1. Trend in Supply Chain Optimization and Humanitarian Logistics
Tokyo University of
Marine Science and Technology
KUBO Mikio
My name is Mikio Kubo from Tokyo University of Marine Science of Technology.
The title of this talk is
Trend in Supply Chain Optimization and Humanitarian Logistics.

2. Agenda Definition of the Supply Chain (SC) and Logistics
Decision Levels of the SC
Classification of Inventory
Basic Models in the SC
Logistics Network Design
Inventory
Production Planning
Vehicle Routing
SC Risk Management and Humanitarian SC
This is the agenda of my talk.
I will start with the definition of the supply chain and logistics, and introduce three decision levels of the SC,and then show you the classification of inventory.
Next I’m going to talk about several models in the SC; they are logistics network design, inventory, production planning, and vehicle routing.
And finally, I will talk about the SC management and humanitarian logistics, if time allows.

3. What’s the Supply Chain?
There are many definitions of the Supply Chain. But my definition is simple.
IT (that means the information technology)＋Logistics＝Supply Chain
To complete the definition, we need the definition of logistics.
As shown in this figure, logistics optimizes the flow of products between the point of origin (here supply point) and the point of consumption (here demand point) in order to meet customers' requirements.
IT(Information Technology)＋Logistics ＝Supply Chain

4. Real System, Transactional IT, Analytic IT
Analytic IT Model＋Algorithm=
Decision Support System
brain
Transactional IT POS, ERP, MRP, DRP… Automatic Information Flow
In general, the supply chain is composed of three systems:
One is the real system that includes real logistics objects such as trucks, ships, plants, products, machines, etc.
Using the metaphor of human beings, the real system is compared to muscle of the body.
Another is the transactional IT; for example, POS that means Point-Of-Sales, you can see such a system in convenience stores or supermarkets, ERP that means Enterprise Resource Planning that is an extension of legacy MRP that means Material Requirement Planning, DRP that means Distribution Requirement Planning, etc.
The transactional IT is compared to a nerve net of human beings that just flows the pulse and executes automatic actions.
The other is the analytic IT composed of some models and algorithms to solve them.
The analytic IT is compared to the brain of human beings.
That’s the main theme of this talk.
nerve
Real System=Truck, Ship, Plant, Product, Machine, …
muscle

5. Levels of Decision Making
Strategic Level
A year to several years; long-term decision making
Analytic IT
Tactical Level
A week to several months; mid-term decision making
The decision support systems or analytic IT models can be categorized into three levels.
The top level is the strategic level that deals with decisions having a long-time effect that spans from a few years to 10 or more years.
Typical decisions in this level are the number, location, and capacity of warehouses and manufacturing plants, and the flow of material through the logistics network.
The tactical level includes decisions which are typically updated between once every month or quarter, or once every year. These include purchasing and production decisions, inventory policies, and transportation strategies.
Finally, the operational level refers to day-to-day or real time decisions such as scheduling, dispatching, vehicle routing, and truck loading.
Using some metaphors, the strategic level is compared to seeing the forest, while the operational level is compared to seeing the tree.
Such a change of the point of view is important for the decision making using analytic IT models.
Operational Level
Transactional IT
Real time to several days; short-term decision making

6. Models in Analytic IT Strategic Tactical Operational Supplier Plant DC
Retailer
Logistics Network Design
Strategic
Multi-period Logistics Network Design
Inventory
Safety stock allocation
Inventory policy
optimization
Production
Lot-sizing
Scheduling
Transportation
Delivery
Vehicle Routing
Tactical
This figure represents an entire supply chain; Procurement of parts or raw materials from suppliers, production at plants, stocking in DCs or warehouses, and distribution to retailers.These are the decision levels; strategic, tactical and operational that means long-term, middle-term, and short-term, respectively.
Operational

7. Models in Analytic IT Strategic Supplier Plant DC Retailer
Logistics Network Design
Strategic
Multi-period Logistics Network Design
Inventory
Safety stock allocation
Inventory policy
optimization
Production
Lot-sizing
Scheduling
Transportation
Delivery
Vehicle Routing
In the strategic level, we have an analytic IT model named the Logistics Network Design that encompasses the whole logistics network and determines new suppliers, a new flow pattern of products through the network, a selection of warehouse locations and capacities, the production levels at each plant or the production line in order to minimize total production, inventory, and transportation costs (whole supply chain costs).
Tactical
Operational

8. Models in Analytic IT Inventory Supplier Plant DC Retailer
Logistics Network Design
Strategic
Multi-period Logistics Network Design
Tactical
Inventory
Safety stock allocation
Inventory policy
optimization
Production
Lot-sizing
Scheduling
Transportation
Delivery
Vehicle Routing
In the tactical and operational levels, we have 3 types of models; they are inventory, production planning and transportation delivery optimization models.
The safety stock allocation model (that is used in tactical level) determines the positions of safety stocks in the supply chain, and simultaneously determines the pull-push boundary of each product.
The inventory policy optimization model (that is in the operational or tactical level) decides at what point to reorder and how much to order so as to minimize inventory ordering and holding costs.
Production planning can be seen as a supply chain optimization in a plant. It optimizes the acquisition of resources such as machines or workers, the size of the production lots to be manufactured or processed in a batch (these are in tactical level) and the sequencing of the production lots (it’s usually in operational level).
Finally, transportation delivery optimization involves the routes and frequencies of vehicles such as ships and trucks. The most important transportation delivery model is the vehicle routing problem that occurs at the final part of the supply chain, that means the final distribution of products to the retailers or customers (this occurs in both tactical and operational levels).
Operational

