Optimal Paths And Costs Of Adjustment In Dynamic DEA Models: With Application To Chilean Department Stores

In this paper we propose a range of dynamic data envelopment analysis (DEA) models which allow information on costs of adjustment to be incorporated into the DEA framework. We first specify a basic dynamic DEA model predicated on a number of simplifying assumptions. We then outline a number of extensions to this model to accommodate asymmetric adjustment costs, non-static output quantities, non-static input prices, and non-static costs of adjustment, technological change, quasi-fixed inputs and investment budget constraints. The new dynamic DEA models provide valuable extra information relative to the standard static DEA models—they identify an optimal path of adjustment for the input quantities, and provide a measure of the potential cost savings that result from recognising the costs of adjusting input quantities towards the optimal point. The new models are illustrated using data relating to a chain of 35 retail department stores in Chile. The empirical results illustrate the wealth of information that can be derived from these models, and clearly show that static models overstate potential cost savings when adjustment costs are non-zero. This paper arises out the senior author's PhD thesis at the University of New England, Australia. The authors gratefully acknowledge Dr. George E. Battese for his comments on earlier drafts of this work.     

Cost allocation in collaborative forest transportation

Transportation planning is an important part of the supply chain or wood flow chain in forestry. There are often several forest companies operating in the same region and collaboration between two or more companies is rare. However, there is an increasing interest in collaborative planning as the potential savings are large, often in the range 5–15%. There are several issues to agree on before such collaborative planning can be used in practice. A key question is how the total cost or savings should be distributed among the participants. In this paper, we study a large application in southern Sweden with eight forest companies involved in a collaboration. We investigate a number of sharing mechanisms based on economic models including Shapley value, the nucleolus, separable and non-separable costs, shadow prices and volume weights. We also propose a new allocation method, with the aim that the participants relative profits are as equal as possible. We use two planning models, the first is based on direct flows between supply and demand points and the second includes backhauling. We also study how several time periods and geographical distribution of the supply and demand nodes affect the solutions. Better planning within each company can save about 5% and collaboration can increase this about another 9% to a total of 14%. The proposed allocation method is shown to be a practical approach to share the overall cost/savings.     

Cooperative game theory approach to allocating benefits of horizontal cooperation

Logistics costs in general, and transportation costs in particular, represent a large fraction of the operating costs of many companies. One way to try to reduce these costs is through horizontal cooperation among shippers. Thus, when the transportation needs of two or more companies are merged, their collective transportation requirements can be met at lower cost. The attainable cost savings are due to economies of scale, which translate into cheaper rates due to increased negotiation power, use of larger vehicles and bundling of shipments. In this paper, a linear model is presented and used to study the cost savings that different companies may achieve when they merge their transportation requirements. On the one hand, solving this optimization model for different collaboration scenarios allows testing and quantifying the synergies among different potential partners, thus identifying the most profitable collaboration opportunities. On the other, the problem of allocating the joint cost savings of the cooperation is tackled using cooperative game theory. The proposed approach is illustrated with an example in which different cooperative game solution concepts are compared. Extensive numerical experiments have also been carried out to gain insight into the properties of the corresponding cost savings game and the behavior of the different solution concepts.     

Allocating the gains from resource pooling with the Shapley Value

To make their cost structure more efficient, firms often pool their critical resources: small divisions of a large firm may negotiate a joint contract to benefit from volume discounts; or firms may outsource their call centres to an independent provider who is able to increase utilization by reducing variability since demand is now pooled. Since pooling demand reduces total joint costs, an immediate question is how the realized savings should be shared. We model the problem as a cooperative game and use the resulting allocation schemes to distribute the savings. One popular scheme is the Shapley Value, which always exists and, we show, represents each player's incremental value to the pool. When the pooled savings depend on the sum of each player's demand, we label the game coalition symmetric and propose, for those games, an algorithm that makes pseudo-polynomial the computation of the Shapley Value.     

Joint Vendor-buyer Policy in JIT Manufacturing

In this study, we show that a co-operative batching policy, based on cost information exchange between the vendor and the buyer, can reduce total cost significantly in the just-in-time (JIT) environment. We examine the impact of such co-operation on total costs, including ordering, set-up, transportation and inventory holding costs for a long-term supply relationship. The study shows that joint optimization of both the vendor and the buyer's operations does not necessarily result in a common lot size. We further examine the sensitivity of the resulting cost savings due to the exchange of cost information to changes in the relevant operating parameters.     

