Capacitated Supply Research Articles

Dynamic Lot Optimization of Assembly Supply Chain with Delivery Time Constraint

In this paper, we investigate operational decision optimization problem of assembly manufacturing capacitated supply chain. Open equations of this system in all planning periods are set up. Delivery time to clients form a time window that limits point to assembly manufacturer delivery start and end time. The system model divide planning time into many equally periods, and decisions can vary with time. Ability constraint in the process of supply chain operation, time constraints and assembly production constrain are all considered in the inventory control dynamic batch optimization model. We solve the optimization problem by hybrid mixed integral optimization and SQP algorithm. At last, we examine a set of numerical examples that reveal the insights into the dynamic inventory control policy and the performance of such an assembly type inventory mode.

Procurement allocation planning with multiple suppliers under competition

This paper examines a procurement planning scenario in which a firm wishes to obtain some quantity of a good from a set of capacitated suppliers whose products are interchangeable. The total cost to acquire the good from a supplier is a nondecreasing concave function of the amount of the product purchased, as a result of economies of scale and/or bulk discounts offered by the supplier. The problem of minimising the total cost incurred in obtaining the required amount of the good is NP-hard in itself, but further complicating the situation is the existence of a competing firm (or set of firms) with its own demand for the same input or good. The existence of such competition leads to a situation in which the first firm (the ‘leader’) must consider the actions of their competitor(s) (whom we model as a single ‘follower’) when minimising procurement cost, because the follower’s procurement amounts decrease the suppliers’ available capacity levels. To mitigate the effects of the follower’s actions, the leader can ‘protect’ any supplier at some cost (e.g. by signing a contract in which the supplier guarantees some level of capacity). Therefore, our problem is a three-stage game in which the leader first chooses which suppliers to protect, the follower satisfies its demand, and the leader satisfies its demand from the remaining capacity. We model this problem as a three-stage mixed-integer programme, and propose algorithms for its optimal solution via reformulation and cutting-plane techniques.

Multi-location transshipment problem with capacitated production

We consider coordination among stocking locations through replenishment strategies that explicitly take into account lateral transshipments, i.e., transfer of a product among locations at the same echelon level. Our basic contribution is the incorporation of supply capacity into the traditional transshipment model. Our goal is to analyze the impact on system behavior and on stocking locations’ performance of the fact that the supplier may fail to fulfill all the replenishment orders. We therefore formulate the capacitated supply scenario as a network flow problem embedded in a stochastic optimization problem, which is solved through a sample average approximation method. We find that, depending on the production capacity, system behavior can vary drastically. Moreover, in a production-inventory system, we find evidence that either capacity flexibility (i.e., extra production) or transshipment flexibility (i.e., pooling) is required to maintain a desired level of service.

Optimization of replenishment policies for decentralized and centralized capacitated supply chains under various demands

In this paper, the optimal replenishment policies of capacitated supply chains (SC) operating under two different control strategies (decentralized vs. centralized) and various demands are determined and insights useful to management are discussed. The details of the system used, including the underlying supply chain inventory model and the simulation-based optimization framework, are presented. The effectiveness and efficiency of the proposed optimization framework is illustrated by comparing it with brute force estimation of the true optimum on three selected scenarios. The entire study was carried out by following a design of experiment, covering ten demand patterns, four levels of capacity constraints, and two control strategies. The main and two-factor interaction effects were analyzed via ANOVA. Detailed analyses of the ordering patterns, cost distribution over the SC and internal service level were carried out to provide useful insights. For demand with high variation, capacity constraint may lead to significant changes in ordering patterns. Failing to detect those changes may lead to unnecessary cost increase. Overall it is beneficial to adopt centralized control and cost savings realized are dependent upon the demand patterns. An incentive mechanism is proposed to coordinate the decentralized system so that each player in the SC will be better off. Additional experiments were also carried out to investigate the effect of using different allocation rules by the distributor.

An improved model for supplier selection under capacity constraint and multiple criteria

Abstract Ghodsypour and O'Brien [2001. The total cost of logistics in supplier selection, under conditions of multiple sourcing, multiple criteria and capacity constraint. International Journal of Production Economics 73(1), 15–27] study multiple sourcing problem with multiple criteria and capacitated suppliers. Considering the buyer's quality requirements as a constraint, they develop a mixed integer non-linear programming model to find the least-cost cyclic ordering policy for the buyer. They propose to solve the model by enumerating over all possible supplier combinations. Although the problem is interesting and their analysis is correct, we point out two issues with their assumptions, namely, capacitated suppliers and cyclic ordering policy. We discuss two different capacitated supplier settings: (i) long-run average annual capacity, and (ii) exact annual capacity. First, under long-run average annual capacity assumption we propose a model which provides the same or a better solution and is much easier to solve than their model. Then, we discuss how to modify our and their models to handle exact annual capacity assumption.

