http://repub.eur.nl/res/aut/5989/ List of Publications en http://repub.eur.nl/static-eur/img/logo.png http://repub.eur.nl http://repub.eur.nl/res/pub/37819/ 2012-08-01T00:00:00Z This paper studies a real-life multi-objective two-dimensional single-bin-size bin-packing problem arising in industry. A packing pattern is defined by one bin, a set of items packed into the bin and the packing positions of these items. A number of bins can be placed with the same packing pattern. The objective is not only to minimise the number of bins used, as in traditional bin-packing problems, but also to minimise the number of packing patterns. Based on our previous study of a heuristic stemming from dynamic programming by aggregating states to avoid the exponential increase in the number of states, we further develop this heuristic by decomposing a pattern with a number of bins at each step. Computational results show that this heuristic provides satisfactory results with a gap generally less than 20% with respect to the optimum. http://repub.eur.nl/res/pub/37686/ 2012-04-01T00:00:00Z Fast deteriorating raw materials such as raw milk, fruit and vegetables are commonly used to produce slowly deteriorating finished products such as milk powders, cheeses, and pastas. This paper studies a Vendor Managed Inventory (VMI) type supply chain where the manufacturing vendor decides how to manage the system-wide inventories of its fast deteriorating raw material and its slowly deteriorating product. The decision variables are a common replenishment cycle of the product and the replenishment frequency of the raw material. We assume the deteriorating rates are known constants and every retailers demand is deterministic. We develop an integrated model to calculate the total inventory and deterioration cost for such a system. We prove the convexity of the cost functions, and based on this a golden search algorithm is developed to find the optimal solution of the model. Our numerical results show that the deteriorating rate of the product may increase the total cost by more than 40% compared to the zero-deteriorating rate, while the deteriorating raw material has less impact on the total cost (commonly less than 5% in our numerical examples). This indicates that more attention should be paid to the product than the raw material. Further, an increase in the number of retailers can make the replenishment frequency of the raw material increase significantly but the common replenishment cycle of the product decreases a little. This indicates that adding a new retailer would not be felt strongly by the other retailers but would be felt by the supplier of the raw material. http://repub.eur.nl/res/pub/37684/ 2012-02-01T00:00:00Z Sequencing unit-load retrieval requests has been extensively reported on in the literature for conventional single-deep automated warehousing systems. A proper sequence can greatly reduce the makespan when carrying out a group of such requests. Although the sequencing problem is NP-hard, some very good heuristics exist. Surprisingly, the problem has not yet been investigated for compact (multi-deep) storage systems, which have greatly increased in popularity the last decade. This article studies how to sequence a group (or block) of storage and retrieval requests in a multi-deep automated storage system with the objective to minimize the makespan. Currently utilized sequencing heuristics for the multi-deep system are adapted in this article and in addition a new heuristic, Percentage Priority to Retrievals with Shortest Leg (PPR-SL), is proposed and evaluated. It is shown that the PPR-SL heuristic consistently outperforms all of the other heuristics. Generally, it can outperform the benchmark First-Come First-Served (FCFS) heuristic by between 20 and 70%. The nearest neighbor heuristic that performs very well in conventional single-deep storage systems appears to perform poorly in the multi-deep system, even worse than FCFS. In addition, based on FCFS and PPR-SL, robust rack dimensions that yield a short makespan, regardless of the number of storage and retrieval requests, are found. http://repub.eur.nl/res/pub/30739/ 2011-10-01T00:00:00Z This paper studies a vendor-managed-inventory (VMI) supply chain where a manufacturer, as a vendor, procures a type of nondeteriorating raw material to produce a deteriorating product, and distribute it to multiple retailers. The price of the product offered by one retailer is also influenced by the prices offered by other retailers because consumers can choose the product from any of the retailers. This paper is one of the first papers that propose an integrated model to study the influence of pricing and deterioration on the profit of such a VMI system. A hybrid approach combining genetic algorithms and an analytical method is developed for efficiently determining the optimal price of the product of each retailer, the inventory policies of the product and the raw material. Our results of a detailed numerical study show that parameters related to the market and deterioration have significant influences on the profit of the VMI system. However, different from common intuition, we find that an increase in the substitution elasticity of the product among different retailers can bring an increase in the retail prices of the product, while the increase of the market scale can reduce the retail prices. http://repub.eur.nl/res/pub/22722/ 2011-02-17T00:00:00Z Sequencing unit load retrieval requests has been studied extensively in literature for conventional single-deep automated warehousing systems. A proper sequence can greatly reduce the makespan when carrying out a group of