运单体积不确定对货运共享平台定价决策的影响研究

货运共享平台订单分析显示顾客对运输货物申报的体积往往比实际体积偏大,平台则会按照客户申报的体积进行收费。本文站在平台利润视角,构建了考虑运单体积不确定的装载与配送路径联合优化模型来研究运单体积不确定对定价决策的影响,研究发现可以提升平台利润达24%。进一步,为了实现平台、顾客与司机的收益共享,并提高平台市场占有率,平台考虑在收费体积存在偏差的情况下,采用降价的策略与平台实际定价策略进行对比。通过数值分析发现,在存在体积偏差率的情况下,价格下降18%以内时,平台的利润呈现增长的趋势,最高可以达到23.26%;当价格下降超过18%时,平台利润出现负增长,因此不适合采取降价的措施。在降价过程中,顾客需要支付的成本最多可减少19.17%,司机的收益最多可增加13.82%,结果表明,采用新型分段定价策略可以更好的实现三方共赢,对平台的实际运营有一定的借鉴意义。     

Concentration and the variability of orthopaedic demand

Concentrating health services with centres providing selected, specialist care offers a number of potential advantages. The benefits may include the opportunity to improve the quality of care by providing more specialist services and greater expertise, more attractive working conditions with a larger pool of specialists providing the on-call rota and an enhanced opportunity for training. Concentration will produce greater volumes of patients in the selected specialties with the possibility of various economies of scale. A series of simulation experiments explored the potential for efficiencies associated with the increasing volume of non-elective patients in an orthopaedic specialty. As the annual volume of patients increases so the relative variability of the demand for operating theatre time declines: concentrating non-elective orthopaedic activity could offer considerable savings in the theatre time allocated to trauma patients. However, the impact on the wards is much less significant, with concentration having a negligible effect on the requirement for beds.     

Cost allocation in the establishment of a collaborative transportation agreement—an application in the furniture industry

Transportation is an important part of the Canadian furniture industry supply chain. Even though there are often several manufacturers shipping in the same market region, coordination between two or more manufacturers is rare. Recently, important potential cost savings and delivery time reduction have been identified through transportation collaboration. In this paper we propose and test on a case study involving four furniture companies, a logistics scenario that allows transportation collaboration. Moreover, we address the key issue of cost savings sharing, especially when heterogeneous requirements by each collaborating company impact the cost-savings. To do so, we propose a new cost allocation method that is validated through a case study. Sensibility analysis and details about the actual outcome of the case study complete the discussion.     

Ship-pack optimization in a two-echelon distribution system

In large distribution systems, distribution centers (DC) deliver some merchandize to their retail stores in size-specific packages, also called ship-packs. These ship-packs include cases (e.g., cartons containing 24 or 48 units), inners (packages of 6 or 8 units) or eaches (individual units). For each Stock Keeping Unit (SKU), a retailer can decide which of these ship-pack options to use when replenishing its retail stores. Working with a major US retailer, we have developed a cost model that balances DC handling costs, store handling costs and inventory-related costs at both the DC and the stores, and therefore can help to determine the optimum warehouse ship-pack for each SKU. We implement our model for a sample of 529 SKUs, and show that by changing ship-pack size for about 30 SKUs, the retailer can reduce its total cost by 0.3% - 0.4%. Interestingly, we find that most of the cost savings occurs at the DC level.     

Balancing fleet size and repositioning costs in LTL trucking

This paper develops an optimization modeling approach for analyzing the trade-off between the cost of a larger fleet of tractors and the cost of repositioning tractors for a trucking company operating a consolidation network, such as a less-than-truckload (LTL) company. Specifically, we analyze the value of using extra tractor repositioning moves (in addition to the ones required to balance resources throughout the network) to reduce the fixed costs of owning or leasing a tractor fleet during a planning horizon. We develop network flow optimization models, some with side constraints and nonlinear objective functions, using event-based, time-expanded networks to determine appropriate fleet sizes and extra repositioning moves under different repositioning strategies, and we compare the optimal costs of the strategies. For repositioning costs, two different cost schemes are explored: one linear and one nonlinear. Computational experiments using real data from a national LTL carrier compare the total system costs obtained with four different strategies and show that extra repositioning may indeed enable fleet size reductions and concomitant cost savings.     

