Problems Solutions in Inventory Management (Dinesh Shenoy, Roberto Rosas)

BOOK LINK:

Here is a summary of the key points from “Problems & Solutions in Inventory Management” by Dinesh Shenoy and Roberto Rosas:

The book covers basic inventory management concepts including inventory definitions, functions, costs, and control systems. It then discusses various mathematical models for single-item and multi-item inventory problems.
Case studies and examples are presented throughout to demonstrate concepts. The running case study is on inventory management at Rosettas Tortilleria.
Part 1 covers introduction to inventory management and inventory control systems/design factors like review frequency, order timing/size. It also discusses holding, ordering and shortage costs.
Part 2 focuses on single-item models like items with deterministic/dynamic/time-varying demand and stochastic models. It includes over 40 solved problems.
Part 3 deals with multi-item models under budget/space/order constraints and covers coordinated replenishment.
Part 4 discusses advanced models for perishable/style items, maintenance inventory and multi-echelon systems.
The book uses simple language and matches theory with numerical examples to make concepts accessible for undergraduate business/industrial engineering students.

Perishable Items Inventory … … … … … … . .

248

9.8

Practice Problems … … … … … … … … … … … .

248

References … … … … … … … … … … … … … … . .

250

Inventory Models with Advance Demand Information … … …

251

10.1

Introduction … … … … … … … … … … … … . .

251

10.2

Types of Advance Demand Information … … … … … …

252

10.3

Models with Probabilistic Advance Demand Information … . .

253

10.3.1 Predictive Distribution Information … … … … . .

254

10.3.2 Finite Lead Time with Predictive Distribution

10.4

Information … … … … … … … … … … .

257

Models with Definite Advance Demand Information … … …

260

10.4.1 Definite Advance Demand Information over a Single Period 260 10.4.2 Definite Advance Demand Information Over

Multiple Periods … … … … … … … … … .

263

10.5

Special Cases … … … … … … … … … … … … .

269

10.6

Summary … … … … … … … … … … … … … .

271

10.7

Case Study – Future Demand Forecast … … … … … … .

272

10.8

Practice Problems … … … … … … … … … … … .

273

References … … … … … … … … … … … … … … . .

274

Multi-echelon Inventory Systems … … … … … … … … …

277

11.1

Introduction … … … … … … … … … … … … . .

277

11.2

Two-echelon Inventory Systems … … … … … … … …

278

11.2.1 Single Warehouse-Retailer System … … … … …

278

11.2.2 Multi-Retailer System … … … … … … … …

284

11.3

Multi-echelon Inventory Systems … … … … … … … . .

288

11.4

Centralized Vs Decentralized Decision Making … … … … .

292

11.5

Bullwhip Effect in Supply Chains … … … … … … … .

293

11.6

Mitigating the Bullwhip Effect … … … … … … … … .

296

11.7

Summary … … … … … … … … … … … … … .

299

11.8

Case Study – Supply Chain Inventory Management … … … .

299

11.9

Practice Problems … … … … … … … … … … … .

301

References … … … … … … … … … … … … … … . .

303

Part V

Advanced Case Studies

Case Study – Inventory Management at Sears Automotive

307

12.1

Background … … … … … … … … … … … … . .

307

12.2

OEM Replenishment System … … … … … … … … . .

308

12.3

Aftermarket Replenishment System … … … … … … …

309

12.4

Challenges … … … … … … … … … … … … …

310

12.5

Proposed Solutions … … … … … … … … … … …

311

12.6

Implementation Plan … … … … … … … … … … . .

312

12.7

Summary … … … … … … … … … … … … … .

313

References … … … … … … … … … … … … … … . .

313

xiv

Contents

Case Study - Inventory Management at Zara

315

13.1

Background … … … … … … … … … … … … . .

315

13.2

Quick Response Strategy … … … … … … … … … . .

316

13.3

Key Elements of Zara’s Inventory Management System … … .

317

13.4

Benefits of Zara’s Inventory Management System … … … . .

318

13.5

Challenges … … … … … … … … … … … … …

319

13.6

Recommendations … … … … … … … … … … … .

320

13.7

Summary … … … … … … … … … … … … … .

320

References … … … … … … … … … … … … … … . .

321

Case Study – Inventory Management at Redbull

323

14.1

Background … … … … … … … … … … … … . .

323

14.2

Current Inventory Management System … … … … … …

324

14.3

Challenges … … … … … … … … … … … … …

325

14.4

Proposed Solution … … … … … … … … … … … .

326

14.5

Key Changes … … … … … … … … … … … … . .

327

14.6

Implementation Plan … … … … … … … … … … . .

328

14.7

Summary … … … … … … … … … … … … … .

328

References … … … … … … … … … … … … … … . .

329

Case Study - Inventory Management at IKEA

331

15.1

Background … … … … … … … … … … … … . .

