What are the assumptions in linear programming?
- contribution of each activity Xj to the value of the objective function Z is proportional to the level of the activity Xj as represented by the CjXj term in the objective function. Similarly, the contribution of each activity to the left-hand side of each functional constraint is proportional to the level of the activity Xj, as represented by the AijXj term in the constraint.
- Every function in a linear programming model (whether the objective function or the function on the left-hand side of a functional constraint) is the sum of the individual contributions of the respective activities.
- Decision variables in a linear programming model are allowed to take any values, including non-integer values, that satisfy the functional and non-negativity constraints.
- Since each decision variable represents the level of some activity, it is assumed that the activities can be run at fractional levels.
- The value assigned to each parameter of a linear programming model is assumed to be a known constant.
Explain the components of a simple queuing system. Give examples
The calling population
- The population which customers/jobs originate
- The size can be finite or infinite (the latter is most common)
- Can be homogeneous (only one type of customer/job) or heterogeneous
The arrival process
- Determines how, when and where customer/jobs arrive to system
- The important characteristic is the customers/jobs inter arrival times
- Correct specification of the arrival process requires data collection of interarrival times and statistical analysis
The queue configuration
- Specifies the number of queues
- Their location
- Effect on customer behaviour (balking or reneging)
- The max size the queue can hold (infinite/finite capacity)
- Can involve one or several service facilities with one or several parallel service channelsThe service provided by a server is characterised by its service time
- Typically involves data gathering and statistical analysis
- Most analytical queuing models are based on the assumption of exponentially distributed service times
The queue discipline
- Specifies the order by which jobs in the queue are served
- Most common principle is FIFO
- Other rules are: LIFO, SPIT, EDD
- Can entail prioritisation based on customer type
Examples of world queuing systems:
Commercial queuing systems
Commercial organisations serving external customers
E.g. dentist, bank, ATM, petrol stations, plumber, garage …
Transportation service systems
Vehicles are customers or servers
E.g. vehicles waiting at toll stations and traffic lights, trucks or ships waiting to be loaded, taxi cabs, fire engines, lifts and buses
Business – internal service systems
Customers receiving service are internal to the organisation providing the service
E.g. inspection stations, conveyor belts, computer support …
Social service systems
E.g. ER at a hospital, waiting lists for organ transplants, waiting lists for primary school places
Explain how to carry out project planning and control
Project planning and control
Stage 1: Understand the project environment
- Geo-social environment
- Geography and national culture
- Econo-political environment
- Economy and government
- Business environment
- Customers, competitors and suppliers
- Internal environment
- Company strategy, resources and other projects
Stage 2: Project definition
- Aim, strategy and scope
Stage 3: Project planning
- Objectives: what is the goal and estimate of cost/ time
- Project scope: how to approach, feasibility, major tasks
- Contract requirements: reporting and performance, responsibilities
- Schedules: activities, tasks, timelines, milestones
- Resources: budget and budget control
- Control: monitoring and evaluating progress and performance
- Risk analysis
- Identify activities
- Estimate the times and resources for activities
- Identify relationship and dependencies between activities
- Identify time and resource schedule constraints
- Fix the schedule for time and resources
Stage 4: Technical execution
Stage 5: Project control
- Earned value analysis
- Probabilistic analysis: program evaluation and review technique
- Most likely time (m), optimistic time (a), pessimistic time (b)
- Mean = a + 4m + b / 6
- Variance = (b – a / 6) ^2
- Use expected times to identify critical path, and compute slack and project time
- Total project variance = Sum of variance of critical path activities
- Project variance is a measure of the risk involved in the project
Crashing project networks
- Process of reducing time spans on activities so that the project is completed in less time.
- Focus must be on critical path activities
- In order to decide which activity to crash, the ‘crash cost slope’ of each is calculated (crash cost per time period).
- Crash the activity on the critical path which has the lowest crash cost slope.
Describe the algorithm for shortest path problem
Objective of the nth iteration:
Find the nth nearest node to the origin
Input to the nth iteration:
n-1 nearest nodes to the origin, including their shortest path and distance from the origin. (These nodes, plus the origin, will be called solved nodes)
Candidates for the nth nearest node:
Each solved node that is directly connected by a link to one or more unsolved nodes provides one candidate – the unsolved node with the shortest connecting link to this solved node. (Ties provide additional candidates).