9. Inventory=Blood of Supply Chain
Inventory acts as glue connecting optimization systems
Supplier
Plant DC
Retailer
Work-in-process
Finished goods
Raw material
Inventory plays an important role in supply chain. Using the metaphor of human body, it’s compared to blood and it acts as glue connecting several models in the SC. Inventory is spread throughout the SC from raw materials, work-in-process (WIP) inventory, to finished products in warehouses and retailers.And such inventory varies day by day or period to period due to many reasons.
Time

10. Classification of Inventory
In-transit (pipeline) inventory Trade-off: transportation cost or production speed
Seasonal inventory Trade-off: resource acquisition or overtime cost，setup cost
Cycle inventory Trade-off : transportation (or production or ordering) fixed cost
Lot-size inventory Trade-off: fixed cost
Safety inventory Trade-off: customer service level， backorder (stock-out) cost
To understand the role of inventory, we need to classify inventory. Inventory is classified by their motivations; We have to ask “Why we have such inventory?” There’s a trade-off between inventory and some other cost factors.　

11. In-transit (pipeline) Inventory
Inventory that are in-transit of products Trade-off: transportation cost or transportation/production speed ->optimized in Logistics Network Design (LND)
In-transit inventory is inventory moving in the SC. It can be seen as a flow thorough a pipeline; so it’s sometimes called pipeline inventory. Such an inventory exists ‘cause transportation time is positive. In-transit inventory is proportional to the flow volume per unit-time. That means if the speed of the flow fast, in-transit inventory becomes smaller. This inventory will be treated and be optimized in the logistics network design model.

12. Seasonal Inventory
Inventory for time-varying (seasonal) demands Trade-off: resource acquisition or overtime cost -> optimized in multi-period LND Trade-off: setup cost -> optimized in Lot-sizing
Demand
Resource Upper Bound
The main role of inventory in the SC is to fill the gap between supply and demand. Seasonal inventory is inventory to counter predictable seasonal demand under the restriction of the limited production resources. A can maker supplies tons of cans to beverage makers such as beer companies. For a high demand during the summer season, the company builds up inventory during low demand periods and store it. This is seasonal inventory.
Period

13. Cycle Inventory
Inventory caused by periodic activities Trade-off : transportation fixed cost -> LND Trade-off: ordering fixed cost -> Economic Ordering Quantity (EOQ)
Inventory
Level
demand
Assume that demand is constant and supply arrives cyclically. In this case, inventory changes like a saw-tooth like this figure. That’s cycle inventory. Many activities in the SC have economy of scale; that means large lots decrease the cost. This is the motivation of cycle inventory. If transportation activity has a non-negative fixed cost, we have to have cyclic inventory. It is optimized in the LND model. If ordering activity has a non-negative fixed cost, we have to have cyclic inventory, which is optimized in the EQO model.
Cycle Time

14. Lot-size Inventory
Cycle inventory when the speed of demand is not constant Trade-off: fixed cost ->Lot-sizing, multi-period LND
Inventory
Level
Lot-sizing inventory is an extension of cycle inventory when the speed of the demand is not constant but time dependent.
That means the demand changes over time, period by period. As in cycle inventory, lot-sizing inventory has the trade-off for fixed costs, especially production set-up costs and is optimized in lot-sizing and multi-period logistics network design models.
Time

15. Safety Inventory
Inventory for the demand variability Trade-off: customer service level ->Safety Stock Allocation, LND Trade-off: backorder (stock-out) cost ->Inventory Policy Optimization
Safety inventory or safety stock is inventory to protect against uncertainties of future events such as customer demands.
So it has the trade-off for the customer service level. If customers request 100% of service level that means no stock out, retailers need a huge amount of safety inventory. Service level is determined by backorder or stock-out penalty costs. So there’s a trade-off between safety inventory costs and backorder costs. Many analytic IT models include the safety inventory such as safety stock allocation, logistics network design, and inventory policy optimization models.

