Knowledge that Transforms

We model a situation where a firm wishes to balance workload requirements by creating a portfolio of recurrent insourcing and outsourcing contracts. We use harmonic analysis to decompose an input workload profile into a portfolio of insourcing and outsourcing contracts using rectangular‐wave basis functions to better achieve some desired constant workload level. However, this initial selection of contracts may result in impractical options. Therefore, we also develop mathematical programs using principles from goal programming and integer programming to refine the portfolio of contracts to more accurately reflect a realistic environment by placing constraints on the available contracts and explicitly considering operational costs. We consider several modeling extensions including the ability to hold limited amounts of inventory and the use of one‐shot contracts to supplement our portfolio of recurrent contracts.

The computer software industry is an extreme example of rapid new product introduction. However, many consumers are sophisticated enough to anticipate the availability of upgrades in the future. This creates the possibility that consumers might either postpone purchase or buy early on and never upgrade. In response, many software producers offer special upgrade pricing to old customers in order to mitigate the effects of strategic consumer behavior. We analyze the optimality of upgrade pricing by characterizing the relationship between magnitude of product improvement and the equilibrium pricing structure, particularly in the context of user upgrade costs. This upgrade cost (such as the cost of upgrading complementary hardware or drivers) is incurred by the user when she buys the new version but is not captured by the upgrade price for the software. Our approach is to formulate a game theoretic model where consumers can look ahead and anticipate prices and product qualities while the firm can offer special upgrade pricing. We classify upgrades as minor, moderate or large based on the primitive parameters. We find that at sufficiently large user costs, upgrade pricing is an effective tool for minor and large upgrades but not moderate upgrades. Thus, upgrade pricing is suboptimal for the firm for a middle range of product improvement. User upgrade costs have both direct and indirect effects on the pricing decision. The indirect effect arises because the upgrade cost is a critical factor in determining whether all old consumers would upgrade to a new product or not, and this further alters the product improvement threshold at which special upgrade pricing becomes optimal. Finally, we also analyze the impact of upgrade pricing on the total coverage of the market.

In this paper, we address the problem of a magazine publishing firm facing stochastic demand over multiple periods. We model the dynamics of customer subscription and retention/attrition. We identify the key decision variables to enhance magazine profitability: production quantity, subscription price, and newsstand price. First, we provide a dynamic programming formulation of the firm's problem and then propose a single‐stage reduction that admits a classical newsvendor characterization. For both the finite and infinite horizon cases, we characterize the optimal policy of the firm where the decision variables are one, two, or all three of the aforementioned variables. Next, we consider the duopolistic setting, where firms benefit from the overflow of the competitor's unmet demand, and we provide analytic solutions in the case of uniform demand distributions. Finally, we report on computational experiments in both monopolistic and duopolistic settings and provide managerial insights.

A few weeks before the start of a major season, movie distributors arrange a private screening of the movies to be released during that season for exhibitors and, subsequently, solicit bids for these movies (from exhibitors). Since the number of such solicitations far exceeds the number of movies that can be feasibly screened at a multiplex (i.e., a theater with multiple screens), the problem of interest for an exhibitor is that of choosing a subset of movies for which to submit bids to the distributors. We consider the problem of the selection and screening of movies for a multiplex to maximize the exhibitor's cumulative revenue over a fixed planning horizon. The release times of the movies that can potentially be selected during the planning horizon are known a priori. If selected for screening, a movie must be scheduled through its obligatory period, after which its run may or may not be extended. The problem involves two primary decisions: (i) the selection of a subset of movies for screening from those that can potentially be screened during the planning horizon and (ii) the determination of the duration of screening for the selected movies. We investigate two basic and popular screening policies: preempt‐resume and non‐preempt. In the preempt‐resume policy, the screening of a movie can be preempted and resumed in its post‐obligatory period. In the non‐preempt policy, a movie is screened continuously from its release time until the time it is permanently withdrawn from the multiplex. We show that optimizing under the preempt‐resume policy is strongly NP‐hard while the problem under the non‐preempt policy is polynomially solvable. We develop efficient algorithms for the problem under both screening policies and show that the revenue obtained from the preempt‐resume policy can be significantly higher as compared with that from the non‐preempt policy. Our work provides managers of multiplexes with valuable insights into the selection and screening of movies and offers an easy‐to‐use computational tool to compare the revenues obtainable from adopting these popular policies.

