We provide a comprehensive characterization of the relationship between optimal capacity and the degree of product substitution/complementarity under price/production postponement, considering different business practices (holdback versus clearance, negative price policies) and different demand models. Specifically, we consider a firm that produces two products, which can be substitutable or complementary. The demand of each product is a linear function of the prices of both products (with the relationship depending on the substitution/complementarity structure), and is subject to an additive stochastic shock. We consider two types of linear demand functions that are commonly used in the economics and operations management literature. The firm operates in a monopolistic setting and acts as a price-setter for both products. Overall the firm needs to make three sets of decisions: capacity, production quantities, and prices. While the capacity investment decision has to be made ex-ante observation of demand curves, price and/or quantity decisions can be postponed until after demand curves are observed. We consider two postponement strategies: price and quantity postponement, and price postponement only. We characterize the optimal pricing/production/investment decisions for each postponement strategy. Using these characterizations, we show that product substitution/complementarity is a key demand characteristic, which has a large impact on the optimal capacity. Our results show that how the optimal capacity behaves in substitution/complementarity parameter is quite similar under both postponement strategies, and under holdback and clearance. However, this behavior depends highly on other underlying assumptions (i.e., whether or not negative prices are allowed) and on the demand model used. / Ph. D.

<p>This study examines several emerging topics in supply chain management including the dynamic product substitution, the joint optimization of price and order quantity with demand ambiguity, and the implementation of the environmental and social responsibility (ESR) programs.</p>

In this thesis, competitive and cooperative newsboy problems for two substitutable products are analyzed by using game theoretic concepts. The demands of the products are assumed to be dependent and normally distributed. Competition is handled for Nash and Stackelberg games. Nash and Stackelberg games are compared in terms of the order quantities and the expected profits. Cooperative newsboy problem is analyzed for the products having equal costs and revenues. The effect of demand correlation on the order quantities and the expected profits in all of the games is investigated through numerical experiments. Optimal solutions of the Nash, Stackelberg and the cooperative games are examined analytically when the demand correlation is 1.

This dissertation focuses on issues associated with the value of information in models of sequential decision making under uncertainty. All of these issues are motivated by inventory management problems. First, we study the effect of the accuracy of inventory counts on system performance when using a zero-memory controller in an inventory system that is modeled as a partially observed Markov decision process (POMDP). We derive conditions for which improving the accuracy of inventory counts will either (i) improve system performance, (ii) degrade system performance or (iii) will not affect system performance. With a computational study, we determine the range of profitability impacts that result from inaccurate inventory counts when using reasonable zero-memory control policies. Second, we assess the value of demand observation quality in an inventory system with Markovian demand and lost sales. Again, the POMDP serves as a problem model, and we develop computationally tractable suboptimal algorithms to enable the computation of effective lower bounds on system profitability when demand observations are noise-corrupted. We then extend our results toconsider the effects that product substitution has on system performance. We show that systems with low demand variability, high holding cost levels, and high levels of substitution benefit more from demand bservability than systems with high demand variability, low holding cost levels, and low levels of substitution. Third, to enhance our understanding of sequential inventory control with substitutable products, we analyze a two-item inventory problem with known deterministic primary demand, but stochastic one-way substitution. We model this problem as a MDP and show that a decision rule that minimizes the single period cost function, when applied at every decision epoch over the infinite horizon, is an optimal policy for the infinite horizon problem. A definition of increased substitutability is presented, and it is shown that increased substitutability never increases optimal expected total discounted cost.

The in-flight catering industry is a major contributor to food wastage. This wastage is a direct result of the deliberate overproduction of in-flight meals to protect against meal shortages and dissatisfied passengers. With the global strive towards sustainability and the resulting impact of wastage on a company's corporate image, in-flight catering companies need a solution that strives to achieve zero waste and a 100% passenger satisfaction level. This dissertation evaluates the value of combining product substitution and demand uncertainty within an inventory decision-making model as a potential solution opportunity for the wastage dilemma faced by the in-flight catering industry. The decision-making model's purpose is to assist in-flight caterers to make improved decisions regarding the quantity of each meal type to produce for the specific flight under consideration. The model developed is defined as a stochastic multi-objective mixed-integer programming model with fixed recourse and two-way, stock-out based, partial consumer-driven (static) product substitution. The model relies on the output of a forecasting model, that consists of a time-inhomogeneous Markov Chain and a multiple regression model, to forecast the probability distribution of a flight's aggregate meal demand. Due to the lack of available data from public sources, synthetic data is generated to evaluate the model developed. The model is compared against three alternative models that lack either demand uncertainty, product substitution or both to validate the value of including these elements in the decision-making model. The comparison results indicate that the inclusion of the passenger load uncertainty improves the model's average reliability to achieve a 92% minimum passenger satisfaction level with at least 9.2%. Furthermore, it is shown that the stochastic passenger load model produces an average of 2.2 fewer surplus meals per flight instance at the expense of a 3.3% lower reliability when including the substitution behaviour of passengers. This substitution model's superior waste minimisation is attributed to the model's inherent risk-pooling capabilities, and further analysis shows that the value of product substitution increases when the model becomes more constrained. It is, therefore, concluded that the value of product substitution depends on the in-flight caterer's bias towards maximising either reliability or performance. / Dissertation (MEng (Industrial Engineering))--University of Pretoria, 2021. / Council for Scientific and Industrial Research (CSIR) / Industrial and Systems Engineering / MEng / Unrestricted