16. Classification of Inventory
Cycle Inventory
Lot-size Inventory
Seasonal Inventory
Safety Inventory
Inventory can be classified into these 5 types of inventory, in-transit, seasonal, cycle or lot-size, and safety inventory.
It’s not so easy to treat them separately in practice. But we should optimize them separately using the analytic IT models I’ll talk next.
In-transit (Pipeline) Inventory
Time
It’s hard to separate them but… They should be determined separately to optimize the trade-offs

17. Logistics Network Design
Decision support in strategic level
Total optimization of overall supply chains
Example
Where should we replenish pars?
In which plant or on which production line should we produce products?
Where and by which transportation-mode should we transport products?
Where should we construct (or close) plants or new distribution centers?
The first model is the logistics network design which involves issues relating to plant, warehouse, and retailer location. These are strategic decisions because they have a long-term effect on the company. The objective is to design or reconfigure the logistics network so as to minimize annual system wide costs, including production and purchasing costs, inventory holding costs, facility costs that include storage, handling, and fixed costs, and transportation costs.
There are many decisions optimized in this model. For example, …

18. Trade-off in LND Model: Ｎumber of Warehouses v.s.
Service lead time ↓
Inventory cost ↑
Overhead cost ↑
Outbound transportation cost ↓
Inbound transportation cost ↑
Number of warehouses
There are many trade-offs in the model: for example, increasing the number of warehouses typically yields:
-An improvement in service level due to the reduction in average travel time to the customers.
-An increase in inventory costs due to increased safety stocks required to protect each warehouse against uncertainties in customer demands.
-An increase in overhead and setup costs.
-A reduction in outbound transportation costs: transportation costs from the warehouses to the customers.
-An increase in inbound transportation costs: transportation costs from the suppliers and/or manufacturers to the warehouses.

19. Trade-off: In-transit inventory cost v.s. Transportation cost
Another trade-off in the LND model is between the in-transit inventory cost and the transportation cost. The in-transit inventory is proportional to the flow volume per unit time. So if we use a fast transportation mode such as a plane that is expensive, the in-transit inventory becomes smaller and decrease the inventory cost. Meanwhile, if we use a slow transportation model such as a ship (or a train in Japan), the in-transit inventory becomes larger. That’s the trade-off and it is optimized in the LND model that selects the appropriate transportation mode for each link by minimizing the sum of the transportation and in-transit inventory costs.

20. Multi-period Logistics Network Design
Decision support in tactical level
An extension of MPS (Master Production System) for production to the Supply Chain
Treat the seasonal demand explicitly
Demand
We can extend the basic LND model to the multi-period LND model. Let us consider situations where demand changes over time because of seasonal factors, or growing or shrinking markers.
It also allows for time-varying purchase, production, transportation, and inventory costs. The problem is to find the right balance between the cost of holding seasonal inventory and the other costs.
This model is in the tactical decision level and can be seen as an extension of the master production system (MPS) usually used in a plant for determining the production level.
Period (Month)

21. Trade-off: Overtime v.s. Seasonal Inventory Cost
Overtime penalty
Seasonal inventory
Demand
Resource Upper Bound
Period
Overtime
Variable
Production
Constant
Production
The multi-period LND model optimizes the trade-off between seasonal inventory cost and overtime penalty cost.
Assume that demand has a seasonal peak, say in summer and our plant has a limited resource. So we cannot supply the peak demand by the production during the peak periods.
One strategy to cope with the peak demand by seasonal inventory. That means the company builds up inventory during low demand periods, say in spring, and stores it for the summer, the peak season.
Another strategy is to vary the production level by hiring new workers or by doing overwork; both require additional costs. The multi-period LND model find the best balance of these strategies.
Inventories

22. Mixed Integer Programming (MIP) + Concave Cost Minimization
Safety Inv. Cost
BOM or Recipe
The LND model can be formulated as a multi-commodity network flow model. Supply chain or logistics network is modeled as a network composed of nodes and arcs. The raw materials, parts, intermediates, final products or items are modeled as commodities or flow through the network. We have to model the bill-of-material (BOM) or recipe structure that represents the relationship between the items. That means which product is composed of which parts or raw materials. We also incorporate the safety inventory cost into the model that is a concave function of the flow volume through the arc. Usually, the concave cost minimization problem is difficult; it is called NP-hard. That means it’s probably impossible to find an efficient algorithm to solve it in general. But by using approximation of concave functions, the LND problem can be formulated as a mixed integer programming problem and can be solved by standard MIP solvers (here MIP means mixed integer programming) such as Gurobi, CPLEX, Xpress-MP, they are commercial solvers, or GLPK, SCIP, they are free solvers.

23. Safety Stock Allocation
Decision support in tactical level
Determine the allocation of safety stocks in the SC for given service levels
Safety Inventory
Service Level
The second model is the safety stock allocation model in tactical level that optimizes the trade-off between the safety stock and the customer service level.
+Risk Pooling
(Statistical Economy of Scale)

24. Basic Principle of Inventory
Economy of scale in statistics: gathering inventory together reduces the total inventory volume. 　
-> Modern supply chain strategies
risk pooling
delayed differentiation
design for logistics
This model is based on a basic principle of inventory called the statistical economy of scale; that means gathering inventory together reduces the total inventory volume and cost. 　
This principle is used in many modern supply chain strategies such as risk pooling, delayed differentiation, and design for logistics.
The safety stock allocation model answers how to use these strategies and also answer the following questions; where to keep safety stock? which facility should produce to stock? and which facility should produce to order?
Where should we allocate safety stocks to minimize the
total safety stock costs so that the customer service level
is satisfied.