Resource flexibility is an important tool for firms to better match capacity with demand so as to increase revenues and improve service levels. However, in service contexts that require dynamically deciding whether to accept incoming jobs and what resource to assign to each accepted job, harnessing the benefits of flexibility requires using effective methods for making these operational decisions. Motivated by the resource deployment decisions facing a professional service firm in the workplace training industry, we address the dynamic job acceptance and resource assignment problem for systems with general resource flexibility structure, i.e., with multiple resource types that can each perform different overlapping subsets of job types. We first show that, for systems containing specialized resources for individual job types and a versatile resource type that can perform all job types, the exact policy uses a threshold rule. With more general flexibility structures, since the associated stochastic dynamic program is intractable, we develop and test three optimization‐based approximate policies. Our extensive computational tests show that one of the methods, which we call the Bottleneck Capacity Reservation policy, is remarkably effective in generating near‐optimal solutions over a wide range of problem scenarios. We also consider a model variant that requires dynamic job acceptance decisions but permits deferring resource assignment decisions until the end of the horizon. For this model, we discuss an adaptation of our approximate policy, establish the effectiveness of this policy, and assess the value of postponing assignment decisions.

Determining appropriate inventory levels has been a subject of interest for both researchers and practitioners. Standard practice is to treat lead time demand as a random sum of random numbers and rely on established probability theory to calculate both reorder point and safety stock levels. A key assumption in these calculations, however, is that lead time and demand are not correlated. In this paper, we first explore situations where this assumption is untrue and then develop equations to determine the reorder point and the safety stock when lead time and demand are correlated. More specifically, we (1) derive formulas for the average and variance of the demand in a lead time, which can then be used to calculate the reorder point and the safety stock, (2) apply these formulas to two distributions for which there is a closed‐form solution: normal and Poisson, and (3) examine the effect of correlation on safety stock requirements under the normal distribution.

Recent advances in approaches and production technologies for the production of goods and services have made just‐in‐time (JIT) a strong alternative for use in intermittent and small batch production systems, especially when time‐based competition is the norm and a low inventory is a must. However, the conventional JIT system is designed for mass production with a stable master production schedule. This paper suggests supplementing the information provided by production kanbans with information about customer waiting lines to be used by operators to schedule production in each work‐station of intermittent and small batch production systems. This paper uses simulation to analyze the effect of four scheduling policy variables—number of kanbans, length of the withdrawal cycle, information about customer waiting lines, and priority rules on two performance measures—customer wait‐time and inventory. The results show that using information about customer waiting lines reduces customer wait‐time by about 30% while also reducing inventory by about 2%. In addition, the effect of information about customer waiting lines overshadows the effect of priority rules on customer wait‐time and inventory.

One way to coordinate workers along an assembly line that has fewer workers than work stations is to form a bucket brigade. The throughput of a bucket brigade on discrete work stations may be compromised due to blocking even if workers are sequenced from slowest to fastest. For a given work distribution on the stations we find policies that maximize the throughput of the line. When workers have very different production rates, fully cross‐training the workers and sequencing them from slowest to fastest is almost always the best policy. This policy outperforms other policies for most work distributions except for some cases in which limiting the work zones of workers produces higher throughput. In environments where the work can be adjusted across stations, we identify conditions for a line to prevent blocking.

L ife‐cycle mismatch occurs when the life cycles of parts end before the life cycles of the products in which those parts are used. Lifetime buys are one tactic for mitigating the effect of part obsolescence, where a quantity of parts is purchased for the remaining life of a product. We extend prior work that determines optimal lifetime buy quantities for one product with one obsolete part by providing an analytic solution and two simple heuristic policies for the optimal lifetime buy quantities when many parts become obsolete over a product's life cycle. We determine which of our two heuristics is most accurate for different product life cycles, which yields a metaheuristic with increased accuracy. That analysis also reveals critical perspectives in making lifetime buy decisions with nonstationary life‐cycle demand patterns.

This paper considers a general industrial setting where multiple manufacturers each produce a different product and sell it to the markets. These products are partially complementary in the sense that there is a common demand stream that requests all these products as complementary sets and there are streams of individual demands each requesting only one of the products. All demands are uncertain and may follow any general, joint distributions. Facing demand uncertainties, the manufacturers each choose a production quantity for its product with an objective to maximize its own expected profit. We formulate the problem as a non‐cooperative game to study the strategic interactions of such firms and their implications to supply chain performance. We show that such a game may have numerous equilibria. Among all the possible equilibria, however, we prove that there always exists a unique one that maximizes each and every manufacturer's profit, and we derive an explicit solution for this Pareto‐optimal equilibrium point. We further study the optimal solution for a centralized system and compare it with the decentralized solution. Managerial insights are drawn as to how system parameters and control mechanisms affect firms' decisions and performance.