Planning and consolidating shipments from a warehouse

A typical warehouse or distribution centre ships material to various customer locations across the country, using various modes of transportation. Each mode has different constraints on size of shipment, different cost structures and different transportation times. Typically, for a given warehouse there are certain customer locations that receive frequent shipments of material. It is often possible, therefore, for the warehouse to consolidate different orders for the same customer location into a single shipment. The transportation mode and the day of shipment must be chosen such that the consolidated shipment meets the size constraints and arrives within an agreed-upon ‘delivery window’. In preparing a warehouse distribution plan, a planner seeks to achieve transportation economies of scale (by consolidating two or more orders into fewer shipments) while levelling the workload on warehouse resources and ensuring that material arrives at a customer location during the acceptable delivery window.The problem of deciding what shipments to make daily can be formulated as a set partitioning problem with side constraints. This paper describes a heuristic solution approach for this problem. Computational experiments using actual warehouse select activity indicate that, for moderate-size problems, the heuristic produces solutions with transportation costs that are within a few percent of optimal. Larger problems found in practice are generally too large to be solved by optimal algorithms; the heuristic easily handles such problems. The heuristic has been integrated into the transportation planning system of a leading distributor of telecommunications products.     

Cyclic-order neighborhoods with application to the vehicle routing problem with stochastic demand

We examine neighborhood structures for heuristic search applicable to a general class of vehicle routing problems (VRPs). Our methodology utilizes a cyclic-order solution encoding, which maps a permutation of the customer set to a collection of many possible VRP solutions. We identify the best VRP solution in this collection via a polynomial-time algorithm from the literature. We design neighborhoods to search the space of cyclic orders. Utilizing a simulated annealing framework, we demonstrate the potential of cyclic-order neighborhoods to facilitate the discovery of high quality a priori solutions for the vehicle routing problem with stochastic demand (VRPSD). Without tailoring our solution procedure to this specific routing problem, we are able to match 16 of 19 known optimal VRPSD solutions. We also propose an updating procedure to evaluate the neighbors of a current solution and demonstrate its ability to reduce the computational expense of our approach.     

Analysis of a Rollout Approach to Sequencing Problems with Stochastic Routing Applications

The paper considers sequencing problems, the traveling salesman problem being their natural representative. It studies a rollout approach that employs a cyclic heuristic as its main base algorithm. The theoretical analysis establishes that it is guaranteed to improve (at least in a weak sense) the quality of any feasible solution to a given sequencing problem. Besides other applications, the paper shows that it is well suited for applications that are embedded in dynamic and stochastic environments. The computational performance of the approach is investigated with applications to two stochastic routing problems. The dynamic version of the heuristic appears to be the first algorithm available in the literature to approximately solve a variant of one of these problems.     

Optimal Market Making in the Foreign Exchange Market

Abstract

This paper is concerned with optimal market making in the foreign exchange market. The market maker's holdings in the different currencies are modelled as stochastic processes that are influenced by both the stochastic exchange rates and the stochastic customer buy and sell orders. The market maker can control their own bid and ask price quotes and, additionally, can buy and sell at other market participants' quotes. The resulting stochastic control problem consists of a controlled diffusion problem for the optimal quotes and a singular control problem for optimal trades at other market participants' quotes. A Markov chain approximation is used to derive optimal strategies.     

Optimal and heuristic lead-time quotation for an integrated steel mill with a minimum batch size

This paper presents a model of lead-time policies for a production system, such as an integrated steel mill, in which the bottleneck process requires a minimum batch size. An accurate understanding of internal lead-time quotations is necessary for making good customer delivery-date promises, which must take into account processing time, queueing time and time for arrival of the requisite volume of orders to complete the minimum batch size requirement. The problem is modeled as a stochastic dynamic program with a large state space. A computational study demonstrates that lead time for an arriving order should generally be a decreasing function of the amount of that product already on order (and waiting for minimum batch size to accumulate), which leads to a very fast and accurate heuristic. The computational study also provides insights into the relationship between lead-time quotation, arrival rate, and the sensitivity of customers to the length of delivery promises.     

Supplier selection in make-to-order environment with risks

The problem of allocation of orders for parts among part suppliers in a customer driven supply chain with operational risk is formulated as a stochastic single- or bi-objective mixed integer program. Given a set of customer orders for products, the decision maker needs to decide from which supplier to purchase parts required for each customer order to minimize total cost and to mitigate the impact of delay risk. The selection of suppliers and the allocation of orders is based on price and quality of purchased parts and reliability of on time delivery. To control the risk of delayed supplies, the two popular percentile measures of risk are applied: value-at-risk and conditional value-at-risk. The proposed approach is capable of optimizing the supply portfolio by calculating value-at-risk of cost per part and minimizing mean worst-case cost per part simultaneously. Numerical examples are presented and some computational results are reported.     