25. Lead-time and Safety Stock
Normal distribution with average demand μ，standard deviation σ
Service level （the probability of no stocking out） 95%->safety stock ratio 1.65
Lead-time (the time between order and arrival） L
The safety stock allocation model is based on the classical formula to compute the safety inventory volume.
Assume that the demand follows the normal distribution with average demand μ and the standard deviation σ.
Service level is the probability of no stocking out and is determined by a decision maker.
Lead-time is the amount of time that elapses from the instant that an order is placed until it arrives.
So the maximum inventory volume is computed by the formula
μ×Ｌ plus safety stock ratio×σ× square root of L..
Here, safety stock ratio can be computed from service level.
If the service level is 95%, then the safety stock ratio becomes 0.95.
Actually this formula is a special case of the classical newsboy problem that I will talk later.

26. The Relation between Lead-time and (Average, Safety, Maximum) Inventory
This figure represents the relationship between the lead-time and the average, safety and maximum inventory.
Horizontal axis is the lead time and the vertical axis is the inventory volume; average inventory (drawn in black line) is a linear function, while maximum inventory (drawn in pink) and safety inventory (drawn in yellow) are both concave that represents the statistical economy of scale.

27. Guaranteed Lead-time
Guaranteed lead-time (LT)：Each facility guarantees to deliver the item to his customer within the guaranteed lead-time
Guaranteed LT to
downstream facility
Li ＝２ days
Safety inv.
＝２ days
One characteristic of the safety stock allocation model is to treat lead-time as a variable instead of a given constant.
First we introduce the guaranteed lead-time that is a committed lead time that the facility guarantees to deliver to its customers, the downstream facilities.
In this example, this facility i guarantees to deliver to its customer within 2 days represented by a yellow arrow in the upper right corner. So the guaranteed lead time denoted by L_i is 2.
This facility has another lead time called the entering LT that is the GLT of his predecessor or upstream (supply) facility.
In this example, the entering LT of facility i represented by a yellow arrow in the lower left corner is 1 ‘cause its predecessor has GLT 1. 2 2
Guaranteed LT of upstream facility
=1 day
= Entering LT LIi 1
Production time Ti ＝3
Facility i

28. Net Replenishment Time
Net replenishment time (NRT)：
　＝LTi +Ti -Li
Guaranteed LT to
downstream facility
Li ＝２ days
Safety inv.
＝２ days
The facility has a given constant production time that is the amount of time that elapses from the instant that the item arrives until it is ready to ship.
In this example it is represented by a greed rectangle in the lower right corner and it is 3 day. The net replenishment time is defined by entering LT + production time –guaranteed LT.
In this example the net replenishment time represented by the red arrow in the upper left corner is 1+3-2=2.
The inventory of the facility is set to the maximum demand volume during the net replenishment time to satisfy the service level. 2 2
Guaranteed LT of upstream facility
=1 day
= Entering LT LIi 1
Production time Ti＝3
Facility i

29. Safety Stock Allocation Formulation
maximum demand
net replenishment time
Next I’ll show you a mathematical programming approach foe solving the safety stock allocation problem in general network.
The main variable is x that represents net replenishment time. The objective function is nonlinear. Here D is the maximum demand function.
It is general nonlinear function. If the demand follows the normal distribution, D becomes a square root function. D minus μsx gives us the safet inventory volume and by multiplying by holding cost h_I, we get the safety inventory cost. The objective function is the sum of this nonlinear functions over all facilities. The first constraint defines the net replenishment time is equal to entering LT (it is a variable)+ processing time (it is a constant) – guaranteed lead time (it is also a variable). The second constraint means that the entering lead time of facility j is greater than or equal to the guaranteed lead time of facility I if I is a supplier of facility j that mean there exits an arc between I and j.
The third constraint restricts the lower and upper bounds of the guaranteed LT, and finally, the forth constraint defines the non-negativity of the net replenishment time.
This is a nonlinear programming problem with a concave objective function. Generally it’s quite hard to solve it (it’s NP-hard problem) but by using the piecewise linear approximation, we can solve the problem by standard MIP solvers.
upper bound of guaranteed LT

30. Algorithms for Safety Stock Allocation
Concave cost minimization using piece-wise linear approximation
Dynamic programming (DP) for tree networks
Metaheuristics Local Search (LS), Iterated LS, Tabu Search
The safety stock allocation problem can be solved by several types of algorithms.
One is the mathematical programming approach that relies on MIP solvers. It can handle middle-size instances with general networks.
Another is based on dynamic programming. We can extend the DP algorithm we discussed to a more general tree network case. But, unfortunately, we cannot extend the DP approach to general networks, .
Other approaches are metaheuristics such as local search, iterated LS, or tabu search, etc. They give approximate solutions instead of the exact solutions but it’s usually faster and more robust.

