrium.     

A multiobjective model for forest planning with adjacency constraints

This work presents a nonlinear goal programming model with binary variables used to plan the management of a tree plantation, taking economic and environmental objectives into account. The aims are to stay within the limits of a given harvesting volume, limit the age of basic units targeted for clearcutting, obtain a forest with a balanced age distribution, and surpass the minimum net present value set at each planning period. This has to be achieved bearing in mind technical restrictions regarding treatments, and spatial adjacency constraints that limit the maximum adjacent surface area to which clearcutting can be applied. The outcome is a highly complex problem that is solved by applying a metaheuristic method based on Scatter Search. The proposed model has been validated by applying it to a Cuban plantation located in the region of Pinar del Río.     

Retailer or e-tailer? Strategic pricing and economic-lot-size decisions in a competitive supply chain with drop-shipping

Drop-shipping is an arrangement whereby an e-tailer, who does not hold inventories, processes orders and requests a manufacturer to ship products directly to the end customers. To explore the economic benefits of adopting drop-shipping distribution strategy in a competitive environment, we investigate the profitability and the efficiency of the drop-shipping channel as compared to the traditional channel. Specifically, we develop Economic Order Quantity (EOQ) games with pricing and lot-sizing decisions to examine the strategic interactions between a manufacturer and its retailer/e-tailer in the traditional/drop-shipping distribution channels. We identify conditions under which the drop-shipping channel profitably outperforms the traditional one. It is found that the economic interests of adopting drop-shipping distribution for the channel members may not always be consistent. There are cases where only the manufacture would favour drop-shipping. In this study, we also reveal that the inefficiency caused by lack of coordination in the traditional channel can be alleviated in the drop-shipping channel where the lot-sizing decision is made by the manufacturer.     

Food chain model with optimal harvesting in fuzzy environment

A multispecies harvesting model with mutual interactions is formulated based on Lotka–Voltera model with three competing species which are affected not only by harvesting but also by the presence of prey, predator and the third species, which is super predator. In order to understand the dynamics of the system, it is assumed that the super predator follows the logistic growth. Further, there is demand for all the above three species in the market and hence harvesting of all species is performed. We derive the condition for global stability of the system using a suitable Lyapunov function. The possibility of existence of bioeconomic equilibrium is discussed. The optimal harvest policy is studied and the solution is derived under imprecise inflation in fuzzy environment using Pontryagin’s maximal principle. Finally some numerical examples are discussed to illustrate the model.     

Modeling the synergy level in a vertical collaborative supply chain through the IMP interaction model and DEA framework

This work develops a mathematical programming model that characterizes the main variables present in the interaction dynamics of each agent in a collaborative vertical logistical system, such as a supply chain, and measures the synergy level of such system. The model is based on the interaction model developed by the IMP (Industrial Marketing and Purchasing) group and also on the DEA (Data Envelopment Analysis) framework. The basics of these two approaches allow modeling of the characteristics of an agent as well as the collaborative relationships with other agents within the chain. The model was validated using information of supply chain of leather and its products, classified by DANE (Departamento Nacional de Estadistica—Colombia) as the sector CIIU323.     

Why are enterprise resource planning systems indispensable to supply chain management?

Supply chain design is becoming a core competency, and the enterprise resource planning (ERP) system is expected to be an integral component of supply chain management (SCM). Installing an ERP system is, however, expensive and risky. IT managers must decide how to use their limited resources and invest in the right product. Can an ERP system directly improve SCM competency? This study proposes a conceptual framework featuring the ERP benefits and SCM competencies, and examines the impacts of the former on the latter. The results confirm the operational, managerial, and strategic benefits of ERP for the SCM competencies, but not the IT infrastructure and organizational benefits as significant predictors of them. Moreover, more than 80% of respondents think it necessary to first adopt an ERP system as the backbone of company operations before deploying other enterprise systems (ES), such as the SCM system.     

