A heuristic for single-warehouse multiretailer supply chains with all-unit transportation cost discounts

In supply chain management research, transportation costs, if explicitly considered at all, are frequently assumed to be linear. These costs often have a more complex form, such as an all-unit discount structure – this piecewise cost function adds significant complexity when included in supply chain management problems and is therefore often ignored due to solution time or tractability concerns. We present and evaluate a new heuristic procedure which provides good solutions to problems involving all-unit discount cost functions while significantly reducing solution times. The general nature of this procedure does not require assumptions about the supply chain structure or policies, and is therefore applicable in a wide range of settings.     

Closed-loop supply chain network equilibrium under legislation

This paper expands previous work dealing with oligopolistic supply chains to the field of closed-loop supply chains. The model presented has been formulated with the intent of examining issues surrounding the recent European Union directive regarding waste of electric and electronic equipment (WEEE). The network modelled consists of manufacturers and consumer markets engaged in a Cournot pricing game with perfect information. Closed-loop supply chain network equilibrium occurs when all players agree on volumes shipped and prices charged. Certain properties of the model are examined analytically. Numeric examples are included and have been solved using an extragradient method with constant step size. The equilibrium solution obtained provide interesting insights that lead into a number of areas for future research.     

Unfair allocation of gains under the Equal Price allocation method in purchasing groups

Certain purchasing groups do not flourish. A supposed reason for this is a creeping dissatisfaction among various members of a group with the allocation of the cooperative gains. In this paper, we analyze unfairness resulting from using the commonly used Equal Price (EP) method for allocating gains under the assumption of continuous quantity discounts. We demonstrate that this unfairness is caused by neglecting a particular component of the added value of individual group members. Next, we develop two fairness ratios and tie these to fairness properties from cooperative game theory. The ratios show among other things that being too-big a player in a purchasing group can lead to decreasing gains. They can be used to assess if EP is an unfair method in specific situations. Finally, we discuss measures a purchasing group could consider in order to attenuate perceived unfairness. Thereby, the group may improve its stability and prosperity.     

WASAN: The development of a facilitated methodology for structuring a waste minimisation problem

This paper contributes a new methodology called Waste And Source-matter ANalyses (WASAN) which supports a group in building agreeable actions for safely minimising avoidable waste. WASAN integrates influences from the Operational Research (OR) methodologies/philosophies of Problem Structuring Methods, Systems Thinking, simulation modelling and sensitivity analysis as well as industry approaches of Waste Management Hierarchy, Hazard Operability (HAZOP) Studies and As Low As Reasonably Practicable (ALARP). The paper shows how these influences are compiled into facilitative structures that support managers in developing recommendations on how to reduce avoidable waste production. WASAN is being designed as Health and Safety Executive Guidance on what constitutes good decision making practice for the companies that manage nuclear sites. In this paper we report and reflect on its use in two soft OR/problem structuring workshops conducted on radioactive waste in the nuclear industry.     

Optimal inventory policies with two modes of freight transportation

Theoretical inventory models with constant demand rate and two transportation modes are analyzed in this paper. The transportation options are truckloads with fixed costs, a package delivery carrier with a constant cost per unit, or using a combination of both modes simultaneously. Exact algorithms for computing the optimal policies are derived for single stage models over both an infinite and a finite planning horizon.     

Cost/risk balanced management of scarce resources using stochastic programming

We consider the situation when a scarce renewable resource should be periodically distributed between different users by a Resource Management Authority (RMA). The replenishment of this resource as well as users demand is subject to considerable uncertainty. We develop cost optimization and risk management models that can assist the RMA in its decision about striking the balance between the level of target delivery to the users and the level of risk that this delivery will not be met. These models are based on utilization and further development of the general methodology of stochastic programming for scenario optimization, taking into account appropriate risk management approaches. By a scenario optimization model we obtain a target barycentric value with respect to selected decision variables. A successive reoptimization of deterministic model for the worst case scenarios allows the reduction of the risk of negative consequences derived from unmet resources demand. Our reference case study is the distribution of scarce water resources. We show results of some numerical experiments in real physical systems.     

Trends in transportation and logistics

Problems in transportation and logistics had to be tackled long before computers and Operational Research (OR) became available to support decision making. After the first optimization models were developed, OR has substantially contributed in making transportation systems efficient and companies with complex transportation and logistics problems competitive. Over the years, technology has evolved and the same has done OR. In this paper, the history of problems and OR contributions in transportation and logistics will be shortly reviewed together with the evolution of technology. Then, the future trends in this area will be discussed together with potential OR contributions.     