31. A Real Example: Ref. Managing the Supply Chain –The Definitive Guide for the Business Professional –by Simchi-Levi, Kaminski,Simchi-Levi 15 x2 37
Part 1
Dallas ($260) 5 28
Part 2
Dallas ($0.5)
Part 4
Malaysia ($180) 30 30 15 15 37
Final Demand
N(100,10)
Guaranteed LT
=30 days 39 15 3 37 17
Part 5
Charleston ($12)
Part 3
Montgomery ($220) 58 29 37
Here is a real example reported in the book written by David Simchi-Levi of MIT and his colleague and his wife, Edith Simchi-Levi.
Final demand (part 1) is sold is Dallas that has a normal distribution with average 100 and standard deviation 10 and customer’s guaranteed LT is 30 days. Many parts are required to produce it and they are produced in many facilities.
By optimizing the allocation of safety inventory, they could save more than 43 thousand dollars. It’s about 40 % cost down from the baseline model. The safety stock allocation model can be usd in “what if” analysis. For example, what if we change the guaranteed lead-time to the customer from 30 days to 15 days that means an improved customer service. The model answers the question. The cost increases to 51 thousand dollars. 58 4 8
43,508$ (40%Down)
Part7
Denver ($2.5)
Part 6
Raleigh ($3)
What if analysis: Guaranteed LT=15 days ->51,136$

32. Inventory Policy Optimization
Decision support in operational/tactical level
Determine various parameters for inventory control policies
Fixed Ordering
Lost Sales
Safety Inventory
Cycle Inventory
Next we will turn our attention to another inventory model called inventory policy optimization.
Inventory policy optimization is in operational or tactical decision level.
We first introduce 2 classical models; newsboy model and economic ordering quantity model.
The newsboy model introduced by Scarf in 1960 is a framework where we optimize the trade-off between lost sales and safety inventory costs.
The EOQ model introduced by Harris in 1915 is a framework where we optimize the trade-off between fixed ordering and cycle inventory costs.
Classical Newsboy Model
Classical Economic Ordering
Quantity Model

33. Base stock Policy (Multi Period Model)
Base stock level s* ＝ target of the inventory position
Inventory (ordering) position= In-hand inventory+In-transit inventory (inventory on order) -Backorder
Base stock policy: Monitoring the inventory position in real time; if it is below the base stock level, order the amount so that it recovers the base stock level
Newsboy model can be extended to multi period model. In this case, the ending inventory at a period becomes the starting inventory in the next period.
In this case we have to monitor the inventory position that is defined as the sum of in-hand or local inventory + inventory on order (that means the amount of orders that has not been arrive yet) – backorder (that means demand not satisfied now but carried over to future).
We determine the ordering quantity so that the inventory position becomes a pre-determined value called the base stock level.

34. (Q,R) and (s,S) Policies
If the fixed ordering cost is positive, the ordering frequency must be considered explicitly.
(Q,R) policy：If the inventory position is below a re-ordering point R, order a fixed quantity Q
(s,S) policy：If the inventory position is below a re-ordering point s, order the amount so that it becomes an order-up-to level S
If the fixed ordering cost is positive, the base stock policy is no more optimal. In such a case, we need modified base stock policies namely (Q,R) policy and (s,S) policy. In (Q,R) policy, we monitor the inventory position and if it reaches a re-order point R, we order a fixed quantity Q. Here R and Q are system parameters. We may use EOQ model to compute the ordering quantity Q.
In (s,S) policy, we again monitor the inventory position and if it is below a re-ordering point small s, we order the amount so that the inventory position becomes an order-up-to level capital S.

35. (Q,R) Policy and (s,S) Policy
R+Q
(=S)
Lead time
Inventory position
(s,S)
(Q,R)
R (=s)
This figure shows the inventory levels of (Q,R) and (s,S) policies. Here is a re-order point R (or small s) and here is the order-up-to level Q+R or capital S. When the inventory position becomes R, both policies order the amount Q and the inventory position becomes R+Q or S.
After the lead time, the order arrives and the in-hand inventory increases and coincides with the inventory position.
If the bulk demand occurs and the system orders below the re-order point, the (Q,R) policy orders Q while the (s,S) policy orders more so that the inventory position becomes capital S.
Under some reasonable assumptions, (s,S) policy is proved to be optimal.
But i believe (Q,R) policy is more practical in Japan ‘cause ordering lot is fixed in many situations.
In-hand inventory
Time

36. Periodic Ordering Policy
Check the inventory position periodically; if it is below the base stock level, order the amount so that it recovers the base stock level
Order
Mon.
Tue.
Wed.
Thu.
In the base stock or (Q,R) or (s,S) policies, we treat the time as continuous variable. But in many situations the timing of decisions is restricted to a discrete time. In such cases, discrete time model is more appropriate.
We now turn our attention to the discrete time inventory model, namely the periodic ordering policy.
In this policy, we check the inventory periodically, say once a day. If the inventory position is below the base stock level, we order the amount so that it recovers the base stock level. We assume the demand occurs during the day, and the ordering quantity is determined at the end of the day, and the order arrives at the beginning of the day after the lead time.
Demand
L=1
Arrival of the order of Mon.（Lead time L＝１day）

37. Algorithms for Inv. Policy Opt.
base stock，(Q,R)， and (s,S) policies ->Dynamic Programming Recursion
Periodic ordering policy -> Infinitesimal Perturbation Analysis During simulation runs, derivatives of the cost function are estimated and are used in non-linear optimization
We have talked about the inventory policy optimization. For the continuous time models, we get the optimal base stock via dynamic programming and we can get similar algorithms for (Q,R) and (s,S) policies.
For the discrete time model, called the periodic order policy model, we used a simulation based optimization algorithm. Such an approach is called the infinitesimal perturbation analysis. I believe this approach will be one of the candidates for solving real inventory problems.