Secure collaborative supply chain planning and inverse optimization – The JELS model

It is a well-acknowledged fact that collaboration between different members of a supply chain yields a significant potential to increase overall supply chain performance. Sharing private information has been identified as prerequisite for collaboration and, at the same time, as one of its major obstacles. One potential avenue for overcoming this obstacle is Secure Multi-Party Computation (SMC). SMC is a cryptographic technique that enables the computation of any (well-defined) mathematical function by a number of parties without any party having to disclose its input to another party. In this paper, we show how SMC can be successfully employed to enable joint decision-making and benefit sharing in a simple supply chain setting. We develop secure protocols for implementing the well-known “Joint Economic Lot Size (JELS) Model” with benefit sharing in such a way that none of the parties involved has to disclose any private (cost and capacity) data. Thereupon, we show that although computation of the model’s outputs can be performed securely, the approach still faces practical limitations. These limitations are caused by the potential of “inverse optimization”, i.e., a party can infer another party’s private data from the output of a collaborative planning scheme even if the computation is performed in a secure fashion. We provide a detailed analysis of “inverse optimization” potentials and introduce the notion of “stochastic security”, a novel approach to assess the additional information a party may learn from joint computation and benefit sharing. Based on our definition of “stochastic security” we propose a stochastic benefit sharing rule, develop a secure protocol for this benefit sharing rule, and assess under which conditions stochastic benefit sharing can guarantee secure collaboration.     

Consignment contracting: Who should control inventory in the supply chain?

Consignment is a popular form of business arrangement where supplier retains ownership of the inventory and gets paid from the retailer based on actual units sold. The popularity of such an arrangement has come with some continued debates on who should control the supply chain inventory, the supplier or retailer. This paper aims at shedding light on these debated issues. We consider a single period supply chain model where a supplier contracts with a retailer. Market demand for the product is price-sensitive and uncertain. The supplier decides his consignment price charged to the retailer for each unit sold, and the retailer then chooses her retail price for selling the product. We study and compare two different consignment arrangements: The first allows the retailer to choose the supply chain inventory, together with her retail price, and is labeled as a Retailer Managed Consignment Inventory (RMCI) program; and the second calls for the supplier to decide the inventory, together with his consignment price, and is labeled as a Vendor Managed Consignment Inventory (VMCI) program. We show that with an RMCI program, the supply chain loses at least 26.4% of its first-best (expected) profit, while with VMCI, it loses just or no more than 26.4% of the first-best profit. Second, we demonstrate that both programs lead to an equal split of the corresponding channel profit between the supplier and the retailer. These results indicate that it is beneficial both to the supplier and to the retailer when delegating the inventory decision to the supplier rather than to the retailer in the channel.     

Vertical cooperative advertising and pricing decisions in a manufacturer–retailer supply chain: A game-theoretic approach

Manufacturers can increase the advertising expenditures of their retailers by bearing a fraction of the occurring costs within the framework of a vertical cooperative advertising program. We expand the existing research which deals with advertising and pricing decisions in a manufacturer–retailer supply chain contemporaneously. By means of game theory, four different relationships between the channel members are considered: Firstly, three non-cooperative games with either symmetrical distribution of power or asymmetrical distribution with one player being the leader in each case, and one cooperative game where both players tend to maximize the total profit. The latter is complemented by a bargaining model, which proposes a fair split of profit on the basis of the players’ risk attitude and bargaining power. Our main findings are as follows: (a) In contrast to previous analyses, we do not limit the ratio between manufacturer’s and retailer’s margin, which provides more general insights into the effects of the underlying distribution of power within the channel. (b) The highest total profit is gained when both players cooperate. This behavior puts also the customers in a better position, as it produces the lowest retail price as well as the highest advertising expenditures compared to the other configurations.     

