Integrating noncyclical preventive maintenance scheduling and production planning for a single machine

This paper deals with the problem of integrating noncyclical preventive maintenance and tactical production planning for a single machine. We are given a set of products that must be produced in lots during a specified finite planning horizon. The maintenance policy suggests possible preventive replacements at the beginning of each production planning period, and minimal repair at machine failure. The proposed model determines simultaneously the optimal production plan and the instants of preventive maintenance actions. The objective is to minimize the sum of preventive and corrective maintenance costs, setup costs, holding costs, backorder costs and production costs, while satisfying the demand for all products over the entire horizon. The problem is solved by comparing the results of several multi-product capacitated lot-sizing problems. The value of the integration and that of using noncyclical preventive maintenance when the demand varies from one period to another are illustrated through a numerical example and validated by a design of experiment. The later has shown that the integration of maintenance and production planning can reduce the total maintenance and production cost and the removal of periodicity constraint is directly affected by the demand fluctuation and can also reduce the total maintenance and production cost.     

Dynamic lot sizing problem with continuous-time Markovian production cost

This paper develops a polynomial algorithm for obtaining dynamic economic lot sizes in a single product multiperiod production system with the objective of minimizing total production and inventory costs over T periods. It is assumed that production costs are linear, inventory costs are concave, setup costs are zero and backlogging is not permitted in all periods. Moreover, the unit production cost is a stochastic variable, which is evolved according to a continuous-time Markov process over the planning horizon. The model is formulated as a stochastic dynamic programming (DP) optimization with the state variable being unit production cost. Then, it is solved using the backward dynamic programming approach. To justify the application of the proposed model, two practical cases are presented.     

A master production scheduling procedure for stochastic demand and rolling planning horizons

The problem of interest is a one product, uncapacitated master production schedule (MPS) in which decisions are made under rolling planning horizons. Demand is stochastic and time varying, and effectiveness is measured by inventory holding, production setup, and backorder costs.Typically, in both the research literature and the business practice the stochastic nature of the problem is modeled in an ad hoc fashion. The stochastic MPS problem is usually solved by adding safety stock to production quantities obtained from a deterministic lot-sizing algorithm. Here, the stochastic nature of the problem is explicitly considered, as an optimal algorithm for solving the static probabilistic dynamic lot-sizing problem is adapted to rolling planning horizons. The resulting algorithm is found to dominate traditional approaches over a wide variety of experimental factors, reducing total costs by an average of 16% over traditional methods.     

Pricing in revenue management for multiple firms competing for customers

We consider the pricing strategies of multiple firms providing the same service in competition for a common pool of customers in a revenue management context. The firms have finite capacity and the demand at each firm depends on the selling prices charged by all firms, each of which satisfies demand up to a given capacity limit. We use game theory to analyze the systems when firms face either a deterministic demand or a general stochastic demand. The existence and uniqueness conditions of a Nash equilibrium are derived, and we calculate the explicit Nash equilibrium point when the demand at each firm is a linear function of price. We also conduct sensitivity analysis of the equilibrium prices with respect to cost and capacity parameters.     

A memetic algorithm for a multistage capacitated lot-sizing problem

We present a heuristic approach to solve a complex problem in production planning, the multistage lot-sizing problem with capacity constraints. It consists of determining the quantity to be produced in different periods in a planning horizon, such that an initially given demand forecast can be attained. We consider setup costs and setup times. Due the complexity to solve this problem, we developed methods based on evolutionary metaheuristics, more specifically a memetic algorithm. The proposed heuristics are evaluated using randomly generated instances and well-known examples in the literature.     

Myopic optimal policy for a multi-period, two-delivery-lead-times, stochastic inventory problem with minimum cumulative commitment and capacity

This paper studies a single-product, multi-period, stochastic inventory problem that imposes the lower and upper bounds on the cumulative order quantity during a planning horizon and allows two delivery lead times. This model includes three features. The first one is that a buyer purchases a fixed capacity from a supplier at the beginning of a planning horizon and the buyer’s total cumulative order quantity during the planning horizon is constrained with the capacity. The second one is that the buyer agrees to purchase the product at least a certain percentage of the purchased capacity during the planning horizon. The third one is that the supplier allows the buyer to order the product with two-delivery-lead-times. We identify conditions under which a myopic ordering policy is optimal. We also develop an algorithm to calculate the optimal capacity when the minimum cumulative order quantity commitment is a certain percentage of the capacity. We then use the algorithm to evaluate the effect of the various parameters on the buyer’s minimum expected total cost during the planning horizon. Our computation shows that the buyer would benefit from the commitments and two-delivery-lead-times.     

Investment under Demand Uncertainty,Ex-Ante Pricing,and Oligopoly

This paper considers the capacity choice of duopolists who set price ex-ante under demand uncertainty with risk-neutrality. The duopolists compete for market shares on the basis of availability of supply, rather than by price competition. Collusive pricing coexists with Cournot–Nash capacity choice. A formal model is presented, where the market share of each firm may deviate from the certainty share due to rationing. With shares reflecting different costs, capacity utilisation for the lower cost firm is expected to be substantially lower. The implications for the price-cost margin and capacity formation are also explored.     

