On upper bounds of sequential stochastic production planning problems

In this paper we consider a class of problems that determine production, inventory and work force levels for a firm in order to meet fluctuating demand requirements. A production planning problem arises because of the need to match, at the firm level, supply and demand efficiently. In practice, the two common approaches to counter demand uncertainties are (i) carrying a constant safety stock from period to period, and (ii) planning with a rolling horizon. Under the rolling horizon (or sequential) strategy the planning model is repeatedly solved, usually at the end of every time period, as new information becomes available and is used to update the model parameters. The costs associated with a rolling horizon strategy are hard to compute a priori because the solution of the model in any intermediate time period depends on the actual demands of the previous periods.In this paper we derive two a priori upper bounds on the costs for a class of production planning problems under the rolling horizon strategy. These upper bounds are derived by establishing correspondences between the rolling horizon problems and related deterministic programs. One of the upper bounds is obtained through Lagrangian relaxation of the service level constraint. We propose refinements to the non-Lagrangian bounds and present limited computational results. Extensions of the main results to the multiple item problems are also discussed. The results of this paper are intended to support production managers in estimating the production costs and value of demand information under a rolling horizon strategy.     

Optimal policy for a dynamic,non-stationary,stochastic inventory problem with capacity commitment

This paper studies a single-product, dynamic, non-stationary, stochastic inventory problem with capacity commitment, in which a buyer purchases a fixed capacity from a supplier at the beginning of a planning horizon and the buyer’s total cumulative order quantity over the planning horizon is constrained with the capacity. The objective of the buyer is to choose the capacity at the beginning of the planning horizon and the order quantity in each period to minimize the expected total cost over the planning horizon. We characterize the structure of the minimum sum of the expected ordering, storage and shortage costs in a period and thereafter and the optimal ordering policy for a given capacity. Based on the structure, we identify conditions under which a myopic ordering policy is optimal and derive an equation for the optimal capacity commitment. We then use the optimal capacity and the myopic ordering policy to evaluate the effect of the various parameters on the minimum expected total cost over the planning horizon.     

Coordination mechanism for capacity reservation by considering production time,production rate and order quantity

In this paper we study the coordination of a dyadic supply chain producing a high-tech product by contracts. The product has a short life cycle and the buyer faces stochastic demands during the selling period. We consider the production time, which causes the inventory costs on supplier’s side. As the supplier builds production capacity in advance, the production rate is limited to the capacity created during the production time. In addition, we take into account the inventory cost and operational cost for the buyer. We examine the model under both full information and partial information updating situations, and propose a coordinating contract for each case. Our analysis includes the study of members’ decisions under both forced and voluntary compliance regimes. Numerical results are presented to provide more insights into the models developed and the mechanisms proposed.     

Operational aircraft maintenance routing problem with remaining time consideration

The aircraft maintenance routing problem is one of the most studied problems in the airline industry. Most of the studies focus on finding a unique rotation that will be repeated by each aircraft in the fleet with a certain lag. In practice, using a single rotation for the entire fleet is not applicable due to stochasticity and operational considerations in the airline industry. In this study, our aim is to develop a fast responsive methodology which provides maintenance feasible routes for each aircraft in the fleet over a weekly planning horizon with the objective of maximizing utilization of the total remaining flying time of fleet. For this purpose, we formulate an integer linear programming (ILP) model by modifying the connection network representation. The proposed model is solved by using branch-and-bound under different priority settings for variables to branch on. A heuristic method based on compressed annealing is applied to the same problem and a comparison of exact and heuristic methods are provided. The model and the heuristic method are extended to incorporate maintenance capacity constraints. Additionally, a rolling horizon based procedure is proposed to update the existing routes when some of the maintenance decisions are already fixed.     

Buyer-supplier currency exchange rate flexibility contracts in global supply chains

This paper analyzes a decentralized global supply chain under a newsvendor setting, where a supplier delivers a certain quantity of a single product to a buyer in accordance with the terms of a mutually agreed upon contract. This contract is signed prior to the delivery of the product and subsequent payment, thus, exposing the supply chain to the risk of currency exchange rate fluctuations. We propose two types of currency exchange rate flexibility contracts to explore the characteristics of exchange rate risk mitigation policies for the buyer and the supplier. Furthermore, we investigate the effects of the contract structures on the optimal order quantity, as well as the expected profits of both supply chain members. Our results show that the optimal order quantity of the buyer decreases when the wholesale price is uncertain due to exchange rate volatility. Also, both our proposed contracts tend to improve the expected profits of both the buyer and the supplier, when the payment is made in the supplier’s currency, indicating the desirability of adopting such contractual agreements from the perspective of both parties. On the other hand, when the payment is made in the buyer’s currency, our suggested contracts do not yield such win-win scenarios. Finally, we examine the effectiveness of availing the services of a local vendor, which is capable of satisfying any demand in excess of the quantity ordered from the foreign source with short notice, in order to mitigate the risks associated with an overseas order.     

