Reference no: EM133743082

Supply Chain Analytics

Assignment

Question 1: Consider a simple supply chain consisting of a supplier and a retailer. The supply chain faces a downward-sloping demand curve where the quantity demanded, Q, and the price charged to the customer, p, are related as Q = 400 - 50 p.
The cost of producing a unit, c = 2$.

What is the retail price that maximizes total supply chain profits for a centralized system (where the supplier sells to the market directly) and what is the quantity sold at this price?

In the decentralized supply chain, the supplier sells the product to the retailer at a wholesale price w = 3$. In order to increase final demand, the supplier decides to give a promotional price discount of 10 % on the wholesale price to the retailer. How much of this discount will the retailer pass on to the end customer?

Question 2: Consider a firm that is deciding where to locate its facilities (alternately, which locations to keep open and which ones to keep closed). The possible locations where it could locate its manufacturing plants are Buffalo (L), Cincinnati (H), Seattle (S), and Memphis (M). The fixed costs of locating a manufacturing facility at these locations are 7.65, 3.5, 5, and 4.1 Million dollars respectively. If set up, the facilities can produce up to 18,000, 24,000, 27,000, and 22,000 units respectively.

The firm produces and ship to five retail outlets located in Atlanta (A), Boston (B), Chicago (C), Denver (D), and Oakland (O). In thousands of units, the demands at these outlets are 10, 8, 10, 6, and 7 respectively.

The unit production and shipping costs per thousand units are given in the matrix below. For example, it costs 1,675 dollars to produce and ship 1000 units from Buffalo to Atlanta.

What is the optimal (lowest cost) production and shipping cost to meet all the demand? In which cities must the firm locate its production facilities?

If the senior management makes the following request: "If you keep the facility in Buffalo open then you must also keep the facility in Seattle open." How does the optimal solution change? (This one requires you to think about the constraint you want to add to your Excel model. It uses the binary variables linked with the decisions of keeping the corresponding locations open or closed.)

Question 3: A manufacturer sells her product in the market at 50 $. It costs her 20 $ to produce a unit. The product is perishable, and currently, the manufacturer can salvage the product at 10 $/unit at the end of the sale season. The demand for the product is distributed Normally with a mean of 500 and a standard deviation of 100. The manufacturer is considering selling her product through a retailer and charging him 30 $ per unit as wholesale price. She wants the retailer to sell the product at the same price of 50 $. The retailer does not have any salvage options and wants the manufacturer to buy back any unsold units at the end of the season. What buy-back price must the manufacturer offer the retailer to achieve the same sales when she sells directly to the market (the retailer buys the same amount from the manufacturer to sell to the market)?