such requests. Although the sequencing problem is NP-hard some very good heuristics exist. Surprisingly the problem has not yet been investigated for compact (multi-deep) storage systems, which have greatly increased in popularity the last decade. This paper studies how to sequence a group (or block) of storage and retrieval requests in a multi-deep automated storage system with the objective to minimize the makespan. We adapt well-known sequencing heuristics for the multi-deep system, and propose and evaluate a new heuristic: percentage priority to retrievals with shortest leg (PPR-SL). Our results show the PPR-SL heuristic consistently outperforms all the other heuristics. Generally, it can outperform the benchmark first-come first-served (FCFS) heuristic by 20-70%. The nearest neighbor (NN) heuristic that performs very well in conventional single-deep storage systems, appears to perform poorly in the multi-deep system; even worse than FCFS. In addition, based on FCFS and PPR-SL, we find robust rack dimensions yielding a short makespan, regardless of the number of storage and retrieval requests. http://repub.eur.nl/res/pub/19234/ 2010-10-16T00:00:00Z This paper discusses how a manufacturer and its retailers interact with each other to optimize their product marketing strategies, platform product configuration and inventory policies in a VMI (Vendor Managed Inventory) supply chain. The manufacturer procures raw materials from multiple suppliers to produce a family of products sold to multiple retailers. Multiple types of products are substitutable each other to end customers. The manufacturer makes its decision on raw materials’ procurement, platform product configuration, product replenishment policies to retailers with VMI, price discount rate, and advertising investment to maximize its profit. Retailers in turn consider the optimal local advertising investments and retail prices to maximize their profits. This problem is modeled as a dual simultaneous non-cooperative game (as a dual Nash game) model with two sub-games. One is between the retailers serving in competing retail markets and the other is between the manufacturer and the retailers. This paper combines analytical, iterative and GA (genetic algorithm) methods to develop a game solution algorithm to find the Nash equilibrium. A numerical example is conducted to test the proposed model and algorithm, and gain managerial implications. http://repub.eur.nl/res/pub/20321/ 2010-07-01T00:00:00Z A stochastic inventory routing problem (SIRP) is typically the combination of stochastic inventory control problems and NP-hard vehicle routing problems, which determines delivery volumes to the customers that the depot serves in each period, and vehicle routes to deliver the volumes. This paper aims to solve a large scale multi-period SIRP with split delivery (SIRPSD) where a customer’s delivery in each period can be split and satisfied by multiple vehicle routes if necessary. This paper considers SIRPSD under the multi-criteria of the total inventory and transportation costs, and the service levels of customers. The total inventory and transportation cost is considered as the objective of the problem to minimize, while the service levels of the warehouses and the customers are satisfied by some imposed constraints and can be adjusted according to practical requests. In order to tackle the SIRPSD with notorious computational complexity, we first propose an approximate model, which significantly reduces the number of decision variables compared to its corresponding exact model. We then develop a hybrid approach that combines the linearization of nonlinear constraints, the decomposition of the model into sub-models with Lagrangian relaxation, and a partial linearization approach for a sub model. A near optimal solution of the model found by the approach is used to construct a near optimal solution of the SIRPSD. Randomly generated instances of the problem with up to 200 customers and 5 periods and about 400 thousands decision variables where half of them are integer are examined by numerical experiments. Our approach can obtain high quality near optimal solutions within a reasonable amount of computation time on an ordinary PC. http://repub.eur.nl/res/pub/20308/ 2010-02-01T00:00:00Z is paper studies the performance of static and dynamic scheduling approaches in vehicle-based internal transport (VBIT) systems and is one of the first to systematically investigate under which circumstances, which scheduling method helps in improving performance. In practice, usually myopic dispatching heuristics are used, often using look-ahead information. We argue more advanced scheduling methods can help, depending on circumstances. We introduce three basic scheduling approaches (insertion, combined and column generation) for the static problem. We then extend these to a dynamic, real-time setting with rolling horizons. We propose two further real-time scheduling approaches: dynamic assignment with and without look-ahead. The performances of the above five scheduling approaches are compared with two of the best performing look-ahead dispatching rules known from the literature. The performance of the various approaches depends on the facility layout and work distribution. However, column generation, the combined heuristic, and the assignment approach with look-ahead consistently outperform dispatching rules. Column generation can require substantial calculation time but delivers very good performance if sufficient look-ahead information is available. For large scale systems, the combined heuristic and the dynamic assignment approach with look ahead are recommended