Coordinating the supply chain in the agricultural seed industry

This paper examines contract practices between suppliers and retailers in the agricultural seed industry. We construct and analyze single-retailer models of various contract types actually used in the industry, which include, for example, certain “bonus” and “penalty” features. With no assumption on the demand distribution, we establish sufficient conditions for contract parameters to guarantee supply chain coordination. Under the assumption of uniform demand, we fully characterize all coordinating contracts. In addition, we compare the models studied herein with other models in the literature and demonstrate that current behavior in the agricultural seed industry is substantively different than that captured by other models. Conversely, we argue why other existing models are not reasonable to implement in the agricultural seed industry.     

An outranking-based general approach to solving group multi-objective optimization problems

This paper presents a general approach to solving multi-objective programming problems with multiple decision makers. The proposal is based on optimizing a bi-objective measure of “collective satisfaction”. Group satisfaction is understood as a reasonable balance between the strengths of an agreeing and an opposing coalition, considering also the number of decision makers not belonging to any of these coalitions. Accepting the vagueness of “collective satisfaction”, even the vagueness of “person satisfaction”, fuzzy outranking relations and other fuzzy logic models are used.     

Speciality oils supply chain optimization: From a decoupled to an integrated planning approach

We study a problem of tactical planning in a divergent supply chain. It involves decisions regarding production, inventory, internal transportation, sales and distribution to customers. The problem is motivated by the context of a company in the speciality oils industry. The overall objective at tactical level is to maximize contribution and, in order to achieve this, the planning has been divided into two separate problems. The first problem concerns sales where the final sales and distribution planning is decentralized to individual sellers. The second problem concerns production, transportation and inventory planning through refineries, hubs and depots and is managed centrally with the aim of minimizing costs. Due to this decoupling, the solution of the two problems needs to be coordinated in order to achieve the overall objective. In the company, this is pursued through an internal price system aiming at giving the sellers the incentives needed to align their decisions with the overall objective. We propose and discuss linear programming models for the decoupled and integrated planning problems. We present numerical examples to illustrate potential effects of integration and coordination and discuss the advantages and disadvantages of the integrated over the decoupled approach. While the total contribution is higher in the integrated approach, it has also been found that the sellers’ contribution can be considerably lower. Therefore, we also suggest contribution sharing rules to achieve a solution where both the company and the sellers attain a better outcome under the integrated planning.     

A linear model for surface mining haul truck allocation incorporating shovel idle probabilities

We present models of trucks and shovels in oil sand surface mines. The models are formulated to minimize the number of trucks for a given set of shovels, subject to throughput and ore grade constraints. We quantify and validate the nonlinear relation between a shovel’s idle probability (which determines the shovel’s productivity) and the number of trucks assigned to the shovel via a simple approximation, based on the theory of finite source queues. We use linearization to incorporate this expression into linear integer programs. We assume in our integer programs that each shovel is assigned a single truck size but we outline how one could account for multiple truck sizes per shovel in an approximate fashion. The linearization of shovel idle probabilities allows us to formulate more accurate truck allocation models that are easily solvable for realistic-sized problems.     

Optimizing Supply Shortage Decisions in Base Stock Distribution Operations

This paper addresses policies and agreements between suppliers and customers for handling supply shortages in base-stock systems under uncertain demand. We investigate the impacts that backlogging and expediting decisions have on inventory and transportation costs in these systems and develop a model for deciding whether a supplier should completely backlog, completely expedite, or employ some combination of backlogging and expediting shortages. Our results indicate that practical cases exist where some combination of both expediting and backlogging supply shortages outperforms either completely expediting or backlogging all shortages. Including transportation costs in our model provides incentive to employ `hybrid' policies that partially expedite and partially backlog excess demands within a given period. Our model demonstrates how inventory policy decisions directly impact transportation costs and provides a heuristic approach for jointly minimizing expected inventory and transportation costs.     

Decision model and analysis for investment interest expense deduction and allocation

Investment income tax planning requires informed, strategic choices. One must determine the amount of qualified dividends and net long-term capital gain to be included in investment income (against which investment interest expense can be deducted). This choice also determines the residual qualified dividends and net long-term capital gain which enjoy a reduced tax rate. Another important decision is whether all or some of this interest expense should be deducted in the current year or carried forward. This paper puts forward a new approach to formulate these questions as a generalized resource allocation problem which permits analysis of the interdependence between, and the tax consequences of, the above decisions. The commonly used approach – deducting investment interest expense sooner rather than later – we consider myopic since the benefit of deferring some of the deduction is not leveraged. Presented here is a tax planning guideline (a necessary and sufficient condition for optimality) to realize a more forward-looking strategy. We also show that, for certain income structures, the tax savings by deducting a one-dollar investment interest expense may be more than the tax rate on the dollar of investment income that is offset.     

