An integrated supplier selection and inventory problem with multi-sourcing and lateral transshipments

In this research, we consider the supplier selection problem of a firm offering a single product via multiple warehouses. The warehouses face stationary, stochastic demand and replenish their inventory via multiple suppliers, to be determined from a set of candidates, with varying price, capacity, quality, and disruption characteristics. Additionally, the warehouses may simultaneously replenish their inventory from other warehouses proactively. With these characteristics, the problem is a multi-sourcing, supplier selection, and inventory problem with lateral transshipments. Even though the benefits of multi-sourcing and lateral transshipments have been presented in the literature individually to mitigate risks associated with uncertain demand and disrupted supply, the intertwined sourcing and inventory decisions under these settings have not been investigated from a quantitative perspective. We develop a decomposition based heuristic algorithm, powered with simulation. While the decomposition based heuristic determines a solution with supplier selection and inventory decisions, the simulation model evaluates the objective function value corresponding to each generated solution. Experimental results show, contrary to the existing literature, inferior decisions may result when considering the selection of suppliers solely on unit and/or contractual costs. We also evaluate the impact of multi-sourcing with rare but long disruptions compared to frequent but short ones.     

Selection of resilient supply portfolio under disruption risks

This paper deals with the optimal selection and protection of part suppliers and order quantity allocation in a supply chain with disruption risks. The protection decisions include the selection of suppliers to be protected against disruptions and the allocation of emergency inventory of parts to be pre-positioned at the protected suppliers. The decision maker needs to decide which supplier to select for parts delivery and how to allocate orders quantity among the selected suppliers, and which of the selected suppliers to protect against disruptions and how to allocate emergency inventory among the protected suppliers. The problem objective is to achieve a minimum cost of suppliers protection, emergency inventory pre-positioning, parts ordering, purchasing, transportation and shortage and to mitigate the impact of disruption risks by minimizing the potential worst-case cost. As a result a resilient supply portfolio is identified with protected suppliers capable of supplying parts in the face of disruption events. A mixed integer programming approach is proposed to determine risk-neutral, risk-averse or mean-risk supply portfolios, with conditional value-at-risk applied to control the risk of worst-case cost. Numerical examples are presented and some computational results are reported.     

直接配送下随机需求库存-路径问题最优平稳策略及其算法

直接配送策略下随机需求库存-路径问题（Stochastic Demand Inventory Routing Problem with Direct Deliveries, SDIRPDD）由于其需求的不确定性、决策的长期性以及其最优策略形式对求解其他库存-路径问题（IRP）的参考价值,使得对SDIPRDD问题的研究成为物流、供应链优化领域研究的一个热点。文章首先证明了无约束SDIRPDD的最优平稳策略为（s,S）形式,并通过分析车辆数约束对客户单阶段期望成本函数的影响,给出了存在车辆数和客户库存容量约束时SDIRPDD问题的最优平稳策略形式,进而提出了一种求解有约束SDIRPDD问题最优平稳策略的近似算法。最后,通过数值算例验证了算法的有效性并分析了结果的现实意义。     

A Heuristic Algorithm for the Capacitated Multiple Supplier Inventory Grouping Problem

This paper presents and solves a model for the multiple supplier inventory grouping problem, which involves the minimization of logistics costs for a firm that has multiple suppliers with capacity limitations. The costs included in the model are purchasing, transportation, ordering, and inventory holding, while the firm's objective is to determine the optimal flows and groups of commodities from each supplier. We present an algorithm, which combines subgradient optimization and a primal heuristic, to quickly solve the multiple supplier inventory grouping problem. Our algorithm is tested extensively on problems of various sizes and structures, and its performance is compared to that of OSL, a state-of-the-art integer programming code. The computational results indicate that our approach is extremely efficient for solving the multiple supplier inventory grouping problem.     

The Retail Planning Problem Under Demand Uncertainty

We consider the retail planning problem in which the retailer chooses suppliers and determines the production, distribution, and inventory planning for products with uncertain demand to minimize total expected costs. This problem is often faced by large retail chains that carry private‐label products. We formulate this problem as a convex‐mixed integer program and show that it is strongly NP‐hard. We determine a lower bound by applying a Lagrangian relaxation and show that this bound outperforms the standard convex programming relaxation while being computationally efficient. We also establish a worst‐case error bound for the Lagrangian relaxation. We then develop heuristics to generate feasible solutions. Our computational results indicate that our convex programming heuristic yields feasible solutions that are close to optimal with an average suboptimality gap at 3.4%. We also develop managerial insights for practitioners who choose suppliers and make production, distribution, and inventory decisions in the supply chain.     