Optimal timing decisions for the introduction of new technologies

High technology industries, such as the communications industry, are characterized by frequent development of new technologies. These new technologies are often available before the capacities of existing facilities that use an old technology are exhausted. Whenever a new technology facility is introduced, a fixed set-up cost is generally incurred; however, the annual operating costs are often reduced. The optimal timing of the introduction of new facilities is therefore of interest.In this paper, we examine such timing decisions. The study was motivated by an application involving electronic plug-in units that enhance the operation of communication facilities. First, we develop optimal timing decisions for linearly growing demand. The analysis is then extended to nonlinear demand. For linear demand, one of two decisions is optimal: Either introduce the new technology immediately, or as late as possible. However, for nonlinear demand, these decisions may be nonoptimal.     

Multi-period capacity expansion for a local access telecommunications network

In this paper, we examine a multi-period capacity expansion problem for a local access telecommunications network with a tree topology. Capacity expansion is realized through the installation of concentrators at the nodes and cables on the links of the network. Clearly, the installation of concentrators reduces the need for additional cables, and conversely. The goal is to find the least cost alternative to satisfy the demand. A heuristic approach is proposed to solve this problem, where local installation decisions at each node are propagated in the network. This information is then used to adjust prices that guide the decision process from one iteration to the next, until a fixed point is reached. Numerical results are reported on problem instances based on different cost and demand structures.     

An inventory system with investment to reduce yield variability and set-up cost

The set-up cost and yield variability are given and fixed in existing production/inventory models with random yields. However, in many practical situations, they can be reduced by investment in modern production technology. In this paper, we consider an inventory system with random yield in which both the set-up cost and yield variability can be reduced through capital investment. The objective is to determine the optimal capital investment and ordering policies that minimize the expected total annual costs for the system. In addition, an iterative solution procedure is presented to find the optimal order quantity and reorder point and then the optimal set-up cost and yield standard deviation. Numerical examples are given to illustrate the results obtained and assess the cost savings by adopting capital investments. Managerial implications are also included.     

Cost Comparisons for Out-of-Phase Inventory Models

Inventory costs for a fixed time period have traditionally been determined by allocating total costs per cycle uniformly throughout that cycle as well as any partial cycles. This procedure for cost allocation has led to the solution of numerous inventory problems, most notable of which is the anticipated price-increase model. When comparing two out-of-phase inventory models, if costs are accounted for when they occur over a fixed planning horizon, inventory policies should be changed to reflect the impact of this different cost-allocation procedure. For the anticipated price-increase model, the ‘optimal’ order quantity as well as the implied savings in inventory costs will be different when cost models are developed based on these different cost-allocation methods. If the objective is to maximize over a fixed planning horizon the actual savings in inventory costs as they occur, the cost models presented here should be used.     

Reducing lost-sales rate in (T, R, L) inventory model with controllable lead time

In order to establish a good image and to enhance customer’s loyalty, many efforts such as upgrading the servicing facilities, maintaining a high quality of products and increasing expenditure on advertisement could be made by a selling shop. Naturally, an extra-added cost must be spent for these efforts and it is expected to have a result to reduce the shortage cost of lost-sales and the total expected annual cost. This paper explores a probabilistic inventory model with optimal lost-sales caused by investment due to two different types of cost functions. We consider that the lead time can be shortened at an extra crashing cost, which depends on the length of the lead time. Moreover, we assume that the lost-sales rate can also be reduced by capital investment. The purpose of this paper is to establish a (T, R, L) inventory model with controllable lead time and to analyze the effects of increasing two different types of investments to reduce the lost-sales rate, in which the review period, lead time and lost-sales rate are treated as decision variables. We first formulate the basic periodic review model mathematically with the capital investment to reduce lost-sales rate. Then two models are discussed, one with normally distributed protection interval demand and another with distribution-free case. For each model, two investment cost functional forms, logarithmic and power, are employed for lost-sales rate reduction. Two computational algorithms with the help of the software Matlab are furnished to determine the optimal solution. In addition, six numerical examples and sensitivity analysis are presented to illustrate the theoretical results and obtain some managerial insights. Finally, the effect of lost-sales rate reduction is investigated. By framing this new model, we observe that a significant amount of savings can be easily achieved to increase the competitive edge in business. The results in the numerical examples indicate that the savings of expected annual total cost are realized through lost-sales reduction.     