Modeling cooperation on a class of distribution problems

In this paper we study models of cooperation between the nodes of a network that represents a distribution problem. The distribution problem we propose arises when, over a graph, a group of nodes offers certain commodity, some other nodes require it and a third group of nodes neither need this material nor offer it but they are strategically relevant to the distribution plan. The delivery of one unit of material to a demand node generates a fixed profit, and the shipping of the material through the arcs has an associated cost. We show that in such a framework cooperation is beneficial for the different parties. We prove that the cooperative situation arising from this distribution problem is totally balanced by finding a set of stable allocations (in the core of an associated cooperative game). In order to overcome certain fairness problems of these solutions, we introduce two new solution concepts and study their properties.     

Locating specialized service capacity in a multi-hospital network

Multi-hospital systems have become very common in today’s healthcare environment. However, there has been limited published research examining the opportunities and challenges of pooling specialized services to a subset of hospitals in the network. Therefore, this paper considers how hospital networks with multiple locations can leverage pooling benefits when deciding where to position specialized services, such as magnetic resonance imaging (MRI), transplants, or neonatal intensive care. Specifically, we develop an optimization model to determine how many and which of a hospital network’s hospitals should be set up to deliver a specialized service. Importantly, this model takes into account both financial considerations and patient service levels. Computational results illustrate the value of optimally pooling resources across a subset of hospitals in the network versus two alternate approaches: (1) delivering the service at all locations and requiring each site to handle its own demand, or (2) locating the service at one hospital that handles all network demand.     

Quantitative models for sustainable supply chain management: Developments and directions

Sustainability, the consideration of environmental factors and social aspects, in supply chain management (SCM) has become a highly relevant topic for researchers and practitioners. The application of operations research methods and related models, i.e. formal modeling, for closed-loop SCM and reverse logistics has been effectively reviewed in previously published research. This situation is in contrast to the understanding and review of mathematical models that focus on environmental or social factors in forward supply chains (SC), which has seen less investigation. To evaluate developments and directions of this research area, this paper provides a content analysis of 134 carefully identified papers on quantitative, formal models that address sustainability aspects in the forward SC. It was found that a preponderance of the publications and models appeared in a limited set of six journals, and most were analytically based with a focus on multiple criteria decision making. The tools most often used comprise the analytical hierarchy process or its close relative, the analytical network process, as well as life cycle analysis. Conclusions are drawn showing that numerous possibilities and insights can be gained from expanding the types of tools and factors considered in formal modeling efforts.     

Contract design and supply chain coordination in the electricity industry

In this article we propose a model of the supply chain in electricity markets with multiple generators and retailers and considering several market structures. We analyze how market design interacts with the different types of contract and market structure to affect the coordination between the different firms and the performance of the supply chain as a whole. We compare the implications on supply chain coordination and on the players’ profitability of two different market structures: a pool based market vs. bilateral contracts, taking into consideration the relationship between futures and spot markets. Furthermore, we analyze the use of contracts for differences and two-part-tariffs as tools for supply chain coordination. We have concluded that there are multiple equilibria in the supply chain contracts and structure and that the two-part tariff is the best contract to reduce double marginalization and increase efficiency in the management of the supply chain.     

A coordinating contract for transshipment in a two-company supply chain

We study a supply chain with two independent companies producing an identical product and cooperating through transshipment. Previous studies of this chain show that only under certain conditions, linear transshipment prices could be found that induce the companies to choose the first best production quantities. Moreover, even if such transshipment prices do exist, they result in a unique division of total expected profit and thus they cannot accommodate arbitrary divisions of the profit. Using the Generalized Nash Bargaining Solution, we derive coordinating transshipment prices that always give rise to a coordinating contract for the chain. This contract relies on an implicit pricing mechanism.     

A fast approach to compute fuzzy values of matrix games with payoffs of triangular fuzzy numbers

The aim of this paper is to develop an effective method for solving matrix games with payoffs of triangular fuzzy numbers (TFNs) which are arbitrary. In this method, it always assures that players’ gain-floor and loss-ceiling have a common TFN-type fuzzy value and hereby any matrix game with payoffs of TFNs has a TFN-type fuzzy value. Based on duality theorem of linear programming (LP) and the representation theorem for fuzzy sets, the mean and the lower and upper limits of the TFN-type fuzzy value are easily computed through solving the derived LP models with data taken from 1-cut set and 0-cut set of fuzzy payoffs. Hereby the TFN-type fuzzy value of any matrix game with payoffs of TFNs can be explicitly obtained. Moreover, we can easily compute the upper and lower bounds of any Alfa-cut set of the TFN-type fuzzy value for any matrix game with payoffs of TFNs and players’ optimal mixed strategies through solving the derived LP models at any specified confidence level Alfa. The proposed method in this paper is demonstrated with a numerical example and compared with other methods to show the validity, applicability and superiority.