M/s Bajaj Auto Ltd. (BAL), a large scooter manufacturing company in North India makes a family of scooters and motorcycles. For this example, we consider two models of scooters, Regular and Sports. The Regular model is essentially a family vehicle, with extra-large seats for pillion riders, and extra leg space in the front for carrying items like 40 litre water drum, grocery cartons, shopping bags or even a cooking gas cylinder. The model appeals to those who use the scooter for evening or weekly shopping with family. The engine of this model is optimised to give good mileage at lower speeds. The sports model is based on sleek design that has less space in front and pillion. This model has a high torque engine that gives burst speed for zipping through city traffic and is ideal for those who will use the scooter for daily commute to office. The company dispatches the scooters to a network of dealers, spread all over the country. For this example, we consider three dealers Zone wise, Zone 1, Zone 2 and Zone 3. The sales persons visit each dealer and collect the Request for Delivery for the next week. Exhibit I shows the dealer demand for the coming week. Dispatch trucks arrive every evening at the company finished goods area for loading the daily production and carry the dispatch to the dealers by next morning. The dispatch of Saturday evening is available at the dealer for Monday morning. The dealers will not have storage space to accept more than this quantity, however shortfall in supply will be accepted as it is with a loss of goodwill (no carry forward of demand). Exhibit I: Dealer demand for next week Dealer Model Mon Tue Wed Thu Fri Sat Sun Zone 1 Regular 300 200 200 150 200 400 0 Zone 1 Sports 200 100 100 100 150 250 0 Zone 2 Regular 400 200 200 300 400 500 0 Zone 2 Sports 500 300 300 300 300 400 0 Zone 3 Regular 300 300 200 150 200 300 0 Zone 3 Sports 300 300 100 100 150 250 0 Total (4900) Regular 1000 700 600 600 800 1200 0 Total (4200) Sports 1000 700 500 500 600 900 0 BAL hires trucks from third party logistics providers to carry out the dispatch from the factory to the dealers. A variety of trucks are available, for this example we consider two types of trucks, Normal and Jumbo. We assume that there is unlimited availability of both these trucks. The capacity of trucks is flexible and use of special fixtures allows a variety of loading patterns within each truck. For this example, we consider four loading patterns for each truck as shown in Exhibit II. Exhibit II: Truck loading patterns (number of scooters in each pattern) Truck Model Pattern_1 Pattern_2 Pattern_3 Pattern_4 Normal Regular 20 12 6 0 Sports 0 5 10 15 Jumbo Regular 30 18 9 0 Sports 0 10 15 25 The cost of hiring each truck depends on location of dealer as shown in Exhibit III. Exhibit III: Hiring Cost per trip (in Rupees) for each truck Truck Zone 1 Zone 2 Zone 3 Normal 20,000 24,000 18,000 Jumbo 30,000 35,000 24,000 The estimated cost of loss in goodwill for short supply at each dealer is shown in Exhibit IV. Exhibit IV: Cost (in Rupees) for each vehicle shortage at dealer Model Zone 1 Zone 2 Zone 3 Regular 1,000 1,800 1,500 Sports 1,200 2,000 1,800 Find the optimal dispatch plan that minimises the total cost of transport and goodwill loss.