Modelling the benefits of information sharing-based partnerships in a two-level supply chain

This paper presents a study aimed at quantifying the benefits of information sharing-based supply chain partnerships. We derive the optimal inventory policies for the manufacturer and the retailer in a two-level decentralized supply chain under different information sharing scenarios. We show that increasing information sharing among the members in a decentralized supply chain will lead to Pareto improvement in the performance of the entire chain. Specifically, the manufacturer can obtain benefits in terms of reductions in inventory levels and cost savings.     

Product-design and pricing strategies with remanufacturing

In this paper, we consider a supply chain that consists of an original equipment manufacturer (OEM) producing new products and a remanufacturer recovering the used items. The OEM often faces a strategic dilemma when determining the degree of disassemblability of its product design, as high disassemblability decreases the OEM’s production costs as well as the remanufacturer’s recovery costs. However, high disassemblability may be harmful to the OEM in a market in which the remanufacturer is encouraged to intensify price competition with the OEM because design for high disassemblability leads to larger cost savings in remanufacturing. We first formulate a two-period model to investigate the OEM’s product-design strategy and the remanufacturer’s pricing strategy in an extensive-form game, in which the equilibrium decisions of the resulting scenarios are derived. Next, we show the thresholds that determine whether remanufacturing is constrained by collection, the thresholds for the remanufacturer’s choice of a profitable pricing strategy, and the thresholds for determining the OEM’s product-design strategy. Finally, we expand the model for a multiple-period problem to show that the main insights obtained from the two-period model can be applied.     

中国股票市场交易量与价格波动关系实证研究

利用个股数据资料和非对称成分GARCH-M模型对中国股票市场的量价关系进行了实证研究.结论显示:股价的短期波动主要由非预期交易量解释,即非预期交易量所揭示的新信息是产生价格波动的根源;中国股票市场部分个股存在明显的杠杆效应,利空消息对市场波动的冲击大于同等程度的利好消息对市场波动的冲击;非预期交易行为对市场波动的冲击存在显著的非对称特征,正的交易量冲击(交易量放量冲击)比同等程度的负交易量冲击(交易量缩量冲击)对市场波动的影响更大.     

Analysis of an industrial component commonality problem

We discuss a case study of an industrial production-marketing coordination problem involving component commonality. For the product line considered, the strategic goal of the company is to move from the current low volume market to a high volume market. The marketing department believes that this can be achieved by substantially lowering the end products’ prices. However, this requires a product redesign to lower production costs in order to maintain profit margins. The redesign decision involves grouping end products into families. All products within one family use the same version of some components. This paper fits in the stream of recent literature on component commonality where the focus has shifted from inventory cost savings to production and development cost savings. Further, we consider both costs and revenues, leading to a profit maximization approach. The price elasticity of demand determines the relationship between the price level and number of units sold. Consequently, we integrate information from different functional areas such as production, marketing and accounting. We formulate the problem as a net-present-value investment decision. We propose a mixed integer nonlinear optimization model to find the optimal commonality decision. The recommendation based on our analysis has been implemented in the company. In addition, the application allows us to experimentally validate some claims made in the literature and obtain managerial insights into the trade-offs.     

The impact of forecasting model selection on the value of information sharing in a supply chain

This paper presents a study on the impact of forecasting model selection on the value of information sharing in a supply chain with one capacitated supplier and multiple retailers. Using a computer simulation model, this study examines demand forecasting and inventory replenishment decisions by the retailers, and production decisions by the supplier under different demand patterns and capacity tightness. Analyses of the simulation output indicate that the selection of the forecasting model significantly influences the performance of the supply chain and the value of information sharing. Furthermore, demand patterns faced by retailers and capacity tightness faced by the supplier also significantly influence the value of information sharing. The result also shows that substantial cost savings can be realized through information sharing and thus help to motivate trading partners to share information in the supply chain. The findings can also help supply chain managers select suitable forecasting models to improve supply chain performance.