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Stochastic Demand (stochastic + demand)
Selected AbstractsSocial Optimal Location of Facilities with Fixed Servers, Stochastic Demand, and CongestionPRODUCTION AND OPERATIONS MANAGEMENT, Issue 6 2009Ignacio Castillo We consider two capacity choice scenarios for the optimal location of facilities with fixed servers, stochastic demand, and congestion. Motivating applications include virtual call centers, consisting of geographically dispersed centers, walk-in health clinics, motor vehicle inspection stations, automobile emissions testing stations, and internal service systems. The choice of locations for such facilities influences both the travel cost and waiting times of users. In contrast to most previous research, we explicitly embed both customer travel/connection and delay costs in the objective function and solve the location,allocation problem and choose facility capacities simultaneously. The choice of capacity for a facility that is viewed as a queueing system with Poisson arrivals and exponential service times could mean choosing a service rate for the servers (Scenario 1) or choosing the number of servers (Scenario 2). We express the optimal service rate in closed form in Scenario 1 and the (asymptotically) optimal number of servers in closed form in Scenario 2. This allows us to eliminate both the number of servers and the service rates from the optimization problems, leading to tractable mixed-integer nonlinear programs. Our computational results show that both problems can be solved efficiently using a Lagrangian relaxation optimization procedure. [source] Branch-and-Price Methods for Prescribing Profitable Upgrades of High-Technology Products with Stochastic Demands*DECISION SCIENCES, Issue 1 2004Purushothaman Damodaran ABSTRACT This paper develops a model that can be used as a decision support aid, helping manufacturers make profitable decisions in upgrading the features of a family of high-technology products over its life cycle. The model integrates various organizations in the enterprise: product design, marketing, manufacturing, production planning, and supply chain management. Customer demand is assumed random and this uncertainty is addressed using scenario analysis. A branch-and-price (B&P) solution approach is devised to optimize the stochastic problem effectively. Sets of random instances are generated to evaluate the effectiveness of our solution approach in comparison with that of commercial software on the basis of run time. Computational results indicate that our approach outperforms commercial software on all of our test problems and is capable of solving practical problems in reasonable run time. We present several examples to demonstrate how managers can use our models to answer "what if" questions. [source] Retailer's Response to Alternate Manufacturer's Incentives Under a Single-Period, Price-Dependent, Stochastic-Demand Framework,DECISION SCIENCES, Issue 4 2005F. J. Arcelus ABSTRACT This article considers the joint development of the optimal pricing and ordering policies of a profit-maximizing retailer, faced with (i) a manufacturer trade incentive in the form of a price discount for itself or a rebate directly to the end customer; (ii) a stochastic consumer demand dependent upon the magnitude of the selling price and of the trade incentive, that is contrasted with a riskless demand, which is the expected value of the stochastic demand; and (iii) a single-period newsvendor-type framework. Additional analysis includes the development of equal profit policies in either form of trade incentive, an assessment of the conditions under which a one-dollar discount is more profitable than a one-dollar rebate, and an evaluation of the impact upon the retailer-expected profits of changes in either incentive or in the degree of demand uncertainty. A numerical example highlights the main features of the model. The analytical and numerical results clearly show that, as compared to the results for the riskless demand, dealing with uncertainty through a stochastic demand leads to (i) (lower) higher retail prices if additive (multiplicative) error, (ii) lower (higher) pass throughs if additive (multiplicative) error, (iii) higher claw backs in both error structures wherever applicable, and (iv) higher rebates to achieve equivalent profits in both error structures. [source] Comparative analysis of three user equilibrium models under stochastic demandJOURNAL OF ADVANCED TRANSPORTATION, Issue 3 2008Zhong Zhou Abstract Recent empirical studies on the value of time and reliability reveal that travel time variability plays an important role on travelers' route choice decision process. It can be considered as a risk to travelers making a trip. Therefore, travelers are not only interested in saving their travel time but also in reducing their risk. Typically, risk can be represented by two different aspects: acceptable risk and unacceptable risk. Acceptable risk refers to the reliability aspect of acceptable travel time, which is defined as the average travel time plus the acceptable additional time (or buffer time) needed to ensure more frequent on-time arrivals, while unacceptable risk refers to the unreliability aspect of unacceptable late arrivals (though infrequent) that have a travel time excessively higher than the acceptable travel time. Most research in the network equilibrium based approach to modeling travel time variability ignores the unreliability aspect of unacceptable late arrivals. This paper examines the effects of both reliability and unreliability aspects in a network equilibrium framework. Specifically, the traditional user equilibrium model, the demand driven travel time reliability-based user equilibrium model, and the ,-reliable mean-excess travel time user equilibrium model are considered in the investigation under an uncertain environment due to stochastic travel demand. Numerical results are presented to examine how these models handle risk under travel time variability. [source] BUYING VERSUS HIRING,AN INDIRECT EVOLUTIONARY APPROACHMETROECONOMICA, Issue 4 2009Siegfried K. Berninghaus ABSTRACT On a symmetric homogeneous oligopoly market with stochastic demand, firms can either hire employees or buy their labor input on a competitive labor market. Whereas the wage of hired labor does not depend on the realization of stochastic demand, the price of ,bought' labor reacts positively to product demand. We