Algorithms for a Facility Location Problem with Stochastic Customer Demand and Immobile Servers

This paper studies a facility location problem with stochastic customer demand and immobile servers. Motivated by applications to locating bank automated teller machines (ATMs) or Internet mirror sites, these models are developed for situations in which immobile service facilities are congested by stochastic demand originating from nearby customer locations. Customers are assumed to visit the closest open facility. The objective of this problem is to minimize customers' total traveling cost and waiting cost. In addition, there is a restriction on the number of facilities that may be opened and an upper bound on the allowable expected waiting time at a facility. Three heuristic algorithms are developed, including a greedy-dropping procedure, a tabu search approach and an -optimal branch-and-bound method. These methods are compared computationally on a bank location data set from Amherst, New York.     

Integrated production and allocation policies with one direct shipping option

We consider a single period inventory problem in which a supplier faces stochastic demands and customer specific waiting costs from multiple customers. The objective is to develop integrated production, allocation, and distribution policies so that the total production and customer waiting costs are minimized. We present an optimal policy for the two customer problem and derive a heuristic for a general problem based on the structural results of the two customer case. We show, numerically, that the heuristic performs very well with error bounds of less than 2% on average, while typical approximations may lead to significant sub-optimality.     

A scatter search heuristic for the capacitated clustering problem

This paper proposes a scatter search-based heuristic approach to the capacitated clustering problem. In this problem, a given set of customers with known demands must be partitioned into p distinct clusters. Each cluster is specified by a customer acting as a cluster center for this cluster. The objective is to minimize the sum of distances from all cluster centers to all other customers in their cluster, such that a given capacity limit of the cluster is not exceeded and that every customer is assigned to exactly one cluster. Computational results on a set of instances from the literature indicate that the heuristic is among the best heuristics developed for this problem.     

Maximizing the profit in customer’s order acceptance and scheduling problem with weighted tardiness penalty

The customer’s order acceptance and scheduling problem in a single machine environment has long been an appealing research subject. In this paper, a situation where a pool of customers exists and each customer tends to place all his orders to a single company is addressed. Hence, the customer’s orders will be entirely either accepted or rejected. In this work, decisions on rejection or acceptance of customers and sequencing of the accepted orders are simultaneously considered. The goal is to maximize the total net profit obtained from accepted orders revenues contributed by tardiness penalty. In response to the computational complexity of the problem, a heuristic algorithm and two optimal branch and bound procedures with upper bound, lower bound, and dominance rules are developed. Computational results demonstrate that the proposed methods perform well in a timely manner.     

Fix and Relax Heuristic for a Stochastic Lot-Sizing Problem

This paper addresses a particular stochastic lot-sizing and scheduling problem. The evolution of the uncertain parameters is modelled by means of a scenario tree and the resulting model is a multistage stochastic mixed-integer program. We develop a heuristic approach that exploits the specific structure of the problem. The computational experiments carried out on a large set of instances have shown that the approach provides good quality solutions in a reasonable amount of time.     

Admission policies for the customized stochastic lot scheduling problem with strict due-dates

This papers considers admission control and scheduling of customer orders in a production system that produces different items on a single machine. Customer orders drive the production and belong to product families, and have family dependent due-date, size, and reward. When production changes from one family to another a setup time is incurred. Moreover, if an order cannot be accepted, it is considered lost upon arrival. The problem is to find a policy that accepts/rejects and schedules orders such that long run profit is maximized. This problem finds its motivation in batch industries in which suppliers have to realize high machine utilization while delivery times should be short and reliable and the production environment is subject to long setup times.We model the joint admission control/scheduling problem as a Markov decision process (MDP) to gain insight into the optimal control of the production system and use the MDP to benchmark the performance of a simple heuristic acceptance/scheduling policy. Numerical results show that the heuristic performs very well compared with the optimal policy for a wide range of parameter settings, including product family asymmetries in arrival rate, order size, and order reward.     

Scheduling with job delivery coordination on single machine

This paper investigates a single machine scheduling problem with job delivery coordination, in which each job demands different amount of storage space during transportation. In this problem, a set of independent jobs from a customer must first be processed on a machine without preemption and then delivered by two homogeneous vehicles to the customer in batches. To minimize the makespan, we develop a best possible polynomial-time heuristic with a worst-case ratio of 2.     