Strategies for protecting supply chain networks against facility and transportation disruptions: an improved Benders decomposition approach

Disruptions rarely occur in supply chains, but their negative financial and technical impacts make the recovery process very slow. In this paper, we propose a capacitated supply chain network design (SCND) model under random disruptions both in facility and transportation, which seeks to determine the optimal location and types of distribution centers (DC) and also the best plan to assign customers to each opened DC. Unlike other studies in the extent literature, we use new concepts of reliability to model the strategic behavior of DCs and customers at the network: (1) Failure of DCs might be partial, i.e. a disrupted DC might still be able to serve with a portion of its initial capacity (2) The lost capacity of a disrupted DC shall be provided from a non-disrupted one and (3) The lost capacity fraction of a disrupted DC depends on its initial investment amount in the design phase.

Optimal Inventory Control with Dual‐Sourcing, Heterogeneous Ordering Costs and Order Size Constraints

We consider a dual‐sourcing inventory system, where procuring from one supplier involves a high variable cost but negligible fixed cost whereas procuring from the other supplier involves a low variable cost but high fixed cost, as well as an order size constraint. We show that the problem can be reduced to an equivalent single‐sourcing problem. However, the corresponding ordering cost is neither concave nor convex. Using the notion of quasi‐convexity, we partially characterize the structure of the optimal policy and show that it can be specified by multiple thresholds which determine when to order from each supplier and how much. In contrast to previous research, which does not consider order size constraints, we show that it is optimal to simultaneously source from both suppliers when the beginning inventory level is sufficiently low. We also show that the decision to source from the low‐cost supplier is not monotonic in the inventory level. Our results require that the variable costs satisfy a certain condition which guarantees quasi‐convexity. However, extensive numerical results suggest that our policy is almost always optimal when the condition is not satisfied. We also show how the results can be extended to systems with multiple capacitated suppliers.

Sourcing from Multiple Suppliers for Price‐Dependent Demands

We analyze a model that integrates demand shaping via dynamic pricing and risk mitigation via supply diversification. The firm under consideration replenishes a certain product from a set of capacitated suppliers for a price‐dependent demand in each period. Under deterministic capacities, we derive a multilevel base stock list price policy and establish the optimality of cost‐based supplier selection, that is, ordering from a cheaper source before more expensive ones. With general random capacities, however, neither result holds. While it is optimal to price low for a high inventory level, the optimal order quantities are not monotone with respect to the inventory level. In general, a near reorder‐point policy should be followed. Specifically, there is a reorder point for each supplier such that no order is issued to him when the inventory level is above this point and a positive order is placed almost everywhere when the inventory level is below this point. Under this policy, it may be profitable to order exclusively from the most expensive source. We characterize conditions under which a strict reorder‐point policy and a cost‐based supplier‐selection criterion become optimal. Moreover, we quantify the benefit from dynamic pricing, as opposed to static pricing, and the benefit from multiple sourcing, as opposed to single sourcing. We show that these two strategies exhibit a substitutable relationship. Dynamic pricing is less effective under multiple sourcing than under single sourcing, and supplier diversification is less valuable with price adjustments than without. Under limited supply, dynamic pricing yields a robust, long‐term profit improvement. The value of supply diversification, in contrast, mainly comes from added capacities and is most significant in the short run.

Production/distribution system design with inventory considerations

AbstractThis study addresses the design of a three‐stage production/distribution system where the first stage includes the set of established retailers and the second and third stages include the sets of potential distribution centers (DCs) and potential capacitated suppliers, respectively. In this problem, in addition to the fixed location/operating costs associated with locating DCs and suppliers, we consider the coordinated inventory replenishment decisions at the located DCs and retailers along with the appropriate inventory costs explicitly. In particular, we account for the replenishment and holding costs at the retailers and selected DCs, and the fixed plus distance‐based transportation costs between the selected plants and their assigned DCs, and between the selected DCs and their respective retailers, explicitly. The resulting formulation is a challenging mixed‐integer nonlinear programming model for which we propose efficient heuristic solution approaches. Our computational results demonstrate the performance of the heuristic approaches as well as the value of integrated decision‐making by verifying that significant cost savings are realizable when the inventory decisions and costs are incorporated in the production distribution system design. © 2012 Wiley Periodicals, Inc. Naval Research Logistics 59: 172–195, 2012

The bullwhip effect in capacitated supply chains with consideration for product life-cycle aspects