A Framework for Facilitating Sourcing and Allocation Decisions for Make‐to‐Order Items

This paper provides a fundamental building block to facilitate sourcing and allocation decisions for make‐to‐order items. We specifically address the buyer's vendor selection problem for make‐to‐order items where the goal is to minimize sourcing and purchasing costs in the presence of fixed costs, shared capacity constraints, and volume‐based discounts for bundles of items. The potential suppliers for make‐to‐order items provide quotes in the form of single sealed bids or participate in a dynamic auction involving open bids. A solution to our problem can be used to determine winning bids amongst the single sealed bids or winners at each stage of a dynamic auction. Due to the computational complexity of this problem, we develop a heuristic procedure based on Lagrangian relaxation technique to solve the problem. The computational results show that the procedure is effective under a variety of scenarios. The average gap across 2,250 problem instances is 4.65%.     

Multi-echelon supply chain network design in agile manufacturing

In this paper, we consider a supply chain network design problem in an agile manufacturing scenario with multiple echelons and multiple periods under a situation where multiple customers have heavy demands. Decisions in our supply chain design problem include selection of one or more companies in each echelon, production, inventory, and transportation. We formulate the problem integrating all decisions to minimize the total operational costs including fixed alliance costs between two companies, production, raw material holding, finished products holding, and transportation costs under production and transportation capacity limits. A Lagrangian heuristic is proposed in this paper. Optimizing a Lagrangian relaxation problem provides a lower bound, while a feasible solution is generated by adjustment techniques based on the solution of subproblems at each iteration. Computational results indicate the high quality solutions with less than 5% optimality gap are provided quickly by the approach in this paper. Further, compared to initiative managerial alternatives, an improvement of 15% to 25% is not unusual in certain cases for the proposed approach.     

Multi-echelon supply chain network design in agile manufacturing

In this paper, we consider a supply chain network design problem in an agile manufacturing scenario with multiple echelons and multiple periods under a situation where multiple customers have heavy demands. Decisions in our supply chain design problem include selection of one or more companies in each echelon, production, inventory, and transportation. We formulate the problem integrating all decisions to minimize the total operational costs including fixed alliance costs between two companies, production, raw material holding, finished products holding, and transportation costs under production and transportation capacity limits. A Lagrangian heuristic is proposed in this paper. Optimizing a Lagrangian relaxation problem provides a lower bound, while a feasible solution is generated by adjustment techniques based on the solution of subproblems at each iteration. Computational results indicate the high quality solutions with less than 5% optimality gap are provided quickly by the approach in this paper. Further, compared to initiative managerial alternatives, an improvement of 15% to 25% is not unusual in certain cases for the proposed approach.     

Managing stochastic demand in an Inventory Routing Problem with transportation procurement

We study an Inventory Routing Problem in which the supplier has a limited production capacity and the stochastic demand of the retailers is satisfied with procurement of transportation services. The aim is to minimize the total expected cost over a planning horizon, given by the sum of the inventory cost at the supplier, the inventory cost at the retailers, the penalty cost for stock-out at the retailers and the transportation cost. First, we show that a policy based just on the average demand can have a total expected cost infinitely worse than the one obtained by taking into account the overall probability distribution of the demand in the decision process. Therefore, we introduce a stochastic dynamic programming formulation of the problem that allows us to find an optimal policy in small size instances. Finally, we design and implement a matheuristic approach, integrating a rollout algorithm and an optimal solution of mixed-integer linear programming models, which is able to solve realistic size problem instances. Computational results allow us to provide managerial insights concerning the management of stochastic demand.     

Supplier competition and its impact on firm׳s sourcing strategy

Most research on firms׳ sourcing strategies assumes that wholesale prices and reliability of suppliers are exogenous. It is of our interest to study suppliers׳ competition on both wholesale price and reliability and firms׳ corresponding optimal sourcing strategy under complete information. In particular, we study a problem in which a firm procures a single product from two suppliers, taking into account suppliers׳ price and reliability differences. This motivates the suppliers to compete on these two factors. We investigate the equilibria of this supplier game and the firm׳s corresponding sourcing decisions. Our study shows that suppliers׳ reliability often plays a more important role than wholesale price in supplier competition and that maintaining high reliability and a high wholesale price is the ideal strategy for suppliers if multiple options exist. The conventional wisdom implies that low supply reliability and high demand uncertainty motivate dual-sourcing. We notice that when the suppliers׳ shared market/transportation network is often disrupted and demand uncertainty is high, suppliers׳ competition on both price and reliability may render the sole-sourcing strategy to be optimal in some cases that depend on the format of suppliers׳ cost functions. Moreover, numerical study shows that when the cost or vulnerability (to market disruptions) of one supplier increases, its profit and that of the firm may not necessarily decrease under supplier competition.     