A Heuristic for a Resource-capacitated Multi-stage Lot-sizing Problem with Lead Times

In this paper we propose a heuristic for the resource-capacitated multi-stage lot-sizing problem with general product structures, set-up costs and resource usage, work-in-process inventory costs and lead times. To facilitate the functioning of the heuristic, we use the formulation of the problem based on Echelon Stock in a rolling horizon scheme. The heuristic first obtains a reasonable solution to the corresponding uncapacitated problem and then tries to attain capacity feasibility by shifting production backwards in time. The concept of echelon stock makes the task of checking the inventory feasibility of proposed shifts easier than would be the case with conventional installation stock. The heuristic is first tested computationally for problems with a five-component product structure over a 12 period planning horizon for which optimal solutions were available and for which optimality precision guarantees were also obtained via Lagrangian Relaxation. The heuristic's performance is also explored with two different 40-component product structures, with high and low set-up costs, and is compared with the Lagrangian precision guarantees.     

A deterministic,multi-item inventory model with supplier selection and imperfect quality

This paper considers the scenario of supply chain with multiple products and multiple suppliers, all of which have limited capacity. We assume that received items from suppliers are not of perfect quality. Items of imperfect quality, not necessarily defective, could be used in another inventory situation. Imperfect items are sold as a single batch, prior to receiving the next shipment, at a discounted price. The demand over a finite planning horizon is known, and an optimal procurement strategy for this multi-period horizon is to be determined. Each of products can be sourced from a set of approved suppliers, a supplier-dependent transaction cost applies for each period in which an order is placed on a supplier. A product-dependent holding cost per period applies for each product in the inventory that is carried across a period in the planning horizon. Also a maximum storage space for the buyer in each period is considered. The decision maker, the buyer, needs to decide what products to order, in what quantities, with which suppliers, and in which periods. Finally, a genetic algorithm (GA) is used to solve the model.     

Endogenous information acquisition in supply chain management

In this paper, we analyze an endogenous determination of efforts put into information acquisition and its impact on supply chain management. More specifically, we consider a supplier who sells a product to a buyer during a single selling season. Prior to placing an order with the supplier, the buyer has an option to acquire additional information about the demand by hiring experts (who are capable of providing forecasts). Because a commission fee must be paid to each hired expert, there exists a tradeoff between the cost and the value of the information, and the buyer needs to determine how much information to acquire. We derive the optimal information-acquisition level in an integrated setting and compare it with that determined in a decentralized setting. We also analyze several types of supply contracts to examine if they can coordinate the supply chain and allow an arbitrary division of system profit between the supplier and the buyer.     

Furniture supply chain tactical planning optimization using a time decomposition approach

We study the supply chain tactical planning problem of an integrated furniture company located in the Province of Québec, Canada. The paper presents a mathematical model for tactical planning of a subset of the supply chain. The decisions concern procurement, inventory, outsourcing and demand allocation policies. The goal is to define manufacturing and logistics policies that will allow the furniture company to have a competitive level of service at minimum cost. We consider planning horizon of 1 year and the time periods are based on weeks. We assume that customer’s demand is known and dynamic over the planning horizon. Supply chain planning is formulated as a large mixed integer programming model. We developed a heuristic using a time decomposition approach in order to obtain good solutions within reasonable time limit for large size problems. Computational results of the heuristic are reported. We also present the quantitative and qualitative results of the application of the mathematical model to a real industrial case.     