and have acceptable calculation times. http://repub.eur.nl/res/pub/18041/ 2010-01-23T00:00:00Z A stochastic inventory routing problem (SIRP) is typically the combination of stochastic inventory control problems and NP-hard vehicle routing problems, for a depot to determine delivery volumes to its customers in each period, and vehicle routes to distribute the delivery volumes. This paper aims to solve a large scale multi-period SIRP with split delivery (SIRPSD) where a customer’s delivery in each period can be split and satisfied by multiple vehicles if necessary. The objective of the problem is to minimize the total inventory and transportation cost while some constraints are given to satisfy other criteria, such as the service level to limit the stockout probability at each customer and the service level to limit the overfilling probability of the warehouse of each customer. In order to tackle the SIRPSD with notorious computational complexity, we propose for it an approximate model, which significantly reduces the number of decision variables compared to its corresponding exact model. We develop a hybrid approach that combines the linearization of nonlinear constraints, the decomposition of the model into sub-models with Lagrangian relaxation, and a partial linearization approach for a sub model. A near optimal solution of the model can be found by the approach, and then be used to construct a near optimal solution of the SIRPSD. Numerical examples show that, for an instance of the problem with 200 customers and 5 periods that contains about 400 thousands decision variables where half of them are integer, our approach can obtain high quality near optimal solutions with a reasonable computational time on an ordinary PC. http://repub.eur.nl/res/pub/16898/ 2009-10-07T00:00:00Z In the past thirty years the full turnover-based storage policy as described by Hausman et al. (1976, Management Science 22(6)) has been widely claimed to outperform the commonly used ABC class-based storage policy, in terms of the resulting average storage and retrieval machine travel time. In practice however, ABC storage is the dominant policy. Hausman et al. (1976) model the turnover-based policy under the unrealistic assumption of shared storage, i.e. the storage space allocated to one product can only accommodate its average inventory level; no specific space is reserved to store the maximum inventory of a product. It appears that many authors citing Hausman et al.’s results overlook this assumption and use the resulting storage and retrieval machine travel times as if it were valid for full turnover-based storage. Full turnover-based storage is a dedicated storage policy where the storage space allocated to one product must accommodate its maximum inventory level. This paper adapts the travel time model of Hausman et al. to accommodate full turnover-based dedicated storage. Surprisingly, the result of the adapted travel time model is opposite to that of Hausman et al. (1976) but, in line with practice, it supports that ABC (2- or 3-) class-based storage normally outperforms full turnover-based storage. http://repub.eur.nl/res/pub/15029/ 2009-03-02T00:00:00Z This paper discusses how a manufacturer and its retailers interact with each other to optimize their product marketing strategies, platform product configuration and inventory policies in a VMI (Vendor Managed Inventory) supply chain. The manufacturer procures raw materials from multiple suppliers to produce a family of products sold to multiple retailers. Multiple types of products are substitutable each other to end customers. The manufacturer makes its decision on raw materials’ procurement, platform product configuration, product replenishment policies to retailers with VMI, price discount rate, and advertising investment to maximize its profit. Retailers in turn consider the optimal local advertising and retail price to maximize their profits. This problem is modeled as a dual simultaneous non-cooperative game (as a Nash game) model with two sub-games. One is between the retailers serving in competing retail markets and the other is between the manufacturer and the retailers. This paper combines analytical, iterative and GA (genetic algorithm) methods to develop a game solution algorithm to find the Nash equilibrium. A numerical example is conducted to test the proposed model and algorithm, and gain managerial implications. http://repub.eur.nl/res/pub/13660/ 2009-02-01T00:00:00Z Vendor managed inventory (VMI) is an inventory management strategy to let a vendor manage his retailers’ inventories, which makes the vendor have the opportunity to obtain some inventory and market-related information of his retailers. This paper discusses how the vendor can take advantage of this information for increasing his own profit by using a Stackelberg game in a VMI system. The vendor here is a manufacturer who procures raw materials to produce a finished product and supplies it at the same wholesale price to multiple retailers. The retailers then sell the product in independent markets at retail prices. Solution procedures are developed to find the Stackelberg game equilibrium that each enterprise is not willing to deviate from for maximizing his own profit. The equilibrium makes the manufacturer benefited, and the retailers’ profits maximized. The equilibrium can then be improved for further benefiting the manufacturer and his retailers if the retailers are willing to cooperate with the manufacturer by using a cooperative contract. Finally, a numerical example and the corresponding sensitivity analysis are given to illustrate that: (1) the manufacturer can benefit from