单产品物流网络系统的联合决策模型

考虑全球制造环境下单产品在多个供应商和多个用户之间的联合物流决策问题,包括供应商指定的生产任务、生产批量、供应商和用户之间的年运输量和订货批量.联合决策过程可以看作是两层决策,其中第一层是供应商指定的生产任务和生产批量的联合决策(APLS),第二层是运输和订货批量的联合决策(TOQ).因此,提出了基于两层分解的启发式算法来求解这样的联合决策模型(JDM).结合实际例子对模型和算法进行了仿真分析,结果证明了基于两层分解的启发式算法的有效性.     

An inventory control policy for liquefied natural gas as a transportation fuel

In this paper, we study a novel stochastic inventory management problem that arises in storage and refueling facilities for Liquefied Natural Gas (LNG) as a transportation fuel. In this inventory problem, the physio-chemical properties of LNG play a key role in the design of inventory policies. These properties are: (1) LNG suffers from both quantity decay and quality deterioration and (2) the quality of on-hand LNG can be upgraded by mixing it with higher-quality LNG. Given that LNG quality can be upgraded, an inventory control policy for this problem needs to consider the removal of LNG as a decision variable. We model and solve the problem by means of a Markov Decision Process (MDP) and study the structural characteristics of the optimal policy. The insights obtained in the analysis of the optimal policy are translated into a simple, though effective, inventory control policy in which actions (i.e., replenishment and/or removal) are driven by both the quality and the quantity of the inventories. We assess the performance of our policy by means of a numerical study and show that it performs close to optimal in many numerical instances. The main conclusion of our study is that it is important to take quality into consideration when design inventory control policies for LNG, and that the most effective way to cope with quality issues in an LNG inventory system involves both the removal and the replenishment of inventories.     

Logic-based Benders decomposition for an inventory-location problem with service constraints

We study an integrated inventory-location problem with service requirements faced by an aerospace company in designing its service parts logistics network. Customer demand is Poisson distributed and the service levels are time-based leading to highly non-linear, stochastic service constraints and a nonlinear, mixed-integer optimization problem. Unlike previous work in the literature, which propose approximations for the nonlinear constraints, we present an exact solution methodology using logic-based Benders decomposition. We decompose the problem to separate the location decisions in the master problem from the inventory decisions in the subproblem. We propose a new family of valid cuts and prove that the algorithm is guaranteed to converge to optimality. This is the first attempt to solve this type of problem exactly. Then, we present a new restrict-and-decompose scheme to further decompose the Benders master problem by part. We test on industry instances as well as random instances. Using the exact algorithm and restrict-and-decompose scheme we are able to solve industry instances with up to 60 parts within reasonable time, while the maximum number of parts attempted in the literature is 5.     

Integrated retail decisions with multiple selling periods and customer segments: Optimization and insights

Integrating retail decisions on such aspects as assortment, pricing, and inventory greatly improves profitability. We examine a multi-period selling horizon where a retailer jointly optimizes assortment planning, pricing, and inventory decisions for a product line of substitutable products, in a market with multiple customer segments. Focusing on fast-moving retail products, the problem is modeled as a mixed-integer nonlinear program where demand is driven by exogenous consumer reservation prices and endogenous assortment and pricing decisions. A mixed-integer linear reformulation is developed, which enables an exact solution to large problem instances (with up to a hundred products) in manageable times. Empirical evidence is provided in support of a classical deterministic maximum-surplus consumer choice model. Computational results and managerial insights are discussed. We find that the optimal assortment and pricing decisions do not exhibit a simple, intuitive structure that could be analytically characterized, which reflects the usefulness of optimization approaches to numerically identify attractive trade-offs for the decision-maker. We also observe that suboptimal inventory policies significantly decrease profitability, which highlights the importance of integrated decision-making. Finally, we find that the seasonality of consumer preferences and supply costs present an opportunity for boosting the profit via higher inventory levels and wider assortments.     

