Programming problems on time scales: Theory and computation

In this dissertation, novel formulations for several classes of programming problems are derived and proved using the time scales technique. The new formulations unify the discrete and continuous programming models and extend them to other cases in between. Moreover, the new formulations yield the exact optimal solution for the programming problems on arbitrary isolated time scales, which solve an important open problem. Throughout this dissertation, six distinct classes of programming problems are presented as follows. First, the primal as well as the dual time scales linear programming models on arbitrary time scales are formulated. Second, separated linear programming primal and dual models have been established using the time scales approach. Third, state-constraints separated linear programming primal and dual models on time scales are considered. Fourth, linear fractional primal and dual models have been constructed on time scales. Fifth, quadratic programming problems are formulated using the time scales technique. Sixth, quadratic fractional programming problems have been constructed using a hybrid of the parametric approach and the time scales technique. In addition, for each class of these programming problems the weak duality theorem and the optimality conditions theorem are established for arbitrary time scales, while the strong duality theorem is given for isolated time scales to ensure that our formulation is indeed a perfect formulation. Furthermore, examples for the most well-known isolated time scales are given to illustrate the main results --Abstract, page iv

An enhanced approximation mathematical model inventorying items in a multi-echelon system under a continuous review policy with probabilistic demand and lead-time

An inventory system attempts to balance between overstock and understock to reduce the total cost and achieve customer demand in a timely manner. The inventory system is like a hidden entity in a supply chain, where a large complete network synchronizes a series of interrelated processes for a manufacturer, in order to transform raw materials into final products and distribute them to customers. The optimality of inventory and allocation policies in a supply chain for a cement industry is still unknown for many types of multi-echelon inventory systems. In multi-echelon networks, complexity exists when the inventory issues appear in multiple tiers and whose performances are significantly affected by the demand and lead-time. Hence, the objective of this research is to develop an enhanced approximation mathematical model in a multi-echelon inventory system under a continuous review policy subject to probabilistic demand and lead-time. The probability distribution function of demand during lead-time is established by developing a new Simulation Model of Demand During Lead-Time (SMDDL) using simulation procedures. The model is able to forecast future demand and demand during lead-time. The obtained demand during lead-time is used to develop a Serial Multi-echelon Inventory (SMEI) model by deriving the inventory cost function to compute performance measures of the cement inventory system. Based on the performance measures, a modified distribution multi-echelon inventory (DMEI) model with the First Come First Serve (FCFS) rule (DMEI-FCFS) is derived to determine the best expected waiting time and expected number of retailers in the system based on a mean arrival rate and a mean service rate. This research established five new distribution functions for the demand during lead-time. The distribution functions improve the performance measures, which contribute in reducing the expected waiting time in the system. Overall, the approximation model provides accurate time span to overcome shortage of cement inventory, which in turn fulfil customer satisfaction

Improving healthcare supply chains and decision making in the management of pharmaceuticals

The rising cost of quality healthcare is becoming an increasing concern. A significant part of healthcare cost is the pharmaceutical supply component. Improving healthcare supply chains is critical not only because of the financial magnitude but also because it impacts so many people. Efforts such as this project are essential in understanding the current operations of healthcare pharmacy systems and in offering decision support tools to managers struggling to make the best use of organizational resources. The purpose of this study is to address the objectives of a local hospital that exhibits typical problems in pharmacy supply chain management. We analyze the pharmacy supply network structure and the different, often conflicting goals in the decisions of the various stakeholders. We develop quantitative models useful in optimizing supply chain management and inventory management practices. We provide decision support tools that improve operational, tactical, and strategic decision making in the pharmacy supply chain and inventory management of pharmaceuticals. On one hand, advanced computerized technology that manages pharmaceutical dispensation and automates the ordering process offers considerable progress to support pharmacy product distribution. On the other hand, the available information is not utilized to help the managers in making the appropriate decisions and control the supply chain management. Quantitative methods are presented that provide simplified, practical solutions to pharmacy objectives and serve as decision support tools. For operational inventory decisions we provide the min and max par levels (reorder point and order up to level) that control the automated ordering system for pharmaceuticals. These parameters are based on two near-optimal allocation policies of cycle stock and safety stock under storage space constraint. For the tactical decision we demonstrate the influence of varying inventory holding cost rates on setting the optimal reorder point and order quantity for items. We present a strategic decision support tool to analyze the tradeoffs among the refill workload, the emergency workload, and the variety of drugs offered. We reveal the relationship of these tradeoffs to the three key performance indicators at a local care unit: the expected number of daily refills, the service level, and the storage space utilization

CONCURRENT MULTI-PART MULTI-EVENT DESIGN REFRESH PLANNING MODELS INCORPORATING SOLUTION REQUIREMENTS AND PART-UNIQUE TEMPORAL CONSTRAINTS

Technology obsolescence, also known as DMSMS (Diminishing Manufacturing Sources and Material Shortages), is a significant problem for systems whose operational life is much longer than the procurement lifetimes of their constitute components. The most severely affected systems are sustainment-dominated, which means their long-term sustainment (life-cycle) costs significantly exceed the procurement cost for the system. Unlike high-volume commercial products, these sustainment-dominated systems may require design refreshes to simply remain manufacturable and supportable. A strategic method for reducing the life-cycle cost impact of DMSMS is called refresh planning. The goal of refresh planning is to determine when design refreshes should occur (or what the frequency of refreshes should be) and how to manage the system components that are obsolete or soon to be obsolete at the design refreshes. Existing strategic management approaches focus on methods for determining design refresh dates. While creating a set of feasible design refresh plans is achievable using existing design refresh planning methodologies, the generated refresh plans may not satisfy the needs of the designers (sustainers and customers) because they do not conform to the constraints imposed on the system. This dissertation develops a new refresh planning model that satisfies refresh structure requirements (i.e., requirements that constrain the form of the refresh plan to be periodic) and develops and presents the definition, generalization, synthesis and application of part-unique temporal constraints in the design refresh planning process for systems impacted by DMSMS-type obsolescence. Periodic refresh plans are required by applications that are refresh deployment constrained such as ships and submarines (e.g., only a finite number of dry docks are available to refresh systems). The new refresh planning model developed in this dissertation requires 50% less data and runs 50% faster than the existing state-of-the-art discrete event simulation solutions for problems where a periodic refresh solution is required

