Questions & explanations
1. Compare the trade-offs between locating a micro-fulfillment center near a highway versus near a residential area.
A micro-fulfillment center near a highway is good for receiving large shipments from suppliers quickly, but trucks then have to drive extra distance into residential areas to deliver. A center near a residential area shortens the last-mile trip to customers, reducing fuel and time, but it may be harder for big trucks to access and rent may be higher. The optimization model weighs these factors: highway locations lower inbound costs but raise outbound costs; residential locations do the opposite. The best choice depends on how many customers are nearby and how often the center gets restocked. For a dense urban zone, residential proximity often wins; for a spread-out suburb, highway access may be better.
2. What is cryopreservation?
Cryopreservation is the process of preserving living cells, tissues, or other biological materials by cooling them to very low temperatures, typically below -150°C. At these cryogenic temperatures, all biological activity stops, allowing long-term storage. Liquid nitrogen, which boils at -196°C, is commonly used. Vapor phase storage means the material is kept in the cold gas above the liquid nitrogen, not submerged, to avoid contamination and reduce risk of freezing damage. Cell viability refers to the percentage of cells that remain alive and functional after thawing. Proper cryopreservation requires careful control of cooling and warming rates to prevent ice crystal formation that can kill cells.
3. Give an example of how a company might decide between one big warehouse or several small micro-fulfillment centers.
A company delivering fresh food might choose several small micro-fulfillment centers near customers instead of one big warehouse far away. With many small centers, each delivery truck travels shorter distances, so food stays fresh and arrives faster. However, running many small centers costs more in rent and staff. The company uses an optimization model to compare total costs: one big warehouse with long truck routes versus many small centers with short routes. The model shows which option gives the lowest total cost while meeting delivery speed targets. For instance, in a dense city, many small centers often win; in a spread-out rural area, one big warehouse might be better.
4. What is a 'capacitated facility location problem' and how does it apply to locker banks?
A capacitated facility location problem adds a limit on how many packages each facility can hold. For locker banks, each locker has a fixed number of compartments. The model must assign customers to lockers without exceeding that capacity. It also decides where to open new lockers to cover demand. For example, if a locker near a train station is full by 10 AM, the model might suggest opening another locker nearby. The goal is to minimize total cost while ensuring every customer has a locker within a reasonable distance. This problem is harder than the simple version because capacity constraints force trade-offs between opening more lockers and using existing ones fully.
5. Compare how queueing theory applies to a warehouse loading dock versus a delivery route scheduling.
At a loading dock, trucks arrive to be loaded, and queueing theory models the dock as a server. The waiting time is how long a truck waits before loading. For delivery route scheduling, the 'server' is the delivery person, and 'customers' are delivery stops. Queueing theory can estimate how long a delivery person spends at each stop and how many stops they can complete in a day. The main difference is that at the dock, trucks queue physically; on a route, stops are sequential and travel time between stops matters. Both use similar math but with different parameters. The dock model focuses on congestion; the route model focuses on balancing workload.
6. How does the choice of modal split affect the environmental impact of a supply chain?
Different transport modes produce different amounts of pollution. Airplanes and trucks produce more carbon dioxide per ton of goods than trains or ships. So shifting freight from truck to rail or ship reduces environmental harm. For example, a company that moves 1,000 containers by rail instead of truck can cut carbon emissions by about 75%. Modal split decisions also affect local air quality and noise. Governments may encourage greener modes through taxes or subsidies. Companies that care about sustainability choose modal splits that lower their carbon footprint. This also improves their public image and may attract eco-conscious customers.
7. How does intermodal terminal design affect the efficiency of moving goods between modes?
An intermodal terminal is a place where goods are transferred from one mode to another, like from ship to train. Good design makes these transfers fast and cheap. For example, a terminal with cranes that can directly lift containers from a ship onto a train reduces handling time. The layout should have enough space for trucks, trains, and storage. If the terminal is poorly designed, trucks may wait long hours, and trains may be delayed. Efficient terminals use technology to track containers and schedule transfers. This reduces costs and speeds up delivery. A well-designed terminal is key to making intermodal transport work.
8. Give an example of how a delivery company might use queueing theory to decide how many delivery vans to have.
A company sees that orders arrive at an average rate of 10 per hour, and each van can deliver 5 orders per hour. Using queueing theory, they model this as a system where orders queue up for a van. If they have 3 vans, the total service rate is 15 per hour, which is more than arrivals, so the queue stays short. But if they have only 2 vans, service rate is 10 per hour, equal to arrivals, and the queue grows over time. The theory shows that with 2 vans, average wait time becomes infinite in the long run. So they need at least 3 vans to keep waiting times reasonable. This helps them invest in the right number of vans.
9. How do free trade zones and bonded warehouses help in managing inventory for international trade?
Both allow companies to hold goods near the market without paying duties immediately. This means a company can keep a large stock of imported items in a bonded warehouse and release them as needed, paying duties only on the released quantity. In a free trade zone, a company can also perform light manufacturing to customize products for different customers. For example, a electronics company can store components in an FTZ, assemble them into devices based on orders, and then ship directly to buyers. This reduces storage costs and speeds up delivery. It also helps manage currency fluctuations and trade regulations.
10. How does the cooling rate affect cell viability during cryopreservation?
The cooling rate is critical because it determines whether ice crystals form inside or outside cells. If cooling is too slow, water leaves cells and forms large ice crystals outside, damaging cell membranes. If too fast, water freezes inside cells, causing lethal internal ice. An optimal rate, often around 1°C per minute, allows water to exit cells gradually and freeze extracellularly without damaging them. Cryoprotectants like glycerol or DMSO are added to protect cells by lowering the freezing point and reducing ice formation. After thawing, rapid warming is usually best to prevent recrystallization of ice.
11. What is the 'critical fractile' in the newsvendor model and how does it guide the order quantity?
The critical fractile is a number that tells the optimal service level. It is calculated as (selling price - cost) / (selling price - salvage value). For perishables, salvage value is often zero or negative (disposal cost). For example, if a sandwich costs $3 to make and sells for $5, and waste costs $1 to dispose, the critical fractile is (5-3)/(5-(-1)) = 2/6 = 0.33. This means the company should order enough to meet demand 33% of the time, i.e., order a quantity that has a 33% chance of being enough. The model then finds the demand level at that percentile. This balances the risk of waste and lost sales.
12. Compare the costs of holding inventory at a central warehouse versus at local lockers.
Holding inventory at a central warehouse usually has lower rent per unit because warehouse space is cheaper than locker space in prime locations. However, shipping from warehouse to customer costs more and takes longer. Local lockers have higher holding cost per unit but lower delivery cost and faster service. Multi-echelon optimization trades off these costs: it might keep slow-moving items at the warehouse and fast-moving items at lockers. For example, a warehouse might hold 1000 units of a slow-selling book, while a locker holds only 10 copies of a bestseller. The total cost is minimized by this split.