Calculation of the nth nearest node
For each such solved node and its candidate, add the distance between them and the distance of the shortest path from the origin to this solved node. The candidate with the smallest such total distance is the nth nearest node (ties provide additional solved nodes), and its shortest path is the one generating this distance.
Minimising the distance travelled
Minimising the total cost of a sequence of activities
Minimising the total time of a sequence of activities
Describe the mimimum spanning tree algorithm and its applications in the real world
Algorithm to solve the MST problem
1. Select any node arbitrarily, and then connect it to the nearest distinct node
2. Identify the unconnected node that is closest to a connected node, and the connect these two nodes. Repeat this step until all nodes have been connected.
3. Tie breaking: Ties for the nearest distinct node (step 1) or the closest unconnected node (step 2) may be broken arbitrarily, and the algorithm must still yield an optimal solution. However, such ties are a signal that there may be (but need not be) multiple optimal solutions. All such optimal solutions can be identified by pursuing all ways of breaking ties to their conclusion.
Applications of the MST problem
Design of telecommunication networks
Design of a lightly used transportation network to minimise the total cost of providing the links
Design of a network of high voltage electrical power transmission lines
Design of a network of wiring on electrical equipment
Design of a network of pipelines to connect a number of locations
Explain the augmenting path algorithm
An augmenting path is a directed path from the source to the sink in the residual network such that every arc on this path has strictly positive residual capacity. The minimum of these residual capacities is called the residual capacity of the augmenting path because it represents the amount of flow that can feasibly be added to the entire path.
1. Identify an augmenting path by finding some directed path from source to sink in the residual network such that every arc on this path has strictly positive residual capacity. (if no augmenting path exists, the net flows already assigned constitute an optimal flow pattern)
2. Identify the residual capacity c* of this augmenting path by finding the minimum of the residual capacities of the arcs on this path. Increase the flow in this path by c*.
3. Decrease by c* the residual capacity of each arc on this augmenting path. Increase by c* the residual capacity of each arc in the opposite direction on this augmenting path. Return to step 1.
Some applications of the maximum flow problem
• Maximise the flow through a company’s distribution network from its factory to its customers
• Maximise the flow through a company’s supply network from its vendors to its factories
• Maximise the flow of oil through a system of pipelines
• Maximise the flow of water through a system of aqueducts
• Maximise the flow of vehicles through a transportation network
What is the objective of locations strategy? What factors impact how it is picked?
Objective of location strategy: to maximise the benefits of location to the firm
Location decisions can be determined by:
- Marketing strategy
- Compete on cost: find low cost location
- Compete on level of responsiveness: close to transportation networks/market
- Cost of doing business
- Potential access to more customers
- Expanding product portfolio
- Depletion of resources
- Industries where resources determine key success
Factors influencing location decisions
- Tariffs, taxes, trade concession, capital subsidies
- Competition, demand patterns, industry dynamics, presence of related industries (clustering), skilled employees’ engagement
- Labour cost, developed infrastructure, proximity to market, cost of inputs, competitors locations, specialised inputs
- Strategic role of a factory amongst multiple plants
What are the different procurement strategies?
Performance based partnership
- High dependence on one supplier
- Used for strategic products
- In general, no long-term supply contract, rather multiple sourcing
- Used for interchangeable products
- Securing continuity of supply
Securing supply of bottleneck products, if necessary, at additional cost
- Reducing dependence on supplier by developing alternative products and looking for alternative suppliers
Category management and e-procurement solutions
- MRO (maintenance, repair, operating supplies) products require a purchasing strategy which is aimed at reducing administrative and logistic complexity
- Electronic catalogues
- Article catalogue (standardisation of product assortment)
How do you choose a sourcing strategy?
Single vs. multiple sourcing
- Assessment with regards to dependence, supply risk and transaction costs
Global vs. local sourcing
- Local sourcing preferred when product is a high-tech product for which specification often changes; high flexibility and precision required in terms of delivery
Partnership or competitive relationship
- Competitive relationship mostly used when commodities are purchased, when the products are purchased in in large volumes and when many suppliers are available
Buying on contract or buying on spot basis
- Contract buying preferred when prices are expected to rise
- Advisable to choose a mix between contract and spot buying
Price agreement vs. performance agreement
- Performance agreement often used when services are purchased (Service level agreement)
- Price agreements might be sufficient if standard quality products are purchased (for example certain types of fabric)
What are the benefits of supplier collaboration and government?