Buyer behavior adaptation based on a fuzzy logic controller and prediction techniques

The current form of Web provides numerous product resources available to users. Users can rely on intelligent agents for purchase actions. These actions are taken in specific environments such as Electronic Markets (EMs). In this paper, we study the interaction process between buyers and sellers and focus on the buyer side. Each buyer has the opportunity to interact with a number of sellers trying to buy the most appropriate products. This interaction can be modeled as a finite horizon Bargaining Game (BG). In this game, players have opposite goals concerning the product price. We adopt a number of techniques in the buyer side trying to give the appropriate level of efficiency in the buyer decision process. The buyer uses a prediction mechanism in combination with the use of Fuzzy Logic (FL) theory in order to be able to predict the upcoming seller proposal and, thus, understand the seller pricing policy. Based on this, he/she can adapt his/her behavior when trying to purchase products. The buyer adaptation mechanism produces the belief that the buyer has about the seller pricing policy and a parameter that indicates his/her own pricing policy which yields the buyer offers in the upcoming rounds. Moreover, the buyer is based on FL system that derives the appropriate actions at every round of the BG. Our results show that the combination of Fuzzy Logic (FL) with the above-mentioned techniques provides an efficient decision mechanism in the buyer side that in specific scenarios outperforms an optimal stopping model.     

The dynamic vehicle rescheduling problem

The pre-planned schedules of a transportation company are often disrupted by unforeseen events. As a result of a disruption, a new schedule has to be produced as soon as possible. This process is called the vehicle rescheduling problem, which aims to solve a single disruption and restore the order of transportation. However, there are multiple disruptions happening over a “planning unit” (usually a day), and all of them have to be addressed to achieve a final feasible schedule. From an operations management point of view the quality of the final solution has to be measured by the combined quality of every change over the horizon of the “planning unit”, not by evaluating the solution of each disruption as a separate problem. The problem of finding an optimal solution where all disruptions of a “planning unit” are addressed will be introduced as the dynamic vehicle rescheduling problem (DVRSP). The disruptions of the DVRSP arrive in an online manner, but giving an optimal final schedule for the “planning unit” would mean knowing all information in advance. This is not possible in a real-life scenario, which means that heuristic solution methods have to be considered. In this paper, we present a recursive and a local search algorithm to solve the DVRSP. In order to measure the quality of the solutions given by the heuristics, we introduce the so-called quasi-static DVRSP, a theoretical problem where all the disruptions are known in advance. We give two mathematical models for this quasi-static problem, and use their optimal solutions to evaluate the quality of our heuristic results. The heuristic methods for the dynamic problem are tested on different random instances.     

Joint replacement in an operational planning phase

We consider the problem of combining replacements of multiple components in an operational planning phase. Within an infinite or finite time horizon, decisions concerning replacement of components are made at discrete time epochs. The optimal solution of this problem is limited to only a small number of components. We present a heuristic rolling horizon approach that decomposes the problem; at each decision epoch an initial plan is made that addresses components separately, and subsequently a deviation from this plan is allowed to enable joint replacement. This approach provides insight into why certain actions are taken. The time needed to determine an action at a certain epoch is only quadratic in the number of components. After dealing with harmonisation and horizon effects, our approach yields average costs less than 1% above the minimum value.     

An MIP-based interval heuristic for the capacitated multi-level lot-sizing problem with setup times

This paper considers the capacitated multi-level lot-sizing problem with setup times, a class of difficult problems often faced in practical production planning settings. In the literature, relax-and-fix is a technique commonly applied to solve this problem due to the fact that setup decisions in later periods of the planning horizon are sensitive to setup decisions in the early periods but not vice versa. However, the weakness of this method is that setup decisions are optimized only on a small subset of periods in each iteration, and setup decisions fixed in early iterations might adversely affect setup decisions in later periods. In order to avoid these weaknesses, this paper proposes an extended relax-and-fix based heuristic that systematically uses domain knowledge derived from several strategies of relax-and-fix and a linear programming relaxation technique. Computational results show that the proposed heuristic is superior to other well-known approaches on solution qualities, in particular on hard test instances.     

Bond portfolio management with repo contracts: the Italian case

In this paper we present a model for management of bond portfolio including financing and investment repo contracts. Different specifications are suggested in order to reduce the problem to a linear programming problem and to consider a self-financing portfolio. The models are tested on historical data assuming a technical time scale equal to the minimum length of the contracts in the portfolio. We also compared different operative strategies on a time horizon of one month. This revised version was published online in June 2006 with corrections to the Cover Date.     

A methodology to solve large-scale cooperative transportation planning problems

In this paper, we suggest a methodology to solve a cooperative transportation planning problem and to assess its performance. The problem is motivated by a real-world scenario found in the German food industry. Several manufacturers with same customers but complementary food products share their vehicle fleets to deliver their customers. After an appropriate decomposition of the entire problem into sub problems, we obtain a set of rich vehicle routing problems (VRPs) with time windows for the delivery of the orders, capacity constraints, maximum operating times for the vehicles, and outsourcing options. Each of the resulting sub problems is solved by a greedy heuristic that takes the distance of the locations of customers and the time window constraints into account. The greedy heuristic is improved by an appropriate Ant Colony System (ACS). The suggested heuristics to solve the problem are assessed within a dynamic and stochastic environment in a rolling horizon setting using discrete event simulation. We describe the used simulation infrastructure. The results of extensive simulation experiments based on randomly generated problem instances and scenarios are provided and discussed. We show that the cooperative setting outperforms the non-cooperative one.     