包含随机客户的选择性旅行商问题建模及求解

针对快递配送过程中客户需求具有不确定性的特征,提出一种新的路径优化问题——包含随机客户的选择性旅行商问题,在该问题中客户每天是否具有配送需求存在一定概率,并且对客户进行配送可获取一定利润。同时考虑以上两种因素,建立该问题的数学模型, 目标为在满足行驶距离限制的条件下,找出一条经过部分客户的预优化路径,使得该路径的期望利润最大。其可用于模拟构建最后一公里快递配送的路径问题,提供更具有经济效益的配送路径。随后提出包含精细化局部搜索策略的改进遗传算法,算法根据问题特点构建初始可行解。最后通过多个计算比对结果表明,该算法具有较高的计算效率。     

A Fast and Effective Algorithm for the Feedback Arc Set Problem

A divide-and-conquer approach for the feedback arc set is presented. The divide step is performed by solving a minimum bisection problem. Two strategies are used to solve minimum bisection problem: A heuristic based on the stochastic evolution methodology, and a heuristic based on dynamic clustering. Empirical results are presented to compare our method with other approaches. An algorithm to construct test cases for the feedback arc set problem with known optimal number of feedback arcs, is also presented.     

A Branch and Bound Algorithm to Minimize the Total Weighed Number of Tardy Jobs and Delivery Costs

This paper addresses the production and delivery scheduling integration problem; a manufacturer receives ₋ orders from one customer while the orders need to be processed on one or two machines and be sent to the customer in batches. Sending several jobs in batches will reduce the transportation cost but it may increase the number of tardy jobs. The objective is to minimize the sum of the total weighted number of tardy jobs and the delivery costs. The structural properties of the problem for a single machine and special cases of the two-machine flow shop problem are investigated and used to set up a new branch and bound algorithm. A heuristic algorithm for upper bound calculation and two approaches for lower bound calculation are also introduced. Results of computational tests show significant improvement over an existing dynamic programming method.     

Production planning with discounting and stochastic demands

A general continuous review production planning problem with stochastic demand is considered. Conditions under which the stochastic problem may be correctly solved using an equivalent deterministic problem are developed. This deterministic problem is known to have the same solution as the stochastic problem. Moreover, conditions are established under which the deterministic equivalent problem differs from a commonly used deterministic approximation to the problem only in the interest rate used in discounting. Thus, solving the stochastic problem is no more difficult than solving a commonly used approximation of the problem.     

Supply capacity acquisition and allocation with uncertain customer demands

We study a class of capacity acquisition and assignment problems with stochastic customer demands often found in operations planning contexts. In this setting, a supplier utilizes a set of distinct facilities to satisfy the demands of different customers or markets. Our model simultaneously assigns customers to each facility and determines the best capacity level to operate or install at each facility. We propose a branch-and-price solution approach for this new class of stochastic assignment and capacity planning problems. For problem instances in which capacity levels must fall between some pre-specified limits, we offer a tailored solution approach that reduces solution time by nearly 80% over an alternative approach using a combination of commercial nonlinear optimization solvers. We have also developed a heuristic solution approach that consistently provides optimal or near-optimal solutions, where solutions within 0.01% of optimality are found on average without requiring a nonlinear optimization solver.     

Dispatch planning using newsvendor dual problems and occupation times: Application to hydropower

We consider price-driven dispatch planning under price uncertainty: A storable commodity is optimally sold and purchased over time. First, we consider models where the storage level is constrained in expectation. The dual of the corresponding optimization problem is related to the newsvendor problem. Exact solutions of bang-bang type are given. The second methodology is for high-frequency dispatch decisions in multistage stochastic programming models: To overcome the curse of dimensionality, prices are modeled by occupation times at price levels. In a case study, we consider a pumped-storage hydropower plant: Numerical solutions are given, which have similar patterns as for the first, exactly solvable problems.     

Stock Rationing in a Continuous Review Two-Echelon Inventory Model

In this paper we consider a 1-warehouse, N-retailer inventory system where demand occurs at all locations. We introduce an inventory model which allows us to set different service levels for retailers and direct customer demand at the warehouse. For each retailer a critical level is defined, such that a retailer replenishment order is delivered from warehouse stock if and only if the stock level exceeds this critical level. It is assumed that retailer replenishment orders, which are not satisfied from warehouse stock, are delivered directly from the outside supplier, instead of being backlogged. We present an analytical upper bound on the total cost of the system, and develop a heuristic method to optimize the policy parameters. Numerical experiments indicate that our technique provides a very close approximation of the exact cost. Also, we show that differentiating among the retailers and direct customer demand can yield significant cost reductions.