Optimal contracts and the manufacturer’s pricing strategies in a supply chain with an inequity-averse retailer

Studies in the supply chain literature have typically focused on profit or revenue maximization and assumed that agents within the supply chain are self-interested and only care about their own monetary payoffs. Research in these areas, however, rarely considers an important phenomenon called inequity aversion in which the object pursued by agents within the supply chain is not only their own profit maximization but also the equity of profit allocation. In fact, when agents within a supply chain collaborate with each other to serve a market, the scheme of profit allocation between them usually plays a determinate role in cooperation. Taking into account the impact of agents’ behavior of inequity aversion on the coordination of the supply chain, this paper investigates the optimal contracts and the manufacturer’s pricing strategies in a single-manufacturer and single-retailer supply chain. In this way, we obtain two interesting results: (1) the retailer’s equity aversion largely affects the manufacturer’s decision making, which is not always bad for the manufacturer; and (2) the retailer’s inequity aversion as well as the consumer’s price-sensitive coefficient plays a dominant role in the manufacturer’s decision making.     

Designing an efficient supply chain network with uncertain data: a robust optimization—data envelopment analysis approach

Designing a supply chain network (SCN) is an important issue for organizations in competitive markets. In this paper, a novel robust SCN that considers the efficiencies and costs simultaneously is proposed. In order to estimate the efficiency of the producers and distributors, data envelopment analysis (DEA) model is incorporated into SCN. Moreover, to handle the uncertainty in data, a scenario-based robust optimization approach is applied. The proposed model finds out the efficient location of producers and distributors and determines the amount of purchases from each supplier in uncertain conditions. To illustrate the application of the proposed model, a numerical example is solved and results are analyzed.     

Establishing Nash equilibrium of the manufacturer–supplier game in supply chain management

We study a game model of multi-leader and one-follower in supply chain optimization where n suppliers compete to provide a single product for a manufacturer. We regard the selling price of each supplier as a pre-determined parameter and consider the case that suppliers compete on the basis of delivery frequency to the manufacturer. Each supplier's profit depends not only on its own delivery frequency, but also on other suppliers' frequencies through their impact on manufacturer's purchase allocation to the suppliers. We first solve the follower's (manufacturer's) purchase allocation problem by deducing an explicit formula of its solution. We then formulate the n leaders' (suppliers') game as a generalized Nash game with shared constraints, which is theoretically difficult, but in our case could be solved numerically by converting to a regular variational inequality problem. For the special case that the selling prices of all suppliers are identical, we provide a sufficient and necessary condition for the existence and uniqueness of the Nash equilibrium. An explicit formula of the Nash equilibrium is obtained and its local uniqueness property is proved.     

Supply chain DEA: production possibility set and performance evaluation model

Performance evaluation is of great importance for effective supply chain management. The foundation of efficiency evaluation is to faithfully identify the corresponding production possibility set. Although a lot of researches have been done on supply chain DEA models, the exact definition for supply chain production possibility set is still in absence. This paper defines two types of supply chain production possibility sets, which are proved to be equivalent to each other. Based upon the production possibility set, a supply chain CRS DEA model is advanced to appraise the overall technical efficiency of supply chains. The major advantage of the model lies on the fact that it can help to find out the most efficient production abilities in supply chains, by replacing or improving inefficient subsystems (supply chain members). The proposed model also directly identifies the benchmarking units for inefficient supply chains to improve their performance. A real case validates the reasonableness and acceptability of this approach.     

Algorithms for the design of network topologies with balanced disjoint rings

We define the Balanced Disjoint Rings (BDR) problem as developing a method to partition of the nodes in a network to form a given number of disjoint rings of minimum total link length in such a way that there is almost the same number of nodes in each ring. The BDR problem has potential applications in the design of survivable network structures in telecommunications as well as in the identification of local distribution/collection routes in logistics. The BDR problem can also be considered a generalization of the traveling salesman problem since we are interested in multiple tours instead of a single tour. We develop an efficient heuristic solution methodology that involves various GRASP-based randomized solution construction routines that allow a multi-start framework and a n effective combination of cyclic-exchange and single-move neighborhoods in a local search improvement procedure. The algorithms perform very well in our numerical studies, providing encouraging optimality and lower bound gaps with very reasonable runtimes.     