his leadership, and monopolize the added profit of the VMI system in some cases; (2) The manufacturer can further improve his own profit, and then the retailers’ profits by the cooperative contract, as compared to the Stackelberg equilibrium; (3) market and raw material related parameters have significant influence on every enterprise’s net profit. http://repub.eur.nl/res/pub/14615/ 2009-01-30T00:00:00Z A warehouse needs to have sufficient open locations to be able to store incoming shipments of various sizes. In combination with ongoing load retrievals open locations gradually spread over the storage area. Unfavorable positions of open locations negatively impact the average load retrieval times. This paper presents a new method to manage these open locations such that the average system travel time for processing a block of storage and retrieval jobs in an automated warehousing system is minimized. We introduce the effective storage area (ESA), a well-defined part of the locations closest to the depot; where only a part of the open locations –the effective open locations-, together with all the products, are stored. We determine the optimal number of effective open locations and the ESA boundary minimizing the average travel time. Using the ESA policy, the travel time of a pair of storage and retrieval jobs can be reduced by more than 10% on average. Its performance depends hardly on the number or the sequence of retrievals. In fact, in case of only one retrieval, applying the policy leads already to beneficial results. Application is also easy; the ESA size can be changed dynamically during storage and retrieval operations. http://repub.eur.nl/res/pub/15031/ 2009-01-20T00:00:00Z Compact, multi-deep three-dimensional (3D), Automated Storage and Retrieval Systems (AS/RS) are becoming more common, due to new technologies, lower investment costs, time efficiency and compact size. Decision-making research on these systems is still in its infancy. This paper studies a particular compact system with rotating conveyors for the depth movement and a Storage/Retrieval (S/R) machine for the horizontal and vertical movement of unit loads. The optimal storage zone boundaries are determined for this system with two product classes: high- and low-turnover, by minimizing the expected S/R machine travel time. We formulate a mixed-integer non-linear programming model to determine the zone boundaries. A decomposition algorithm and a one-dimensional search scheme are developed to solve the model. The algorithm is complex, but the results are appealing since most of them are in closed-form and easy to apply to optimally layout the 3D AS/RS rack. The results show that the S/R machine travel time is significantly influenced by the zone dimensions, zone sizes and ABC curve skewness (presenting turnover patterns of different products). The presented results are compared with those under random storage and it is shown that significant reductions of the machine travel time are obtainable by using class-based storage. http://repub.eur.nl/res/pub/13659/ 2008-09-16T00:00:00Z This paper studies an inventory routing problem (IRP) with split delivery and vehicle fleet size constraint. Due to the complexity of the IRP, it is very difficult to develop an exact algorithm that can solve large scale problems in a reasonable computation time. As an alternative, an approximate approach that can quickly and near-optimally solve the problem is developed based on an approximate model of the problem and Lagrangian relaxation. In the approach, the model is solved by using a Lagrangian relaxation method in which the relaxed problem is decomposed into an inventory problem and a routing problem that are solved by a linear programming algorithm and a minimum cost flow algorithm, respectively, and the dual problem is solved by using the surrogate subgradient method. The solution of the model obtained by the Lagrangian relaxation method is used to construct a near-optimal solution of the IRP by solving a series of assignment problems. Numerical experiments show that the proposed hybrid approach can find a high quality near-optimal solution for the IRP with up to 200 customers in a reasonable computation time. http://repub.eur.nl/res/pub/11878/ 2008-03-01T00:00:00Z In this paper, we consider a newly designed compact three-dimensional automated storage and retrieval system (AS/RS). The system consists of an automated crane taking care of the pallets' movements in the horizontal and vertical direction. A gravity or powered conveying mechanism takes care of the pallets' depth movement in the rack. Our research objective is to analyze the system performance and optimally dimension the system. For single-command cycles, the crane's expected retrieval travel time is the same for gravity and powered conveyors; we give a closed-form expression. From the expected travel time, we calculate the optimal ratio between three dimensions that minimizes the travel time for a random storage strategy. In addition, we derive an approximate travel time expression for dual command cycles for the system with powered and gravity conveyors, respectively, and use it to optimize the system dimensions. Finally, we illustrate the findings of the study by a practical example. http://repub.eur.nl/res/pub/10180/ 2007-05-10T00:00:00Z Compact, multi-deep (3D), Automated Storage and Retrieval Systems (AS/RS) are becoming more common, due to new technologies, lower investment costs, time efficiency and compact size. Decision-making research on these systems is still in its infancy. We study a particular compact system with rotating conveyors for the depth movement and a