derive the equilibrium price vector to define an evolutionary process, assuming that the number of hiring firms increases when they earn more than buying firms. We then derive and discuss the stationary distribution of this stochastic adaptation process. [source] A two-echelon inventory-location problem with service considerationsNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 8 2009Ho-Yin Mak Abstract We study the problem of designing a two-echelon spare parts inventory system consisting of a central plant and a number of service centers each serving a set of customers with stochastic demand. Processing and storage capacities at both levels of facilities are limited. The manufacturing process is modeled as a queuing system at the plant. The goal is to optimize the base-stock levels at both echelons, the location of service centers, and the allocation of customers to centers simultaneously, subject to service constraints. A mixed integer nonlinear programming model (MINLP) is formulated to minimize the total expected cost of the system. The problem is NP-hard and a Lagrangian heuristic is proposed. We present computational results and discuss the trade-off between cost and service. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009 [source] Optimal capacity in a coordinated supply chainNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 2 2008Xiuli Chao Abstract We consider a supply chain in which a retailer faces a stochastic demand, incurs backorder and inventory holding costs and uses a periodic review system to place orders from a manufacturer. The manufacturer must fill the entire order. The manufacturer incurs costs of overtime and undertime if the order deviates from the planned production capacity. We determine the optimal capacity for the manufacturer in case there is no coordination with the retailer as well as in case there is full coordination with the retailer. When there is no coordination the optimal capacity for the manufacturer is found by solving a newsvendor problem. When there is coordination, we present a dynamic programming formulation and establish that the optimal ordering policy for the retailer is characterized by two parameters. The optimal coordinated capacity for the manufacturer can then be obtained by solving a nonlinear programming problem. We present an efficient exact algorithm and a heuristic algorithm for computing the manufacturer's capacity. We discuss the impact of coordination on the supply chain cost as well as on the manufacturer's capacity. We also identify the situations in which coordination is most beneficial. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008 [source] On the first come,first served rule in multi-echelon inventory controlNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 5 2007Sven Axsäter Abstract A two-echelon distribution inventory system with a central warehouse and a number of retailers is considered. The retailers face stochastic demand and replenish from the warehouse, which, in turn, replenishes from an outside supplier. The system is reviewed continuously and demands that cannot be met directly are backordered. Standard holding and backorder costs are considered. In the literature on multi-echelon inventory control it is standard to assume that backorders at the warehouse are served according to a first come,first served policy (FCFS). This allocation rule simplifies the analysis but is normally not optimal. It is shown that the FCFS rule can, in the worst case, lead to an asymptotically unbounded relative cost increase as the number of retailers approaches infinity. We also provide a new heuristic that will always give a reduction of the expected costs. A numerical study indicates that the average cost reduction when using the heuristic is about two percent. The suggested heuristic is also compared with two existing heuristics. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007 [source] Contractual agreements for coordination and vendor-managed delivery under explicit transportation considerationsNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 5 2006egül Toptal Abstract We consider the coordination problem between a vendor and a buyer operating under generalized replenishment costs that include fixed costs as well as stepwise freight costs. We study the stochastic demand, single-period setting where the buyer must decide on the order quantity to satisfy random demand for a single item with a short product life cycle. The full order for the cycle is placed before the cycle begins and no additional orders are accepted by the vendor. Due to the nonrecurring nature of the problem, the vendor's replenishment quantity is determined by the buyer's order quantity. Consequently, by using an appropriate pricing schedule to influence the buyer's ordering behavior, there is an opportunity for the vendor to achieve substantial savings from transportation expenses, which are represented in the generalized replenishment cost function. For the problem of interest, we prove that the vendor's expected profit is not increasing in buyer's order quantity. Therefore, unlike the earlier work in the area, it is not necessarily profitable for the vendor to encourage larger order quantities. Using this nontraditional result, we demonstrate that the concept of economies of scale may or may not work by identifying the cases where the vendor can increase his/her profits either by increasing or decreasing the buyer's order quantity. We prove useful properties of the expected profit functions in the centralized and decentralized models of the problem, and we utilize these properties to develop alternative incentive schemes for win,win solutions. Our analysis allows us to quantify the value of coordination and, hence, to identify additional opportunities for the vendor to improve his/her profits by potentially turning a nonprofitable transaction into a profitable one through the use of an appropriate tariff schedule or a vendor-managed delivery contract. We demonstrate that financial gain associated with these opportunities is truly tangible under a vendor-managed delivery arrangement that potentially improves the centralized solution. Although we take the viewpoint of supply chain coordination and our goal is to provide insights about the effect of transportation considerations on the channel coordination objective and contractual agreements, the paper also contributes to the literature by analyzing and developing efficient approaches for solving the centralized problem with stepwise freight costs in the single-period setting. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006 [source] Optimal machine capacity expansions with nested limitations under stochastic demandNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 2 2004Metin Çakany This paper studies capacity expansions for a production facility that faces uncertain customer demand for a single product family. The capacity of the facility is modeled in three tiers, as follows. The first tier consists of a set of upper bounds on production that correspond to different resource types (e.g., machine types, categories of manpower, etc.). These upper bounds are augmented in increments of fixed size (e.g., by purchasing machines of standard types). There is a second-tier resource that constrains the first-tier bounds (e.g., clean room floor space). The third-tier resource bounds the availability of the second-tier resource (e.g., the total floor space enclosed by the building, land, etc.). The second and third-tier resources are expanded at various times in various amounts. The cost of capacity expansion at each tier has both fixed and proportional elements. The lost sales cost is used as a measure for the level of customer service. The paper presents a polynomial time algorithm (FIFEX) to minimize the total cost by computing optimal expansion times and amounts for all three types of capacity jointly. It accommodates positive lead times for each type. Demand is assumed to be nondecreasing in a "weak" sense. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004. [source] A single-period inventory placement problem for a serial supply chainNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 6 2001Chia-Shin Chung Abstract This article addresses the inventory placement problem in a serial supply chain facing a stochastic demand for a single planning period. All customer demand is served from stage 1, where the product is stored in its final form. If the demand exceeds the supply at stage 1, then stage 1 is resupplied from stocks held at the upstream stages 2 through N, where the product may be stored in finished form or as raw materials or subassemblies. All stocking decisions are made before the demand occurs. The demand is nonnegative and continuous with a known probability distribution, and the purchasing, holding, shipping, processing, and shortage costs are proportional. There are no fixed costs. All unsatisfied demand is lost. The objective is to select the stock quantities that should be placed different stages so as to maximize the expected profit. Under reasonable cost assumptions, this leads to a convex constrained optimization problem. We characterize the properties of the optimal solution and propose an effective algorithm for its computation. For the case of normal demands, the calculations can be done on a spreadsheet. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48:506,517, 2001 [source] Social Optimal Location of Facilities with Fixed Servers, Stochastic Demand, and CongestionPRODUCTION AND OPERATIONS MANAGEMENT, Issue 6 2009Ignacio Castillo We consider two capacity choice scenarios for the optimal location of facilities with fixed servers, stochastic demand, and congestion. Motivating applications include virtual call centers, consisting of geographically dispersed centers, walk-in health clinics, motor vehicle inspection stations, automobile emissions testing stations, and internal service systems. The choice of locations for such facilities influences both the travel cost and waiting times of users. In contrast to most previous research, we explicitly embed both customer travel/connection and delay costs in the objective function and solve the location,allocation problem and choose facility capacities simultaneously. The choice of capacity for a facility that is viewed as a queueing system with Poisson arrivals and exponential service times could mean choosing a service rate for the servers (Scenario 1) or choosing the number of servers (Scenario 2). We express the optimal service rate in closed form in Scenario 1 and the (asymptotically) optimal number of servers in closed form in Scenario 2. This allows us to eliminate both the number of servers and the service rates from the optimization problems, leading to tractable mixed-integer nonlinear programs. Our computational results show that both problems can be solved efficiently using a Lagrangian relaxation optimization procedure. [source] Industry dynamics with stochastic demandTHE RAND JOURNAL OF ECONOMICS, Issue 1 2008James Bergin We study the dynamics of an industry subject to aggregate demand shocks where the productivity of a firm's technology evolves stochastically over time. To characterize the intertemporal evolution of the distribution of firms, we discuss in particular how exit decisions, aggregate output, profits, and distributions of firm productivities vary (a) across different demand realization paths; (b) along a demand history path, detailing the effects of continued good or bad market conditions; and (c) for different anticipated future market conditions. We show how poor demand conditions can lead to increased exit of low-productivity firms at all future dates and states and raise welfare due to the impact on exit decisions. [source] A scenario-based stochastic programming model for the control or dummy wafers downgrading problemAPPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 3 2009Shu-Hsing Chung Abstract The subject of this paper is to study a realistic planning environment in wafer fabrication for the control or dummy (C/D) wafers problem with uncertain demand. The demand of each product is assumed with a geometric Brownian motion and approximated by a finite discrete set of scenarios. A two-stage stochastic programming model is developed based on scenarios and solved by a deterministic equivalent large linear programming model. The model explicitly considers the objective to minimize the total cost of C/D wafers. A real-world example is given to illustrate the practicality of a stochastic approach. The results are better in comparison with deterministic linear programming by using expectation instead of stochastic demands. The model improved the performance of control and dummy wafers management and the flexibility of determining the downgrading policy. Copyright © 2008 John Wiley & Sons, Ltd. [source] | ||||||||||||||||