This paper presents an analysis of the bullwhip effect and net-stock amplification in a three-echelon supply chain considering step-changes in the production rates during a product's life-cycle demand. The analysis is focused around highly complex and engineered products (e.g., automobiles), that have relatively long production life-cycles and require significant capital investment in manufacturing. Using a simulation approach, we analyze three stages of the product life-cycle including low volumes during product introduction, peak demand, and eventual decline toward the end of the life-cycle. Parts of the simulation model have been adopted by a major North-American automotive OEM as part of a scenario analysis tool for strategic supply network design and analysis. The simulation results show that performance of a system as a whole deteriorates when there is a step-change in the life-cycle demand. While restriction in production capacity does not significantly impact the bullwhip effect, it increases the net stock amplification significantly for the supply chain setting under consideration. Furthermore, a number of important managerial insights are presented based on sensitivity analysis of interaction effect of capacity constraints with other supply chain parameters.

Integrated use of fuzzy c-means and convex programming for capacitated multi-facility location problem

In this study a fuzzy c-means clustering algorithm based method is proposed for solving a capacitated multi-facility location problem of known demand points which are served from capacitated supply centres. It involves the integrated use of fuzzy c-means and convex programming. In fuzzy c-means, data points are allowed to belong to several clusters with different degrees of membership. This feature is used here to split demands between supply centers. The cluster number is determined by an incremental method that starts with two and designated when capacity of each cluster is sufficient for its demand. Finally, each group of cluster and each model are solved as a single facility location problem. Then each single facility location problem given by fuzzy c-means is solved by convex programming which optimizes transportation cost is used to fine-tune the facility location. Proposed method is applied to several facility location problems from OR library (Osman & Christofides, 1994) and compared with centre of gravity and particle swarm optimization based algorithms. Numerical results of an asphalt producer's real-world data in Turkey are reported. Numerical results show that the proposed approach performs better than using original fuzzy c-means, integrated use of fuzzy c-means and center of gravity methods in terms of transportation costs.

Multi-period supply chain network equilibrium with capacity constraints and purchasing strategies

In this paper, we propose a capacitated supply chain network equilibrium model in which three tiers of decision makers (manufacturers, retailers and consumers at demand markets) seek to determine their optimal plans over a multi-period planning horizon. Unlike other studies in the extent literature, we use a new concept of purchasing strategy to model the strategic behavior of retailers and consumers at demand markets in a capacitated supply chain network. A purchasing strategy denotes an ordered set of manufacturers (or retailers) from which each retailer (or each consumer at a demand market) prefers to purchase a product. We show that the equilibrium conditions governing the multi-period capacitated supply chain network equilibrium problem can be formulated as a variational inequality in terms of strategies and strategic flows. To find a solution to this variational inequality, we propose an iterative algorithm that generates strategies for retailers and consumers as required by solving a dynamic program. We prove that the solution set is nonempty and provide a numerical example to illustrate the validity of our model.

Coordination in a two-stage capacitated supply chain with multiple suppliers

The aim of this paper is to coordinate the inventory policies in a decentralized supply chain with stochastic demand by means of contracts. The system considered is a decentralized two-stage supply chain consisting of multiple independent suppliers and a manufacturer with limited production capacities. The suppliers operate on a make-to-stock basis and apply base stock policy to manage their inventories. On the other hand, the manufacturer employs a make-to-order strategy. Under the necessary assumptions, each supplier is modeled as an M/ M/1 make-to-stock queue; and the manufacturer is modeled as a GI/ M/1 queue after deriving an approximate distribution for the interarrival times of the manufacturer. Once the supply chain is modeled as a queuing system, centralized and decentralized models are developed. Comparison of the optimal solutions to these models reveals that the supply chain needs coordination. Three different transfer payment contracts are examined in this paper. These are the backorder and holding cost subsidy contracts, the transfer payment contract based on Pareto improvement, and the cost sharing contract. Each contract is evaluated according to its coordination ability and whether it is Pareto improving or not. The results indicate that all three contracts can coordinate the supply chain. However, when the Pareto improvement is taken into account, the cost sharing contract seems to be the one that will be preferred by all parties.

A computer simulation model for analysing performance of inventory policy in multi-product mode in two-echelon supply chain

In this paper, a simulation model is presented for analysing performance of inventory policy in multi-product mode in two-echelon supply chain including four retailers and one capacitated supplier. The inventory policies include: Economic Order Quantity (EOQ), Periodic Order Quantity (POQ), Silver-Meal (SM), and Part-Period Balancing (PPB). The results also show that sharing planned order information (OIS) is better than sharing only demand information (DIS), which, in turn, is better than No Information Sharing (NIS), for all inventory policies used by the retailers.