The valuation of options on capacity with cost and demand uncertainty

Options contracts can provide trading partners with enhanced flexibility to respond to uncertain market conditions and allow for superior capacity planning thanks to early information on future demand. We develop an analytical framework to value options on capacity for production of non-storable goods or dated services. The market consists of a sequence of contract and spot market. Reservations are made during the contract market session in period 0, where the buyer’s future demand, the seller’s future marginal costs as well as the future spot price are uncertain, the latter being impacted neither by the buyer nor the seller. During the spot market session in period 1, the buyer may execute his options or satisfy his entire or additional demand from a competing seller in the spot market. The seller allocates reserved capacity now being called and attempts to sell remaining capacity into the spot market. Analytical expressions for the buyer’s optimal reservation quantity and the seller’s tariff are derived, making explicit the risk-sharing benefits of options contracts. The combination of an options contract and a spot market is demonstrated to be Pareto improving as compared to alternative market schemes. An analysis of the determinants of the efficiency gain characterizes industries particularly suitable to the options approach.     

Pareto-optimal insurance contracts with premium budget and minimum charge constraints

In view of the fact that minimum charge and premium budget constraints are natural economic considerations in any risk-transfer between the insurance buyer and seller, this paper revisits the optimal insurance contract design problem in terms of Pareto optimality with imposing these practical constraints. Pareto optimal insurance contracts, with indemnity schedule and premium payment, are solved in the cases when the risk preferences of the buyer and seller are given by Value-at-Risk or Tail Value-at-Risk. The effect of our constraints and the relative bargaining powers of the buyer and seller on the Pareto optimal insurance contracts are highlighted. Numerical experiments are employed to further examine these effects for some given risk preferences.     

Robust Management and Pricing of Liquefied Natural Gas Contracts with Cancelation Options

Liquefied Natural Gas contracts offer cancelation options that make their pricing difficult, especially if many gas storages need to be taken into account. We develop a valuation mechanism from the buyer’s perspective, a large gas company whose main interest in these contracts is to provide to clients a reliable supply of gas. The approach combines valuation with hedging, taking into account that price-risk is driven by international markets, while volume-risk depends on local weather and is stage-wise dependent. The methodology is based on setting risk-averse stochastic mixed 0-1 programs, for different contract configurations. These difficult problems are solved with light computational effort, thanks to a robust rolling-horizon approach. The resulting pricing mechanism not only shows how a specific set of contracts will impact the company business, but also provides the manager with alternative contract configurations to counter-propose to the contract seller.     

Forecast frequency in rolling horizon hedging heuristics for capacity expansion

This paper describes a simulation study of the effect of forecast revisions and hedges against demand uncertainty in a rolling horizon heuristic for capacity expansion. The model is based on data collected in the utilities division of a large chemical manufacturing plant. A seasonal integrated moving average model for the demand is used to generate forecasts, while capacity additions are determined by applying a simple timing rule to various hedges around the forecast. The simulation results indicate that hedging forecasts by their prediction limits rather than a fixed buffer significantly reduces undercapacity at the expense of a small increase in capacity cost. The prediction limit hedge is more robust to delays in reforecasting.     

A rolling horizon approach for disruption management of railway rolling stock

This paper deals with real-time disruption management of rolling stock in passenger railway transportation. We describe a generic framework for dealing with disruptions of railway rolling stock schedules. The framework is presented as an online combinatorial decision problem, where the uncertainty of a disruption is modeled by a sequence of information updates. To decompose the problem and to reduce the computation time, we propose a rolling horizon approach: rolling stock decisions are only considered if they are within a certain time horizon from the time of rescheduling. The schedules are then revised as time progresses and new information becomes available. We extend an existing model for rolling stock scheduling to the specific requirements of the real-time situation, and we apply it in the rolling horizon framework. We perform computational tests on instances constructed from real-life cases of Netherlands Railways (NS), the main operator of passenger trains in the Netherlands. We explore the consequences of different settings of the approach for the trade-off between solution quality and computation time.