Modelling load retrievals in puzzle-based storage systems

Puzzle-based storage systems are a new type of automated storage systems that allow storage of unit loads (e.g. cars, pallets, boxes) in a rack on a very small footprint with individual accessibility of all loads. They resemble the famous 15-sliding tile puzzle. Current models for such systems study retrieving loads one at a time. However, much time can be saved by considering multiple retrieval loads simultaneously. We develop an optimal method to do this for two loads and heuristics for three or more loads. Optimal retrieval paths are constructed for multiple load retrieval, which consists of moving multiple loads first to an intermediary ‘joining location’.We find that, compared to individual retrieval, optimal dual load retrieval saves on average 17% move time, and savings from the heuristic is almost the same. For three loads, savings are 23% on average. A limitation of our method is that it is valid only for systems with a very high space utilisation, i.e. only one empty location is available. Future research should investigate retrieving multiple loads for systems with multiple empty slots

Optimal competitive capacity strategies:Evidence from the container shipping market

For nearly two decades, ocean carriers have been locked in an arms race for capacity, which has led to huge losses for many and even bankruptcy for some. We investigate the nature of this investment race by studying a long-term capacity investment problem in a duopoly under demand uncertainty. In our model, two firms make sequential capacity decisions, responding to each other’s current and future capacity. We consider two types of strategies which differ in terms of how a firm considers the opponent’s future capacity in its own strategy: a proactive strategy where the firm assumes that the opponent will respond using a certain strategy, or a reactive strategy where the firm assumes that the opponent’s future capacity remains unchanged. In the proactive case, we allow the firm to have different assumptions on the opponent’s strategy, representing different amounts of information the firm has on the opponent. For each type of strategies, we derive the firm’s optimal decisions on both the timing and size of capacity adjustments, specified by an array of intervals for the optimal capacity in a given capacity space in each period. Using detailed data from the container shipping market (2000–2015), we illustrate how to plan competitive capacity investments, following our model. By comparing the optimal decisions specified by our model with the reality, we show that the realized capacity decisions of the leading carriers, which were often questioned as irrational, are close to optimal, assuming these carriers follow proactive strategies. By revealing the underlying structures of different strategies, that is, the stayput intervals, we show how a specific strategy brings value to firms under competition. Based on our results, we provide practical guidelines to carriers and firms which operate in a similar competitive market for implementing an effective competitive capacity strategy

When to Allocate Capacity for Upward Line Extensions Under Competition and Consumer Taste Uncertainty?

An upward line extension is a new improved product within an existing product category for the high end of the market. Many firms pursue line-extension strategies, but such strategies carry risks due to uncertain consumer taste, the internal competition between products, and the external competition between firms. Bad timing is often mentioned as one of the main reasons for new product failures. Using game-theoretic models, we study when a firm should allocate production capacity for an upward line extension under competition and consumer taste uncertainty. The firm can either act early, at which point consumer taste is still uncertain, to benefit from a first-mover advantage or wait until consumer taste is realized. We develop two indexes to evaluate consumer taste risk and to evaluate the firm's competitive advantage, respectively. Consumer taste risk can be measured by the correlation between the average consumer taste and the density of consumer taste with a strong correlation meaning a large risk exposure, indicating a more likely hit-or-miss result for the new product. The firm's competitive advantage is based on both firms' expected marginal revenues of capacity allocation, considering the internal competition (represented by the firm's profitability for the line extension) and the external competition (represented by the firm's cost advantage over its competitor). We show how a competitive advantage will be amplified in the presence of consumer taste uncertainty, and characterize the firm's decision policy by deriving a threshold for the risk index against the competitive advantage index. When the threshold is exceeded, it implies that the firm's competitive advantage is not large enough and so it should postpone allocating capacity. Otherwise, it should act early. We apply our results to two industry examples and provide practical guidelines

Capacity Deployment for Next-Generation Products in a Competitive Market

An upward line extension is a new improved product in the same product category for the high end of the market. Most firms are pursuing line-extension strategies, however, such strategies carry risk due to uncertain consumer taste, the internal competition between products, and the external competition between firms. “Bad timing” is often mentioned as one of the main reasons for new product failures. Using game-theoretic models, we study when a firm should deploy production capacity for an upward line extension in a competitive market. A firm can either deploy capacity early when consumer taste is still uncertain to benefit from a first-mover advantage or wait until consumer taste is realized. We develop two indexes to evaluate consumer taste risk and a firm's competitive advantage, respectively. Consumer taste risk can be measured by the correlation between the average consumer taste and the density of consumer taste: a strong correlation implies a large exposure to risk, indicating more likely a hit-or-miss result for the new product. A firm's competitive advantage is evaluated based on both firms' expected marginal revenues of capacity expansion, each of which considers a firm's capacity cost advantage over the competitor and the competitor's gain from offering the same quality upgrade. We show how a firm's large competitive advantage will be magnified in the evaluation under the impact of consumer taste uncertainty, and characterize the decision policy for a firm as a threshold for the consumer taste risk index with respect to the competitive advantage index. Exceeding this threshold, a firm's competitive advantage is insufficiently large so that it should postpone capacity deployment. Otherwise, it should act early. We apply our results to two industry examples and provide practical guidelines