331

15.2

IKEA’s Inventory Management System … … … … … … .

332

15.3

Benefits of IKEA’s Approach … … … … … … … … . .

333

15.4

Challenges Faced … … … … … … … … … … … .

334

15.5

Recommendations … … … … … … … … … … … .

335

15.6

Summary … … … … … … … … … … … … … .

336

References … … … … … … … … … … … … … … . .

337

Case Study - Inventory Management at Walmart

339

16.1

Background … … … … … … … … … … … … . .

339

16.2

Walmart’s Inventory Management Approach … … … … …

340

16.3

Benefits of Walmart’s System … … … … … … … … .

341

16.4

Challenges … … … … … … … … … … … … …

342

16.5

Recommendations … … … … … … … … … … … .

342

16.6

Summary … … … … … … … … … … … … … .

343

References … … … … … … … … … … … … … … . .

344

Part VI

Inventory Management in Practice

Applications of Inventory Management

347

17.1

Applications in Manufacturing … … … … … … … … .

347

17.2

Applications in Retailing … … … … … … … … … . .

350

17.3

Applications in Health Care … … … … … … … … …

352

17.4

Applications in Transportation and Logistics … … … … …

355

17.5

Applications in Services Industries … … … … … … … .

357

Contents

17.6

Emerging Applications … … … … … … … … … … .

358

17.7

Summary … … … … … … … … … … … … … .

360

References … … … … … … … … … … … … … … . .

361

Contemporary Issues in Inventory Management

363

18.1

Omnichannel Inventory Management … … … … … … . .

363

18.2

Supply Chain Collaboration and Vendor Managed Inventory . .

367

18.3

Sustainability and Green Inventory Management … … … …

370

18.4

Big Data Analytics and Inventory Optimization … … … … .

373

18.5

Blockchain and Inventory Management … … … … … … .

376

18.6

Post-Pandemic Inventory Management Challenges … … … .

378

18.7

Summary … … … … … … … … … … … … … .

381

References … … … … … … … … … … … … … … . .

382

Simulations and Games in Inventory Management

385

19.1

Role of Simulations in Inventory Management … … … … . .

385

19.2

Beer Game … … … … … … … … … … … … …

387

19.3

Supply Chain Strategy Game … … … … … … … … . .

389

19.4

Inventory Mgmt Simulation Game … … … … … … … . .

391

19.5

Learning Outcomes … … … … … … … … … … …

393

19.6

Other Simulation Games … … … … … … … … … …

394

19.7

Summary … … … … … … … … … … …

Here are the key points about inventory functions:

Decoupling inventory detaches manufacturing processes to minimize impact of fluctuations and smoothen workflow between workstations.
Cycle inventory results from ordering materials in batches to benefit from economies of scale. The optimal batch size (order quantity) is determined based on several economic factors.
Pipeline inventory accounts for uncertainties in supply lead time as materials are not received instantly after order placement due to transportation time. It is equal to demand multiplied by lead time.
Buffer inventory acts as a safety stock to protect against uncertainties in demand and supply. It accounts for variations in demand and uncertainties in lead times.
Anticipation inventory is held to meet unexpected increase in demand or shortages due to uncertainties. It allows the organization to take advantage of sales opportunities.

So in summary, the key inventory functions are to decouple processes, achieve economies of scale in procurement, account for transportation and demand uncertainties, and enable responsiveness to opportunities. The optimal levels are determined by relevant cost and service factors.

Here is a summary of the case study:

(a) Raw materials inventory:

Agave piñas (bulbous base of the agave plant) that are procured from farms. This is the key raw material for tequila production.

(b) Work-in-process inventory:

Cut pieces of piñas that are washed, cooked, and crushed to extract the juice.
Juice extracted from the piñas that is fermented with yeast.
Partially fermented liquid in different stages (head, middle, tail) of the fermentation and settling process.
Liquid stored in wooden barrels for aging.

Aged tequila liquid that is bottled and packaged in 2L bottles. These bottles are then shipped to distributor warehouses for commercial sale.

The case study provides a good overview of the different stages and associated inventory in a complex production process like tequila manufacturing.

Here is a summary of the key sources:

D., Cochran, J. J., Fry, M. J., & Ohlmann, J. W. (2016) provides an introduction to management science and quantitative approaches to decision making. It discusses quantitative models and methods for decision making.
APICS Dictionary (2015) defines important terms and concepts related to supply chain management and operations.
Chopra, S., & Meindl, P. (2010) focuses on supply chain management strategies, planning, and operations.
Gaither (1987) addresses production and operations management with a problem-solving approach.
Harding, M., & Harding, M. L. (2001) discusses principles and practices related to purchasing.
Hill, A., & Hill, T. (2012) covers topics in operations management.
Mahadevan (2015) provides an overview of operations management theories and practices.
Naddor (1966), Silver et al. (1998), and Vrat (2014) discuss inventory management systems, planning, and related topics.
Nahmias (2005) addresses production and operations analysis.