In this dissertation, we study the interplay between a firm’s operations strategy, with regard to its capacity management, and its marketing decision of product differentiation. For this, we study a market comprising heterogeneous customers who differ in their preferences for time and price. Time sensitive customers are willing to pay a price premium for a shorter delivery time, while price sensitive customers are willing to accept a longer delivery time in return for a lower price. Firms exploit this heterogeneity in customers’ preferences, and offer a menu of products/services that differ only in their guaranteed delivery times and prices. From demand perspective, when customers are allowed to self-select according to their preferences, different products act as substitutes, affecting each other’s demand. Customized product for each segment, on the other hand, results in independent demand for each product. On the supply side, a firm may either share the same processing capacity to serve the two market segments, or may dicate capacity for each segment. Our objective is to understand the interaction between product substitution and the firm’s operations strategy (dedicated versus shared capacity), and how they shape the optimal product differentiation strategy. To address the above issue, we first study this problem for a single monopolist firm, which offers two versions of the same basic product: (i) regular product at a lower price but with a longer delivery time, and (ii) express product at a higher price but with a shorter delivery time. Demand for each product arrives according to a Poisson process with a rate that depends both on its price and delivery time. In addition, if the products are substitutable, each product’s demand is also influenced by the price and delivery time of the other product. Demands within each category are served on a first-come-first-serve basis. However, customers for express product are always given priority over the other category when they are served using shared resources. There is a standard delivery time for the regular product, and the firm’s objective is to appropriately price the two products and select the express delivery time so as to maximize its profit rate. The firm simultaneously needs to decide its installed processing capacity so as to meet its promised delivery times with a high degree of reliability. While the problem in a dedicated capacity setting is solved analytically, the same becomes very challenging in a shared capacity setting, especially in the absence of an analytical characterization of the delivery time distribution of regular customers in a priority queue. We develop a solution algorithm, using matrix geometric method in a cutting plane framework, to solve the problem numerically in a shared capacity setting. Our study shows that in a highly capacitated system, if the firm decides to move from a dedicated to a shared capacity setting, it will need to offer more differentiated products, whether the products are substitutable or not. In contrast, when customers are allowed to self-select, such that independent products become substitutable, a more homogeneous pricing scheme results. However, the effect of substitution on optimal delivery time differentiation depends on the firm’s capacity strategy and cost, as well as market characteristics. The optimal response to any change in capacity cost also depends on the firm’s operations strategy. In a dedicated capacity scenario, the optimal response to an increase in capacity cost is always to offer more homogeneous prices and delivery times. In a shared capacity setting, it is again optimal to quote more homogeneous delivery times, but increase or decrease the price differentiation depending on whether the status-quo capacity cost is high or low, respectively. We demonstrate that the above results are corroborated by real-life practices, and provide a number of managerial implications in terms of dealing with issues like volatile fuel prices. We further extend our study to a competitive setting with two firms, each of which may either share its processing capacities for the two products, or may dedicate capacity for each product. The demand faced by each firm for a given product now also depends on the price and delivery time quoted for the same product by the other firm. We observe that the qualitative results of a monopolistic setting also extend to a competitive setting. Specifically, in a highly capacitated system, the equilibrium prices and delivery times are such that they result in more differentiated products when both the firms use shared capacities as compared to the scenario when both the firms use dedicated capacities. When the competing firms are asymmetric, they exploit their distinctive characteristics to differentiate their products. Further, the effects of these asymmetries also depend on the capacity strategy used by the competing firms. Our numerical results suggest that the firm with expensive capacity always offers more homogeneous delivery times. However, its decision on how to differentiate its prices depends on the capacity setting of the two firms as well as the actual level of their capacity costs. On the other hand, the firm with a larger market base always offers more differentiated prices as well as delivery times, irrespective of the capacity setting of the competing firms.