38. Lot-size Optimization
Decision support in tactical level
Optimize the trade-off between set-up cost and lot-size inventory
Setup Cost
Lot-size Inv.
Next we consider a model in production planning. The first model is the lot-size optimization model.
This model supports the decision maker in tactical level and optimizes the trade-off between the set-up cost and lot-size inventory.
This model can be seen as an extension of the EOQ model in which the customer demand is not constant.

39. Algorithms for Lot-sizing
MIP solver with strong forumulation
(Meta)heuristics
Metaheuristics using MIP solver
Relax and Fix
Capacity scaling
ＭＩＰ based neighborhood local search
To solve the real lot-sizing problems is very difficult.
One approach is to use the MIP solver using strong formulation.
Another approach is to construct heuristics or meta-heuristics.
The other approach is the MIP-based meta-heuristics. The example of such approaches are: The relax and fix, capacity scaling, and MIP based neighborhood local search.

40. Scheduling Optimization
Decision support in operational level
Optimization of the allocation of activities (jobs, tasks) over time under finite resources (such as machines)
Time 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Machine 1
Next we consider the second model in production planning. That is the scheduling optimization model.
This model supports the decision maker in operational level and optimizes the allocation of activities, which are jobs or tasks or operations to be executed (represented by rectangles in this figure), over time under the constraints of finite resources (in this example, we have 3 machines as finite resources).
Machine 2
Machine 3

41. What is Scheduling? Allocation of activities (jobs, tasks) over time
Resource constraints. For example, machines, workers, raw material, etc. may be scare resources.　
Precedence relation. For example., some activities cannot start unless other activities finish.
Time 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Machine 1
The key concepts of the scheduling optimization are the activities and resources.
There are many resources in production lines; machines, workers, raw materials, or money can be seen as scare resources.
The scheduling must satisfy some precedence constraints between activities. In this example the red activities have to be
executed in this order. The red activity on machine 2 cannot start unless the red activity on machine 3, and also
the red activity on machine 1 cannot start before the finish time of the red activity on machine 2.
Machine 2
Machine 3

42. Solution Methods for Scheduling
Myopic heuristics
Active schedule generation scheme
Non-delay schedule generation scheme
Dispatching rules
Constraint programming
Metaheuristics
The history of the scheduling theory is long; many researcher have been proposed a number of algorithms.
The first category of algorithms is myopic heuristic algorithms such as active scheduling scheme, non-day scheduling scheme, or dispatching rules. Such heuristic algorithms are heavily used in practice. Constraint programming and metaheuristic approaches are well-studied recently.

43. Vehicle Routing Optimization
Depot
Customers
Routes
earliest time
latest time
Customer
waiting
time
service time
Finally, I’ll show the model for transportation and delivery named the vehicle routing problem.
The vehicle routing occurs at the final part of the SC; the distribution from a depot to customers. Customers have to be served by a fleet of vehicles with a limited capacity. The vehicles are initially located at a given depot. The objective is to find a set of routes for the customers and returns to the depot without violating the capacity constraint. In many distribution systems, each customer specifies the load volume to be delivered and a period of time, called a time window, that specifies the earliest and latest service start time.
service time

44. Algorithms for Vehicle Routing
Saving (Clarke-Wright) method
Sweep (Gillet-Miller) method
Insertion method
Local Search
Metaheuristics
As in the scheduling problem, many algorithms have been proposed for the vehicle routing problem. The classical approaches are:
the saving method by Clarke and Wright, the sweep method by Gillet and Miller, Insertion method, and local search.
Recently many mataheuristic algorithms are used for solving difficult real problems.

45. History of Algorithms for Vehicle Routing Problem
Approximate Algorithm
Genetic Algorithm
AMP
(Adaptive Memory
Programming)
Tabu Search
Local Search
Simulated Annealing
Sweep
Method
Generalized
Assignment
Location Based
Heuristics
Route Selection
Heuristics
GRASP
(Greedy Randomized
Adaptive Search Procedure)
Construction Method
(Saving, Insertion)
Hierarchical
Building Block
Method
This figure shows the family tree of the vehicle routing algorithms.
in 1970 or before, many ad hoc methods have been proposed such as saving, insertion, sweep, and local search.
Local search is brushed up to metaheuristics such as tabu search, simulated annealing, and then more general adaptive memory programming
that also includes genetic algorithm as a special case.
Sweep method that can be seen as a cluster-first route second approach is refined to generalized assignment heuristics, location based heuristics that is proved to be asymptotically optimal under some assumptions.
Saving and insertion methods that can be sees as a construction algorithm. They have a descendant named GRASP that is a construction type metaheuristics. And we have another branch of exact algorithms.
These algorithms are unified to the hierarchical building block method proposed by me.
Exact Algorithm
Set Partitioning Approach
State Space Relax.
Cutting Plane
K-Tree Relax.
1970
1980
1990
2000