Pricing and advertisement in a manufacturer–retailer supply chain

We use a game theoretical approach to study pricing and advertisement decisions in a manufacturer–retailer supply chain when price discounts are offered by both the manufacturer and retailer. When the manufacturer is the leader of the game, we obtained Stackelberg equilibrium with manufacturer’s local allowance, national brand name investment, manufacturer’s preferred price discount, retailer’s price discount, and local advertising expense. For the special case of two-stage equilibrium when the manufacturer’s price discount is exogenous, we found that the retailer is willing to increase local advertising expense if the manufacturer increases local advertising allowance and provides deeper price discount, or if the manufacturer decreases its brand name investment. When both the manufacturer and retailer have power, Nash equilibrium in a competition game is obtained. The comparison between the Nash equilibrium and Stackelberg equilibrium shows that the manufacturer always prefers Stackelberg equilibrium, but there is no definitive conclusion for the retailer. The bargaining power can be used to determine the profit sharing between the manufacturer and the retailer. Once the profit sharing is determined, we suggest a simple contract to help the manufacturer and retailer obtain their desired profit sharing.     

A game theory approach in seller–buyer supply chain

In this paper, several seller–buyer supply chain models are proposed which incorporate both cost factors as well as elements of competition and cooperation between seller and buyer. We assume that unit marketing expenditure and unit price charged by the buyer influence the demand of the product being sold. The relationships between seller and buyer will be modeled by non-cooperative and cooperative games, respectively. The non-cooperative game is based on the Stackelberg strategy solution concept, where we consider separately the case when the seller is the leader (Seller-Stackelberg) and also when the buyer is the leader (Buyer-Stackelberg). Pareto efficient solutions will be provided for the cooperative game model. Numerical examples presented in this paper, including sensitivity analysis of some key parameters, will compare the results between different models considered.     

Sustainable vegetable crop supply problem with perishable stocks

In this paper, we deal with a vegetable crop supply problem with two main particularities: (i) the production must respect certain ecologically-based constraints and (ii) harvested crops can be stocked but only for a limited period of time, given that they are perishable. To model these characteristics, we develop a linear formulation in which each variable is associated to a crop rotation plan. This model contains a very large number of variables and is therefore solved with the aid of a column generation approach. Moreover, we also propose a two-stage stochastic programming with recourse model which takes into consideration that information on the demands might be uncertain. We provide a discussion of the results obtained via computational tests run on instances adapted from real-world data.     

Incremental-like bundle methods with application to energy planning

An important field of application of non-smooth optimization refers to decomposition of large-scale or complex problems by Lagrangian duality. In this setting, the dual problem consists in maximizing a concave non-smooth function that is defined as the sum of sub-functions. The evaluation of each sub-function requires solving a specific optimization sub-problem, with specific computational complexity. Typically, some sub-functions are hard to evaluate, while others are practically straightforward. When applying a bundle method to maximize this type of dual functions, the computational burden of solving sub-problems is preponderant in the whole iterative process. We propose to take full advantage of such separable structure by making a dual bundle iteration after having evaluated only a subset of the dual sub-functions, instead of all of them. This type of incremental approach has already been applied for subgradient algorithms. In this work we use instead a specialized variant of bundle methods and show that such an approach is related to bundle methods with inexact linearizations. We analyze the convergence properties of two incremental-like bundle methods. We apply the incremental approach to a generation planning problem over an horizon of one to three years. This is a large scale stochastic program, unsolvable by a direct frontal approach. For a real-life application on the French power mix, we obtain encouraging numerical results, achieving a significant improvement in speed without losing accuracy.     

Retailer’s optimal CSR investment in closed-loop supply chains: the impacts of supply chain structure and channel power structure

4OR - This paper studies the retailer’s optimal corporate social responsibility (CSR) investment decisions in manufacturer-collecting closed-loop supply chains (CLSCs). We establish a...