Storage/Retrieval (S/R) machine for the horizontal and vertical movement of unit loads. We determine the optimal storage zone boundaries for such systems with two product classes: high and low turnover, by minimizing the expected Storage/Retrieval (S/R) machine travel time. We propose a mixed-integer nonlinear programming model to determine the zone boundaries. A decomposition algorithm and a one dimensional search scheme are developed to solve the model. The algorithm is complex, but the results are appealing since most of them are in closed-form and easy to apply to optimally layout the 3D AS/RS rack. The results are compared with those under random storage, and show that a significant reduction of the machine travel time can be obtained. Finally, a practical example is studied to demonstrate the use and validate our findings. http://repub.eur.nl/res/pub/8194/ 2006-12-20T00:00:00Z VMI (Vendor Managed Inventory) is a widely used cooperative inventory policy in supply chains in which each enterprise has its autonomy in pricing. This paper discusses a leader-follower Stackelberg game in a VMI supply chain where the manufacturer, as a leader, produces a single product with a limited production capacity and delivers it at a wholesale price to multiple different retailers, as the followers, who then sell the product in dispersed and independent markets at retail prices. An algorithm is then developed to determine the equilibrium of the Stackelberg game. Finally, a numerical study is conducted to understand the influence of the Stackelberg equilibrium and market related parameters on the profits of the manufacturer and its retailers. Through the numerical example, our research demonstrates that: (a) the market related parameters have significant influence on the manufacturer’ and its retailers’ profits; (b) a retailer’s profit may not be necessarily lowered when it is charged with a higher inventory cost by the manufacturer; (c) the equilibrium of the Stackelberg equilibrium benefits the manufacturer. http://repub.eur.nl/res/pub/8129/ 2006-11-28T00:00:00Z This paper studies the performance of static and real-time scheduling approaches in vehicle-based internal transport (VBIT) systems, which can be found in manufacturing and warehouse facilities. We propose three heuristic approaches for static VBIT problems (insertion, combined and column generation), extend them to a dynamic, real-time setting and compare their performance over a rolling time horizon. This time horizon can be seen either as a fixed-time interval in which advance information about loads’ arrivals is available, or as a fixed number of loads which are known to become available in the near future. We also propose two dynamic assignment approaches: with and without look-ahead, respectively. Performance (primarily average load waiting time) of the above five dynamic scheduling approaches is compared with two nearest-vehicle-first rules (with and without look-ahead), which are the best vehicle dispatching rules known from literature and which are commonly used in practice. Experimental results show that, if sufficient prior information is available, our dynamic scheduling approaches consistently outperform vehicle dispatching rules. Results also reveal that guide-path layout, load arrival rate and variance, and amount of load pre-arrival information have strong impacts on the performance of vehicle control approaches. Column generation or the combined heuristics are recommended in small or medium-scale VBIT systems, whereas for large scale VBIT systems, both the combined heuristic and the dynamic assignment approach with look ahead perform best. http://repub.eur.nl/res/pub/7839/ 2006-06-23T00:00:00Z In this paper, we consider a newly-designed compact three-dimensional automated storage and retrieval system (AS/RS). The system consists of an automated crane taking care of movements in the horizontal and vertical direction. A gravity conveying mechanism takes care of the depth movement. Our research objective is to analyze the system performance and optimally dimension of the system. We estimate the crane’s expected travel time for single-command cycles. From the expected travel time, we calculate the optimal ratio between three dimensions that minimizes the travel time for a random storage strategy. In addition, we derive an approximate closed-form travel time expression for dual command cycles. Finally, we illustrate the findings of the study by a practical example. http://repub.eur.nl/res/pub/7831/ 2006-06-19T00:00:00Z Compact, multi-deep (3D) automated storage and retrieval systems (AS/RS) are becoming increasingly popular for storing products with relatively low turnover on a compact area. An automated storage/retrieval crane takes care of movements in the horizontal and vertical direction in the rack, and a gravity conveying mechanism takes care of the depth movement. An important question is how to layout such systems to minimize the product storage and retrieval times. Although much attention has been paid to 2D AS/RS, multi-deep systems have hardly been studied. This paper studies the impact of system layout on crane travel time. We calculate the rack dimensions that minimize single-command cycle time under the full-turnover-based storage policy. We prove the expected travel time is minimized when the rack is square-in-time in horizontal and vertical directions and the conveyor’s dimension is the longest. We compare the model’s results with the performance of the random storage policy and show a significant crane travel time reduction can be obtained. We illustrate the findings of the study by applying them in a practical example.