A model and methodologies for the location problem with logistical components

This paper significantly extends traditional facility location models by introducing several logistical cost components such as holding, ordering, and transportation costs in a multi-commodity, multi-location framework. Since location and logistical costs are highly inter-related, the paper provides an integrated model, and seeks to minimize total physical distribution costs by simultaneously determining optimal locations, flows, shipment compositions, and shipment cycle times. Two sophisticated heuristic methodologies, based on Lagrangian relaxation and simulated annealing, respectively, are provided and compared in an extensive computational experiment

Development of spreadsheet simulation models of gas cylinders inventory management

The solution of the problem of managing the inventory of an enterprise whose activities are related to the purchase and sale of gas cylinders is considered. To solve the problem, it was necessary to investigate and choose the best inventory management strategy that provides the minimum value of the average inventory balance in the warehouse with the established upper limit of the average deficit. The problem of determining the best strategy is presented as a discrete programming problem, the required variables of which depend on the replenishment method. With a periodic replenishment strategy, the controlled variables are the volume of the delivery line and the delivery interval, with a threshold one, the minimum inventory level and the volume of the delivery line. Let’s also consider replenishment with a predicted inventory level, where the delivery level and the minimum inventory level are used as control variables. Three tabular simulation models with a given delivery time and random demand are proposed. Using the Chi-square test, it was found that the quantity demanded has a normal distribution law. By carrying out computational experiments, the optimal values of controlled variables were determined. The best objective function values were obtained using a model with a predicted inventory level and a threshold replenishment strategy. Experiments conducted on the basis of historical data have shown the advantage of the two model strategies compared to the strategy currently used in the enterprise. The use of a model with a predictable inventory level would reduce the average inventory balance by 46 %, and, consequently, save working capital. The results of the study can be useful for managers of enterprises whose activities are related to inventory managemen

Lot-Sizing Problem for a Multi-Item Multi-level Capacitated Batch Production System with Setup Carryover, Emission Control and Backlogging using a Dynamic Program and Decomposition Heuristic

Wagner and Whitin (1958) develop an algorithm to solve the dynamic Economic Lot-Sizing Problem (ELSP), which is widely applied in inventory control, production planning, and capacity planning. The original algorithm runs in O(T^2) time, where T is the number of periods of the problem instance. Afterward few linear-time algorithms have been developed to solve the Wagner-Whitin (WW) lot-sizing problem; examples include the ELSP and equivalent Single Machine Batch-Sizing Problem (SMBSP). This dissertation revisits the algorithms for ELSPs and SMBSPs under WW cost structure, presents a new efficient linear-time algorithm, and compares the developed algorithm against comparable ones in the literature. The developed algorithm employs both lists and stacks data structure, which is completely a different approach than the rest of the algorithms for ELSPs and SMBSPs. Analysis of the developed algorithm shows that it executes fewer number of basic actions throughout the algorithm and hence it improves the CPU time by a maximum of 51.40% for ELSPs and 29.03% for SMBSPs. It can be concluded that the new algorithm is faster than existing algorithms for both ELSPs and SMBSPs. Lot-sizing decisions are crucial because these decisions help the manufacturer determine the quantity and time to produce an item with a minimum cost. The efficiency and productivity of a system is completely dependent upon the right choice of lot-sizes. Therefore, developing and improving solution procedures for lot-sizing problems is key. This dissertation addresses the classical Multi-Level Capacitated Lot-Sizing Problem (MLCLSP) and an extension of the MLCLSP with a Setup Carryover, Backlogging and Emission control. An item Dantzig Wolfe (DW) decomposition technique with an embedded Column Generation (CG) procedure is used to solve the problem. The original problem is decomposed into a master problem and a number of subproblems, which are solved using dynamic programming approach. Since the subproblems are solved independently, the solution of the subproblems often becomes infeasible for the master problem. A multi-step iterative Capacity Allocation (CA) heuristic is used to tackle this infeasibility. A Linear Programming (LP) based improvement procedure is used to refine the solutions obtained from the heuristic method. A comparative study of the proposed heuristic for the first problem (MLCLSP) is conducted and the results demonstrate that the proposed heuristic provide less optimality gap in comparison with that obtained in the literature. The Setup Carryover Assignment Problem (SCAP), which consists of determining the setup carryover plan of multiple items for a given lot-size over a finite planning horizon is modelled as a problem of finding Maximum Weighted Independent Set (MWIS) in a chain of cliques. The SCAP is formulated using a clique constraint and it is proved that the incidence matrix of the SCAP has totally unimodular structure and the LP relaxation of the proposed SCAP formulation always provides integer optimum solution. Moreover, an alternative proof that the relaxed ILP guarantees integer solution is presented in this dissertation. Thus, the SCAP and the special case of the MWIS in a chain of cliques are solvable in polynomial time