Diversification of cable television firms into broadband products

This research provides a new perspective to investigate the broadband diffusion in eight states of the U.S. by studying the two-stage entry decisions, namely, upgrading and subsequent product decisions, by the cable television system operators, one of the early dominant players in the broadband market, and examines the role of competition, market characteristics and firm heterogeneity in the cable company's decisions in a dynamic setting. Comparing the empirical results of the decision models of both stages can give new insights into the dynamics of broadband diffusion. The empirical results show that the subsequent product decision is affected more by the demand determinants, while the upgrading decision is affected more by the cost determinants. The results also indicate that policies which aim to reduce the entry cost such as a low city fee can largely encourage firms to upgrade the network, while subsequent policies that help boost the demand can help firms diversify into new digital services early. The effectiveness of competition policy in the broadband diffusion is confirmed in both stages. Strategic responses by cable firms to the presence of RBOCs are more noticeable in the second-staged product decision than in the first-staged upgrading decision.     

Multi-item dynamic lot-sizing with delayed transportation policy

We optimize ordering and inbound shipment decisions for a manufacturer that sources multiple items from a single supplier. The objective is to satisfy the requirements in the production plan with minimum transportation and inventory holding costs over a multi-period planning horizon. Transportation costs are charged to the manufacturer on a per truck shipment basis. We investigate the option of delaying a less-than-full truckload shipment to the next period, by utilizing the safety stocks as needed. We analyze the impact of delaying shipments on both cost and service levels in stochastic environments through experiments with data from a bus manufacturer. The results indicate that the proposed policy reduces both holding and transportation costs without creating much stock-out risk.     

A network approach to modeling the multi-echelon spare-part inventory system with backorders and interval-valued demand

A multi-echelon inventory system implies the existence of a hierarchy of stocking locations, and the dependence and interaction between them. We consider a multi-echelon, spare-part inventory management problem with outsourcing and backordering. The problem is characterized by deterministic repair time/cost, and supply and demand that lie within prescribed intervals and that vary over time. The objective is to minimize the total inventory and transportation costs. We develop a network model for problem analysis and present a network flow algorithm for solving the problem. We prove that the Wagner-Whitin property, known for the lot-sizing problem, can be extended to the spare-part inventory management problem under study.     

DYNAMIC PRICE DISCRIMINATION WITH ASYMMETRIC FIRMS*

This paper considers variants of a dynamic duopoly model where one firm has a stronger market position than its competitor. Consumers' past purchases may reveal their different valuations for the two firms' products. Price discrimination based on purchase histories tends to benefit consumers if it does not cause the weaker firm to exit; otherwise it can harm consumers. The effect of price discrimination also depends on firms' cost differences, market competitiveness, and consumers' time horizon. The stronger firm may price below cost in the presence of consumer switching costs, with the purpose and effect of eliminating competition.     

The effects of emission trading on production and inventories in the Arrow–Karlin model

The paper deals with the effect of introduction of tradable permits on the production–inventory strategy of a firm. It is assumed that the firm will minimize its costs. The cost function consists of linear holding and convex production costs. After introducing emission trading, the cost function will contain a linear emission procurement/selling cost. We will compare the optimal production–inventory strategy before tradable permits and thereafter. The mathematical investigation is based on the well-known dynamic Arrow–Karlin model.     

Optimal inventory and pricing policies for remanufacturable leased products

In this paper we consider a company which leases new products and also sells remanufactured versions of the new product that become available at the end of their lease periods. When the amount of end-of-lease items in stock is not sufficient to meet the demand for remanufactured products, the firm may purchase additional cores from a third-party supplier. We develop a dynamic programming formulation for determining the optimal price of remanufactured products, and optimal payment structure for the leased products. Our objective is to maximize the discounted system-wide profit over a finite horizon. The profit function consists of revenues that are obtained from remanufactured product sales and leasing, remanufacturing and manufacturing costs, inventory holding and shortage costs. We consider a consumer choice based demand model for mapping a potential customer into one of the product segments (a remanufactured product customer or a customer for a leased product with a particular lease period) for a given price/lease payment vector. We explore several properties of the discounted profit function and provide insight on the behavior of pricing and inventory policies. We also investigate the effect of key product characteristics such as deterioration in age, cost of shortage in remanufacturable product inventory, and key market characteristics such as relative willingness-to-pay for buying a remanufactured product and relative willingness-to-pay for leasing a new product on optimal pricing policies through a computational study.     

A heuristic algorithm for a multi-product dynamic lot-sizing and shipping problem

This paper analyzes a dynamic lot-sizing problem, in which the order size of multiple products and a single container type are simultaneously considered. In the problem, each order (product) placed in a period is immediately shipped by some containers in the period and the total freight cost is proportional to the number of containers used. It is also assumed that backlogging is not allowed. The objective of this study is to simultaneously determine the lot-sizes and the transportation policy that minimizes the total costs, which consist of production cost, inventory holding cost, and freight cost. Because this problem is NP-hard, a heuristic algorithm with an adjustment mechanism is proposed based on the optimal solution properties. The computational results from a set of simulation experiment are also presented.     