An Integrated Forward/Reverse Logistics Network Optimization Model for Multi-Stage Capacitated Supply Chain

In this study, the integrated forward/reverse logistics network is investigated, and a capacitated multi-stage logistics network design is proposed by formulating a generalized logistics network problem into a bi-objective mixed-integer programming model (MIP). The purpose is to minimize the total costs and maximize the responsiveness of the closed- loop supply chain network simultaneously. Moreover branch and bound algorithm is applied to find a global optimum for this model which provides the decisions related to the facility location problem, optimum quantity of shipped product, and facility capacity. Finally, a numerical example is conducted in order to show the power of the proposed MIP model to avoid the sub-optimality caused by separate design of the forward and reverse logistics networks. It has been shown that such an approach can significantly help the managers to make decisions about the problems associated with integrated logistics network design.

Bertrand-Edgeworth Auction with Multiple Asymmetric Bidders

Motivated by supply competitions in the service sector, we consider a version of the Bertrand-Edgeworth game where capacitated suppliers compete in prices to serve a deterministic demand and a price cap is imposed exogenously. We characterize the equilibrium structure for games with multiple suppliers that are asymmetric in cost and capacity. A pure-strategy equilibrium exists only in special cases, otherwise a mixed-strategy equilibrium prevails. For a mixed-strategy equilibrium, we show there exists an anchoring supplier whose pricing range covers those of the other suppliers, and we pin down the lower and upper bounds of that price range. We derive a canonical closed-form solution for a set of games, and for other more general cases, we demonstrate a numerical scheme for equilibrium calculation. In contrast to a well-known intuition established in the existing literature, we identify a new equilibrium pricing structure in games with N >= 3 suppliers who have similar costs but different capacities: A low-capacity supplier's price distribution is more concentrated than those of its high-capacity competitors, by spanning a smaller interval. We demonstrate an interesting strategy for a buyer with a competitive supply base: Subsidizing a cost-competitive incumbent may reduce the total procurement cost.

Hybrid Heuristics for Multiple Production Forward/Reverse Logistics System

We consider a multiple production two-stage forward/reverse logistics system design problem where a fixed number of capacitated distribution/reclaiming centers are to be located with respect to capacitated suppliers and retail locations while minimizing the total costs, and take the random of demand/reclaiming into consideration. We also provide hybrid heuristic procedures for the problem, and develop transshipment heuristic to improve the duration of the proposed approaches. Finally we present computational results that show the high performance and effectiveness of the solution approaches.

Analysis of healthcare supply chain systems exposed to random capacity disruptions

Capacity disruptions caused by forces of nature, process-related hazards, and man-made malignant interventions have shown to be a profound risk factor for lean healthcare supply chain systems, such as pharmaceutical and medical equipment/devices enterprises. At the same time, decision support methodologies suitable for analysing healthcare supply chain risk incurred through capacity disruptions have been largely unavailable. In this paper, we examine capacitated healthcare supply chain systems using a framework of feed-forward flow-matching networks with multiple points of delivery. We analyse two models of stochastic dynamics of such systems in the presence of random disruptions. The proposed closed-form analytics will serve as a foundation for future mathematical methodologies for risk-based design of resilient healthcare supply chains.

OPTIMAL PRICING AND PRODUCTION POLICIES OF A MAKE-TO-STOCK SYSTEM WITH FLUCTUATING DEMAND

We study the effects of different pricing strategies available to a production–inventory system with capacitated supply, which operates in a fluctuating demand environment. The demand depends on the environment and on the offered price. For such systems, three plausible pricing strategies are investigated: static pricing, for which only one price is used at all times, environment-dependent pricing, for which price changes with the environment, and dynamic pricing, for which price depends on both the current environment and the stock level. The objective is to find an optimal replenishment and pricing policy under each of these strategies. This article presents some structural properties of optimal replenishment policies and a numerical study that compares the performances of these three pricing strategies.

Approximate analysis and optimization of batch ordering policies in capacitated supply chains

Devising manufacturing/distribution strategies for supply chains and determining their parameter values have been challenging problems. Linking production management to stock keeping processes improves the planning of the supply chain activities, including material management, culminating in improved customer service levels. In this study, we investigate a multi-echelon supply chain consisting of a supplier, a plant, a distribution center and a retailer. Material flow between stages is driven by reorder point/order quantity inventory control policies. We develop a model to analyze supply chain behavior using some key performance metrics such as the time averages of inventory and backorder levels, as well as customer service levels at each echelon. The model is validated against simulation, yielding good agreement of robust performance metrics. The metrics are then used within an optimization framework to design the supply chain so as to minimize expected total system costs. The outcome of the optimization framework specifies how to move inventory throughout the supply chain and how to set inventory control parameters, i.e., reorder levels and replenishment batch sizes.