- Access to innovation
- Improved customer satisfaction
- Better quality
- Improved on time delivery
- Increased responsiveness
- Less SC disruption
- Less reputational damage
- Less product scarcity
- Fewer delayed responses to crises
- Lower operational cost
- Motivation to innovate
- Increased efficiency
- Better planning
- Product development time shortening
- Quality improvements
- Cost reduction
- Smooth release of new product
- Value co creation
Explain the different methods of supplier evaluation (procurement)
- Evaluation based on suppliers’ production or service processes.
- Evaluation based on (objective) performance measures
- Cost Ratio
- Weighted point (linear averaging)
Value based sourcing:
- Can the supplier decrease our risk (e.g., reducing bottlenecks/critical parts purchasing; disruption response; exchange rates)?
- Can the supplier provide some other competitive advantage (e.g., differentiating factor; new product variant)?
- Can the supplier help expand the portfolio to address new customer needs?
- Categorization of every supplier, in specific areas, based on a pre-defined list of performance variables.
- Categorical assessment, e.g. ‘good’, ‘neutral’, ‘unsatisfactory’.
- Easy to implement, minimal data required, low-cost
- Lacks reliability, subjective, manual process
Cost ratio method
- Categorization of every supplier by standard cost analysis.
- Rating performance at each performance factor.
- Specific underperformance areas are identified, objective supplier ranking, long-term improvement potential, comprehensive assessment
- Cost-accounting required, complex process, information technology resources required
- Categorization of every supplier by weights on a list of performance variables.
- Flexible system, supplier ranking, moderate capital costs, combines qualitative and quantitative factors
- Tendency to focus on price, information technology resources required
What are the key concepts that make up supply chain risks?
Key concepts that make up supply chain risks
- Occurrence happening at a determinable time and place, with or without the participation of human agents
- Financial shock, trade dispute, geopolitics, natural disaster, disease
- Inability to withstand the effects of an event.
- Uncertainty related to a known event (risk) and uncertainty related to an unknown event (pure uncertainty)
- Chance of event happening that will have negative or positive consequences
- Risk is made up of uncertainty, impact, context and nature
- Probability of an event x impact of that event
- Ability to recover from network failure, which is achieved by continuously changing supply networks in response to risks by using risk mitigation approaches, such as adopting new processes and /or practices or by reconfiguration
Explain why a changing world creates supply chain risks? Give examples of supply chain risks
- Vertical integration vs specialisation
- Integral products vs modular assembly
- Centralised vs dispersed
Changing technology landscape
- faster life cycles
Increasing dependence on suppliers and subcontractors
Implications for future
Value chains are increasingly fragmented and complex
Competition between global supply chains
Managing uncertainty is a key requirement
Emergence of new business models
What are the different types of supply chain risks?
- Product /process design and technology
- Skill set
- Supplier relationship
- Raw material
- Product, process technology
Sales and marketing risk
- Demand projection
What are the two approaches for supply chain risk evaluation and management?
Two approaches for supply chain risk evaluation and management
- Identify supply chain characteristics
- Identify risks linked to these
- Evaluate risks (impact and probability)
- Choose mitigations
- Evaluate impact of mitigations
- Plan mitigations
- Monitor risks and risk mitigation
2. Configuration approach
- Network structure
- Process flow
- Value structure
- Product characteristics
- Overlaying event data on SC map
- Identification of vulnerability led risk
- Change in network structure
- Alternative process flow
- Adjusting value structure
- Product redesign
What are the different supply chain risk mitigation strategies?
Risk mitigation strategies:
- Increase capacity
- Acquire redundant suppliers
- Increase responsiveness
- Increase inventory
- Increase flexibility
- Pool or aggregate demand
- Increase capability
What are the assumptions of the mean square linear regression model?
- Mean of zero: at any given value of x, the population of the error term values has a mean equal to zero
- Constant variance assumption: at any value of x the population of the potential error term values has a variance that does not depend on the value of x
- Normality assumption: At any given value of x, the population of potential error term values has a normal distribution. If this assumption holds, a histogram of residuals should look bell and symmetric
- Independence assumption:Any one value of the error term is statistically independent of another.