THE ROLE OF SUNK COSTS IN THE DECISION TO INVEST IN R&D*

We present a dynamic empirical model of a firm's R&D decisions that is consistent with the existence of sunk R&D costs, taking into account that these costs may differ between small and large firms, and among different technological regimes. We estimate a multivariate dynamic discrete choice model using firm‐level data of Spanish manufacturing for 1990–2000. Conditional on firm heterogeneity and serially correlated unobservable factors, we find that R&D history matters. This true state dependence allows inferring the existence of sunk R&D costs associated with performing R&D. Sunk R&D costs are found to be higher for large, high‐tech firms.     

Entry,imperfect competition,and futures market for the input

We analyze firms' entry, production and hedging decisions under imperfect competition. We consider an oligopoly industry producing a homogeneous output in which risk-averse firms face an entry cost upon entering the industry, and then compete in Cournot with one another. Each firm faces uncertainty in the input cost when making production decision, and has access to the futures market to hedge the random cost. We provide two sets of results. First, under general assumptions about risk preferences, demand, and uncertainty, we characterize the unique equilibrium. In contrast to previous results in the literature (without entry), both production and output price depend on uncertainty and risk aversion. Specifically, when entry is endogenized and the futures price is not actuarially fair, access to the futures market does not lead to separation. Second, to study the effect of access to the futures market on entry and production, we restrict attention to constant absolute risk aversion (CARA) preferences, a linear demand, and a normal distribution for the spot price. In general, the effect of access to the futures market on the number of firms and production is ambiguous.     

Channel coordination with the newsvendor model using asymmetric information

In this paper, after surveying short-term two-echelon supply channel coordination methods, we present an extended version of the newsvendor model in which the supplier has to fulfil all demand of the customer, even if this calls for an additional setup of production. Given uncertain demand forecast, the solution is an optimal production quantity that minimises the expected total cost including setup, inventory holding and obsolete inventory costs. Then, the model is studied in a decentralised setting where the customer has private information about the demand forecast, while the supplier knows the various cost factors. We suggest such a coordination protocol and payment scheme that provides both partners the right incentive for minimising the total cost: the customer is interested in sharing her unbiased demand forecast and uncertainty, while the supplier's rational decision concurs with the overall optimum. Hence, local decisions based on asymmetric information coordinate the channel in the global sense. The results are also demonstrated by taking some real-life test cases from an industrial study that motivated our work.     

Capacity flexibility allocation in an outsourced supply chain with reservation

We consider a contract manufacturer that serves a limited number of outsourcers (customers) on a single capacitated production line. The outsourcers have different levels of demand uncertainty and the contract manufacturer faces the question how to allocate the contractual capacity flexibility in an optimal way. The contractual capacity flexibility is a contract parameter that sets the amount of demand the contract manufacturer is obliged to accept from the outsourcers. We develop a hierarchical model that consists of two decision levels. At the tactical level, the contract manufacturer allocates the capacity flexibility to the different outsourcers by maximizing the expected profit. Offering more flexibility to the more uncertain outsourcer generates higher expected revenue, but also increases the expected penalty costs. The allocated capacity flexibilities (determined at the tactical level) are input parameters to the lower decision level, where the operational planning decisions are made and actual demands are observed. We perform a numerical study by solving the two-level hierarchical planning problem iteratively. We first solve the higher level problem, which has been formulated as an integer program, and then perform a simulation study, where we solve a mathematical programming model in a rolling horizon setting to measure the operational performance of the system. The simulation results reveal that when the acceptance decision is made (given the allocated capacity flexibility decision), priority is given to the less uncertain outsourcer, whereas when the orders are placed, priority is given to the most uncertain outsourcer. Our insights are helpful for contract manufacturers when having contract negotiations with the outsourcers. Moreover, we show that hierarchical integration and anticipation are required, especially for cases with high penalty cost and tight capacities.     

Costly interviews

In this paper, we show how the interaction between costly screening and competition in decentralized markets may prevent efficient matching. We examine this phenomenon in a simple dynamic model of a professional labor market, where firms can pay a cost to interview applicants who have private information about their own ability. Inefficiencies arise when a firm decides not to interview potentially able candidates since it infers that sufficiently good candidates will be hired by more productive firms. This effect is robust to changes in the information structure of the market, but it can be mitigated by subsidizing screening costs.     

Strategic segmentation of a market

When competing firms target information towards specific consumers through direct marketing activities, complete segmentation of markets can result. We analyze a two-stage duopoly where, prior to price competition, each firm targets information to specific consumers and only consumers informed by a firm can buy from it. This has the effect of endogenously determining market segments in a model of ‘sales'. In equilibrium, pure local monopoly emerges; firms target and sell to mutually exclusive market segments. When the cost of marketing approaches zero, market shares reflect relative production efficiency (equal shares when firms are symmetric); this may not be the case when marketing cost is high.