46. Supply Chain “Risk” Management
Proactive and response approaches to cope with supply chain disruptions.
Performance
Disruption
Recovery
Recently, we Japanese had a large disruption caused by an earthquake, and then Tsunami, and finally an explosion of nuclear plants in Fukushima.
Many supply chains are stopped; so we recognized supply chains should be not only efficient
but also robust with respect to such disruptions.
Supply Chain Risk Management (SCRM) is a new area of SCM to copy with the supply chain disruptions.
This figure represents the change of the performance of a supply chain before and after a disruption event.
The action before the disruption is called “proactive” , while the action after the disruption is called “response”.
Our aim is to use the supply chain optimization models so that the supply chain becomes robust w.r.t the disruption and recovers quickly after the disruption.
Proactive
Response
Time

47. Importance of Supply Chain “Risk”
Increase of disasters
Natural disasters: earthquake, tsunami, SARS (Severe Acute Respiratory Syndrome), BSE (Bovine Spongiform Encephalopathy), hurricanes, cyclones and typhoons, floods, droughts, volcanic eruption, famine and food insecurity, etc.
Man-made disasters: terrorist attack, CBRNE (Chemical Biological, Radiological, Nuclear, Explosive) disaster, war, strike, riot, etc.
Lean supply chain: increases vulnerability.
Globalization: induces long lead time, outsourcing.
The SCRM has been becoming important recently. There are many reasons. The first one is the increase of disasters. These 10 years, we –human beings- encountered many disasters.
Examples of natural disasters are:earthquake, tsunami, SARS, BSE, hurricanes, cyclones and typhoons, floods, droughts, volcanic eruption, famine and food insecurity, etc.
Man-made disasters are: terrorist attack, CBRNE disaster, war, strike, riot, etc.
The other reasons are the trend in SCM such as lean SC and globalization of SC.
The lean system makes the inventory low, so increases vulnerability of the SC, while
globalization makes the lead time longer and the trend of outsourcing makes the supply un-stable.

48. Related Area Risk Management
Business Continuity Planning (BCP)/ Business Continuity Management (BCM) But, both did not work well …
Humanitarian Logistics / Humanitarian Supply Chain
Two communities of business management and consulting are closely related to SCRM.
One is the risk management that is defied as the identification, assessment, and prioritization of risks.
Another is the Business Continuity Planning whose objective is to write a thick manual.
But, unfortunately, a series of disasters in Japan proved that both did not work well, or useless.
More important related area is the humanitarian logistics.

49. Humanitarian Logistics / Humanitarian Supply Chain
… is a branch of logistics which specializes in organizing the delivery and warehousing of supplies during natural disasters to the affected area and people.
Decentralized
No SCM unit nor trained staffs
Everything is ad hoc
No performance measure (fairness, speed, …)
No information & communication technology
Many players (government, NGOs)
Humanitarian Logistics can be defied as a branch of logistics which specializes in organizing the delivery and warehousing of supplies during natural disasters to the affected area and people.
It is different from the usual (commercial) logistics with respect to the following points.
It is decentralized and there are many players (government, self defense force, NGOs).
And No SCM unit nor trained staffs
Everything is ad hoc
No performance measure (fairness, speed, …)
No information & communication technology

50. Risk Mapping Regular risk : demand/supply uncertainty
Irregular risk : disruption / disaster
Frequency
Strike
Line Stop
Exchange Rate
Supply Delay
To cope with risks, we have to classify them.
The first approach named risk mapping classifies risks into 2-dimensional space;
That is usually used in risk management.
The horizontal axes is the impact of risks, while the vertical axis represents the frequency of risks.
This figure shows a risk mapping of an imaginary company.
For example. this company categorized typhoon and earthquake into the area that
has large impact but rare.
This red area represents that the impact is large and high frequency.
That includes strike and the fluctuation of exchange rate.
This yellow area represents that the impact is small but frequency is high.
That includes line stops in the plant and supply delay.
This white zone is that both the impact and frequency is small.
Typhoon
Defective Product
Earthquake
Impact

51. Risk Classification (1)
Plant
Warehouse
Supply Risk
Demand Risk
Transportation
Resource
Production
Line
Risks can be classified into supply, internal and demand risks.
Environmental risk is outside of the corresponding SC.
Internal Risk
Environmental Risk

52. Risk Classification (2)
Disaster risk: natural and man-made disasters such as landslides, volcanic eruption, drought, asteroid impacts
Political risk: contracts, laws, regulations
Social risk: child labor / abuse
Intellectual property risk: patents, trademarks, copyrights
Financial risk, employment risk, reputation risk, ...
Another classification.
Disaster risk that is caused by natural and man-made disasters
Political risk that is caused by contracts, laws, regulations
Social risk such as child labor / abuse
Intellectual property risk related to patents, trademarks, copyrights
Example of other types of risks are:
Financial risk, employment risk, reputation risk, …

53. Strategies to Cope with Risk
Accept: just do nothing!
Avoid: remove the risk factor, if possible
Transfer: insurance, option
Alignment: share risk and profit by contract
Strengthen: make the SC robust, resilient, redundant, flexible, …
Strategies to copy with risks are:
Accept the risk and do nothing.
2) Avoid the risk factor, if possible,
3) Transfer the risk using insurance or option
4) Alignment that means share risk with other SC partners by contract,
5) Or, finally, strengthen the supply chain, by adding desirable properties to the SC.

