DiscussionThe Traveling Salesman Problem - Essay Example

Delivery Problem of Business management involves planning, coordinating, and controlling interrelated activitieswith limited resources. Business managers look for and depend on dynamic planning and scheduling systems that produce best results. According to Shenoy et al (1989), one role of business managers is control of supply to various destinations. Delivery problems occur when business managers are required to send a maximum flow to various destinations at a least cost and time. This paper explores the issue of transport problems using New York, Los Angeles, Chicago, Houston, and Philadelphia as delivery cities.

In particular, the paper discusses how a business manager can effectively deliver a specific food product to major hotels located in the five cities.Transport problems, in business management, are considered as networks. A network, according to Shenoy et al (1989), is a set of nodes and arcs, where nodes are destinations and arcs are routes followed. In the problem, nodes are the cities, while arcs are the routes linking the cities. Apart from the nodes and arcs, a business manager considers capacity of a route, maximum flow of an entire system, and activity times in each path or route.

In solving delivery problems, business managers use Critical Path Method (CPM) and Project Evaluation Review Technique (PERT). CPM uses the concept of critical activity and critical path in solving transport problems. A critical activity, in a network, is an activity whose time of start affects completion time of the entire project. In delivery problems, critical activities include loading and offloading, fueling and servicing, and drivers’ exchange times. In the delivery problem, critical activities also include time taken by a driver and/or a turn-boy to have breakfast, lunch, dinner, or supper.

All these activities determine how fast or slow delivery to hotels in the five cities will be. Therefore, in CPM, a manager identifies points with these activities and organizes them such that minimum time and cost is spent in one complete flow of the food product (Shenoy et al., 1989).In PERT, direction of a flow is not fixed and is thus, considered as random variable. A probabilistic model is, therefore, used to identify a route with the shortest flow time. PERT considers activity time (t0), optimistic time (a), pessimistic time (b), and most likely time (m).

Activity time measures duration of an activity, while optimistic time is the shortest possible time an activity can take. Pessimistic time is the longest possible time an activity can take, while most likely time is the duration an activity can take under normal conditions. The model below is used to determine activity time In other words, while CPM considers various critical activities, PERT considers duration of all activities in a network. A combination of the two methods enables a manager to identify a route where all activities are less expensive.

In other words, a manager will pick a route which is not only cheap, but also has the least overall activity time. In sum, the manager should consider cost and duration of various activities in possible supply routes. The most efficient and cheap route for supplying the five cities is the one with a minimum supply cost and a low time for all deliveries.ReferenceShenoy, G. V., Sharma, S. C. & Shrivastava, U. K. (1989). Quantitative techniques for managerial decisions. 2nd Edition. New Delhi: New Age International (P) Limited publishers.