In this dissertation, we study the interplay between a firm’s operations strategy, with regard to its capacity management, and its marketing decision of product differentiation. For this, we study a market comprising heterogeneous customers who differ in their preferences for time and price. Time sensitive customers are willing to pay a price premium for a shorter delivery time, while price sensitive customers are willing to accept a longer delivery time in return for a lower price. Firms exploit this heterogeneity in customers’ preferences, and offer a menu of products/services that differ only in their guaranteed delivery times and prices. From demand perspective, when customers are allowed to self-select according to their preferences, different products act as substitutes, affecting each other’s demand. Customized product for each segment, on the other hand, results in independent demand for each product. On the supply side, a firm may either share the same processing capacity to serve the two market segments, or may dicate capacity for each segment. Our objective is to understand the interaction between product substitution and the firm’s operations strategy (dedicated versus shared capacity), and how they shape the optimal product differentiation strategy. To address the above issue, we first study this problem for a single monopolist firm, which offers two versions of the same basic product: (i) regular product at a lower price but with a longer delivery time, and (ii) express product at a higher price but with a shorter delivery time. Demand for each product arrives according to a Poisson process with a rate that depends both on its price and delivery time. In addition, if the products are substitutable, each product’s demand is also influenced by the price and delivery time of the other product. Demands within each category are served on a first-come-first-serve basis. However, customers for express product are always given priority over the other category when they are served using shared resources. There is a standard delivery time for the regular product, and the firm’s objective is to appropriately price the two products and select the express delivery time so as to maximize its profit rate. The firm simultaneously needs to decide its installed processing capacity so as to meet its promised delivery times with a high degree of reliability. While the problem in a dedicated capacity setting is solved analytically, the same becomes very challenging in a shared capacity setting, especially in the absence of an analytical characterization of the delivery time distribution of regular customers in a priority queue. We develop a solution algorithm, using matrix geometric method in a cutting plane framework, to solve the problem numerically in a shared capacity setting. Our study shows that in a highly capacitated system, if the firm decides to move from a dedicated to a shared capacity setting, it will need to offer more differentiated products, whether the products are substitutable or not. In contrast, when customers are allowed to self-select, such that independent products become substitutable, a more homogeneous pricing scheme results. However, the effect of substitution on optimal delivery time differentiation depends on the firm’s capacity strategy and cost, as well as market characteristics. The optimal response to any change in capacity cost also depends on the firm’s operations strategy. In a dedicated capacity scenario, the optimal response to an increase in capacity cost is always to offer more homogeneous prices and delivery times. In a shared capacity setting, it is again optimal to quote more homogeneous delivery times, but increase or decrease the price differentiation depending on whether the status-quo capacity cost is high or low, respectively. We demonstrate that the above results are corroborated by real-life practices, and provide a number of managerial implications in terms of dealing with issues like volatile fuel prices. We further extend our study to a competitive setting with two firms, each of which may either share its processing capacities for the two products, or may dedicate capacity for each product. The demand faced by each firm for a given product now also depends on the price and delivery time quoted for the same product by the other firm. We observe that the qualitative results of a monopolistic setting also extend to a competitive setting. Specifically, in a highly capacitated system, the equilibrium prices and delivery times are such that they result in more differentiated products when both the firms use shared capacities as compared to the scenario when both the firms use dedicated capacities. When the competing firms are asymmetric, they exploit their distinctive characteristics to differentiate their products. Further, the effects of these asymmetries also depend on the capacity strategy used by the competing firms. Our numerical results suggest that the firm with expensive capacity always offers more homogeneous delivery times. However, its decision on how to differentiate its prices depends on the capacity setting of the two firms as well as the actual level of their capacity costs. On the other hand, the firm with a larger market base always offers more differentiated prices as well as delivery times, irrespective of the capacity setting of the competing firms.

abstract: The use of Red Blood Cells (RBCs) is a pillar of modern health care. Annually, the lives of hundreds of thousands of patients are saved through ready access to safe, fresh, blood-type compatible RBCs. Worldwide, hospitals have the common goal to better utilize available blood units by maximizing patients served and reducing blood wastage. Managing blood is challenging because blood is perishable, its supply is stochastic and its demand pattern is highly uncertain. Additionally, RBCs are typed and patient compatibility is required. This research focuses on improving blood inventory management at the hospital level. It explores the importance of hospital characteristics, such as demand rate and blood-type distribution in supply and demand, for improving RBC inventory management. Available inventory models make simplifying assumptions; they tend to be general and do not utilize available data that could improve blood delivery. This dissertation develops useful and realistic models that incorporate data characterizing the hospital inventory position, distribution of blood types of donors and the population being served. The dissertation contributions can be grouped into three areas. First, simulations are used to characterize the benefits of demand forecasting. In addition to forecast accuracy, it shows that characteristics such as forecast horizon, the age of replenishment units, and the percentage of demand that is forecastable influence the benefits resulting from demand variability reduction. Second, it develops Markov decision models for improved allocation policies under emergency conditions, where only the units on the shelf are available for dispensing. In this situation the RBC perishability has no impact due to the short timeline for decision making. Improved location-specific policies are demonstrated via simulation models for two emergency event types: mass casualty events and pandemic influenza. Third, improved allocation policies under normal conditions are found using Markov decision models that incorporate temporal dynamics. In this case, hospitals receive replenishment and units age and outdate. The models are solved using Approximate Dynamic Programming with model-free approximate policy iteration, using machine learning algorithms to approximate value or policy functions. These are the first stock- and age-dependent allocation policies that engage substitution between blood type groups to improve inventory performance. / Dissertation/Thesis / Doctoral Dissertation Industrial Engineering 2020