54. Strengthen Strategies
Proactive
Robustness
Resiliency
Redundancy
Flexibility
Compatibility
Response
Agility
Visibility
Performance
Disruption
Robustness
Such desirable properties to strengthen the SC are:
robustness,
resiliency,
redundancy,
flexibility,
compatibility for proactive strategies,
and agility and visibility for response strategies.
Such technical terms are not well-defied and sometimes called BUZZWORDS.
We propose the robustness is defied as the depth of the valley.
The time resiliency is the duration between the disruption and recovery.
The performance resiliency is the percentage of the performance recovery.
Performance
Resiliency
Time Resiliency
Proactive
Response
Time

55. Redundancy -Strategic Inventory-
Inventory for supply (or production) disruptions.
That is shared by many supply chain partners.
We have to distinguish it with the safety stock to copy with demand uncertainty.
An example of redundancy is the strategic inventory that is the inventory for preparing the disruption.
Also it is shard by many SC partners. Remark that it must be considered separately to the safety stock that is for
the demand uncertainty.

56. Flexibility of Sourcing -Multiple Sourcing Strategy-
Plant
Supplier
Single sourcing
Supplier A
Plant
Dual sourcing
Supplier B
(Contract)
A concrete example of flexibility is the multiple sourcing strategy
that procures from two or more suppliers. Make-and-buy strategy can be seen as another type of multiple sourcing.
Remark that these two suppliers should not be located in the same area. Otherwise, both suppliers may be down. or
Plant
Supplier
Make-and-buy

57. Flexible Production Strategy
1-flexibility
2-flexibility
Full-flexibility
This is another concrete example of flexibility called the process flexibility.
If each plant can produce exactly one products, it is called 1-flex.
If each plant can produce 2 products like this, it is called 2-flex.
Graves and Tomlin at MIT show that 2-flex has the similar performance as Full-flexibility
that means each plant can produce all the products.
But recent simulation study shows that it is not true when the supply disrupts.
Graves-Tomlin: 2-flex. is enough for demand uncertainty, i.e., flex. has the similar performance with full-flex. Simulation : 2-flex. is NOT enough for supply uncertainty.

58. Flexible Transportation Strategy
Multi-mode
Multi-carrier
The other types of flexibility is transportation flexibility. That is multi-mode (that means using ship and air) ,
multi-carrier (that means using DHL and UPS) and also
multi-route (that means using ship for the south coast (and then using ground transportation) and via Panama channel).
Multi-route

59. Compatibility Risk Pooling Delayed Differentiation / Postponement
An example of compatibility is the risk pooling strategy that is very common in modern SC.
Before the Earthquake in Japan, we Japanese had too many types of caps of the bottles.
After the Earthquake, caps became a bottleneck to produce bottles. So Japanese beverage makers recognized that
the compatibility is important and switched to produce the white cap only.

60. Coping Strategies / Risk Mapping
Reduce Probability
Frequency
Robustness
by PM
Strike
Avoid
Line Stop
Exchange Rate
Visibility
Alignment
Transfer
Supply Delay
Typhoon
Redundancy
Robustness
by KAIZEN/
TQC
Defective
Product
Using the strategies to copy with risks, we can avoid, transfer and reduce the impact and probability of the risks.
Earthquake
Flexibility
Impact
Reduce Impact

61. Supply Chain “Risk” Optimization
What If Analysis
Stochastic Programming (Scenario Approach)
Here & Now
Variables
Recourse Variables
Disruption
Performance
Scheduling
Vehicle Routing
Transportation
(Operational)
We can also use optimization techniques to the SCRM.
Basically we can apply all the SC optimization models using what if analysis.
For proactive decisions, strategic and tactical models are useful.
For response decisions, we use operational models such as scheduling, transportation and vehicle routing models.
If you want to model both decisions simultaneously, we need to use the framework of stochastic programming
in which decisions before the disruption is modeled as here and now variables, while
decisions after the disruption is modeled as recourse variables.
Logistics Network Design
Safety Stock Allocation
(Strategic, Tactical)
Proactive
Response
Time

62. Optimization Models for SCRM
Stochastic /Robust
Extensions
Dynamic Pricing
Logistics Network Design
Strategic
Sourcing Decision
Multi-period Logistics Network Design
Inventory
Safety stock allocation
Inventory policy
optimization
Production
Lot-sizing
Scheduling
Transportation
Delivery
Vehicle Routing
Tactical
We have developed many SC optimization systems; we are now extending them for the SCRM.
For example, LND should be extended using stochastic and robust optimization framework.
Safety stock allocation model is extended by incorporating sourcing decision.
We are also developing quick and dirty solution system for the vehicle routing problem without using ITs.
We wish such a non-IT system can be used in humanitarian logistics for last-mile delivery.
Anyway, much remains to be done in this are. Thanks for your attention.
Operational
Quick Solution without IT