一种能力外包且费用时变批量问题的启发式算法

当企业自身能力不能满足需求时考虑外包,可以有效提高企业的竞争力。一种带能力外包的多产品动态经济批量问题得以提出,并设定外包能力使用价格较高且费用时变。建立混合整数规划模型,通过约束松弛与模型分解,设计出一个基于拉格朗日松弛理论的启发式算法进行模型求解。大量随机实验表明,无论解的质量还是求解时间都表现较好。     

Tighter MIP models for Barge Container Ship Routing

This paper addresses the problem of optimal planning of a liner service for a barge container shipping company. Given estimated weekly demands between pairs of ports, our goal is to determine the subset of ports to be called and the amount of containers to be shipped between each pair of ports, so as to maximize the profit of the shipping company. In order to save possible leasing or storage costs of empty containers at the respective ports, our approach takes into account the repositioning of empty containers. The line has to follow the outbound–inbound principle, starting from the port at the river mouth. We propose a novel integrated approach in which the shipping company can simultaneously optimize the route (along with repositioning of empty containers), the choice of the final port, length of the turnaround time and the size of its fleet. To solve this problem, a new mixed integer programming model is proposed. On the publicly available set of benchmark instances for barge container routing, we demonstrate that this model provides very tight dual bounds and significantly outperforms the existing approaches from the literature for splittable demands.We also show how to further improve this model by projecting out arc variables for modeling the shipping of empty containers. Our numerical study indicates that the latter model improves the computing times for the challenging case of unsplittable demands. We also study the impact of the turnaround time optimization on the total profit of the company.     

Passenger and pilot risk minimization in offshore helicopter transportation

In the offshore petroleum industry, employees are transported to and from the offshore installations by helicopter, which represents a major risk. This paper analyzes how to improve transportation safety by solving the helicopter routing problem with a risk objective expressed in terms of expected number of fatalities. A mathematical model is proposed and a tabu search heuristic is applied to this problem. Three routing policies are considered: a direct routing policy, a Hamiltonian routing policy, and a general routing policy. Extensive computational experiments are conducted on instances derived from real data in order to assess and compare these policies under a travel time, a passenger risk and a combined passenger and pilot risk objective. Several management insights can be derived from this study. In particular, our results show that passenger transportation risk can be reduced by increasing travel time at the expense of pilot risk. This can be achieved through a reduction of the average number of passengers onboard by applying either a Hamiltonian or a general routing policy. Our methodology can also be used to derive an equitable distribution of risk between passengers and pilots, considering that pilots fly much more frequently than passengers.     

Multi-item single-source ordering with detailed consideration of transportation capacities

We consider multi-item single-source ordering with detailed consideration of transportation capacities. Such problems are characteristic for companies which operate direct links as part of their supply chain to transport loads with heterogeneous physical dimensions and fluctuating demands. Given knowledge on transportation demands, companies can eliminate future transports by shifting the load to fill the inflexible capacity of prior transports. While reducing transportation costs, doing so will ceteris paribus imply inventory. The problem is to coordinate orders across multiple items such that transport costs are minimized at minimal increase in inventory. The approach is distinct from prior works in that it considers detailed loading restrictions. We therefore interpret the problem as a multi-period version of the container loading problem. A wall building approach is used and incorporated into a heuristic rolling horizon procedure. We test the proposed procedure on some random problems which resemble a real inbound case from the automotive industry. As compared to period-by-period planning and two benchmarks with aggregated capacity models from the literature and practice, cost savings are possible under a wide range of operating conditions and mostly independent of the shipping volume. The largest potential exists for mid- to long-distance transports. There is a relevant potential to improve short-distance transports as well, however, only if inventory cost rates are moderate.     

Flexibility or Cost Saving? Sourcing Decisions with Two Suppliers

This article studies a decentralized supply chain in which there are two suppliers and a single buyer. One supplier offers the quantity flexibility (QF) contract to the buyer, while the other offers the cheaper price. Under the QF contract, the buyer does not assume full responsibility for the forecast, yet the supplier guarantees the availability of the forecasted quantity with additional buffer inventory. On the other hand, the price‐only contract places full inventory burden on the buyer, but with a cheaper price. We study this problem from the buyer's perspective and solve for the buyer's optimal procurement and forecasting decisions. We identify areas where flexibility and cheaper price have an advantage, one over the other. Our results indicate that the buyer significantly benefits from having multiple sources of supply. We also find that, from the system's standpoint, a multisupplier system may outperform a single‐supplier supply chain under certain conditions. Interestingly, we observe that providing too much flexibility may benefit the low‐price supplier rather than benefiting the QF supplier. We discuss the managerial implications and provide directions for future research opportunities.     

Multiperiod Models with Capacities in Competitive Supply Chain

This paper considers a supply chain setting where several capacitated suppliers compete for orders from a single retailer in a multiperiod environment. At each period, the retailer places orders to the suppliers in response to the prices they announce. Each supplier has a fixed capacity. We consider a make‐to‐stock setting where the retailer can carry inventory. The retailer faces exogenous, price‐dependent demand. We study the problem using ideas from fluid models. In particular, we (i) analyze when there are pure equilibrium policies in this setting and characterize the structure of these policies; (ii) consider coordination mechanisms; and (iii) present some preliminary computational results. We also consider a modified model that uses option contracts to coordinate the supply chain.