The sources cover key aspects of management science, operations management, supply chain management, inventory management, and purchasing. They provide introductions, definitions, frameworks, and problem-solving approaches related to quantitative decision making.

Chapters 3 and 6 describe how to determine key decision variables in inventory control systems like reorder level (s), order quantity (Q), maximum inventory level (S), and time between review periods (T).
There are three main types of inventory costs: carrying costs, ordering costs, and shortage costs.
Carrying costs include costs like cost of capital, cost of storage, inventory risk costs, and inventory servicing costs. An example is given of calculating carrying costs for a vegetable vendor.
Ordering costs include administrative costs, transportation costs, inspection costs, and other costs like expediting. An example breakup of ordering costs is provided.
Formulas are provided for calculating carrying costs based on inventory carrying rate and unit cost. An example problem demonstrates calculating different types of carrying costs.
Ordering costs are typically represented by Co and can be calculated by dividing total ordering expenses by number of orders placed in a given period.

So in summary, it outlines the key decision variables, defines the different types of inventory costs, and provides examples of how to calculate carrying costs and determine an ordering cost amount.

Here is a summary of section 2.4 Ordering cost calculation from the passage:

It calculates the total annual expenditure on various expense heads that contribute to ordering costs, such as stationery, communication, salaries, transportation, etc.
It then apportions the total annual expenditure of each expense head to the ordering cost computation based on relevant weightages.
It calculates the total expenses as the sum of all apportioned costs.
Given the number of orders placed in a year, it calculates the order cost per order by dividing the total expenses by the number of orders.
In this example, the total annual expenditure is $165,245. The number of orders placed is 3406. Therefore, the order cost per order works out to be $48.5.
This provides a method to calculate the ordering costs, which is an important parameter in inventory models. The ordering cost per order estimated here can be used while applying other formulas like economic order quantity.

Here is a summary of the key points regarding how Rosetta’s manages inventory of items whose demand is uncertain:

Rosetta’s manages inventory of many items used in production, like corn flour, vegetable oil, cooking gas, etc. The stocking decisions for one item impacts the decisions for other items.
The management wants to restrict the amount of money locked up in inventory. This creates constraints on the inventory system.
The demand for many items is uncertain and can vary on a weekly or monthly basis. This makes inventory management challenging.
Analytical and graphical methods will be introduced in later chapters to help manage multiple inventory items together while accounting for constraints and uncertain demand.
Simple analytical solutions for inventory problems subject to constraints like budgets, space, and number of orders will be discussed.
Historical demand data is used to help forecast future demand and determine optimal order quantities and reorder points.
The goal is to minimize costs associated with stockouts/shortages, excess inventory carrying costs, and ordering/procurement while meeting uncertain customer demand.

So in summary, Rosetta’s faces the common inventory management challenge of dealing with uncertain demand for multiple items while operating under financial and space constraints. Analytical forecasting and optimization methods will help them address this ongoing concern.

Rosetta’s storage area is small and sometimes cannot fit all incoming materials.
The inventory strategy should be to adopt an economic order quantity (EOQ) model to determine how much vegetable oil to order in each lot.
The EOQ model aims to minimize total inventory costs by balancing ordering costs and carrying costs.
Given the information provided, the EOQ for Rosetta’s vegetable oil orders should be calculated using the EOQ formula.
Oxxa can deliver oil gradually up to 24 liters per day. So Rosetta’s should ask Oxxa to deliver the complete oil order from the EOQ calculation gradually over multiple days rather than in one large lot. This will help avoid storing excess inventory that may not fit in their storage area.

So in summary, Rosetta’s should use the EOQ model to calculate order quantities and have Oxxa gradually deliver orders over multiple days to better manage their limited storage capacity.

When replenishments occur gradually at a uniform rate rather than all at once, the EOQ model needs to be modified.
The inventory build-up rate (IBR) is the supply rate (p) minus the demand rate (d).
The maximum inventory level is the order quantity (Q) divided by the IBR.
The average inventory level incorporates the IBR.
The total inventory cost (TIC) function includes terms for ordering cost, holding cost and purchase cost, with the holding cost term modified to reflect the IBR.
Differentiating the TIC function and setting it equal to 0 yields a modified EOQ formula that incorporates the IBR (Equation 3.13).
This modified EOQ formula can be used to calculate the economic order quantity when supplies are received gradually rather than all at once, as in the example of Rosetta’s receiving vegetable oil from their supplier over time rather than in a single delivery.

Here is a summary of the key details and solutions provided in Solved Problem 3.11:

Gradual supply at

Back-ordering

25 strips/day allowed

EOQ (strips)

397

888

441

TIC ($)

183.75

82.18

165.59

The problem examined the optimal order quantity and total inventory costs for three scenarios of inventory management for strips of paracetamol tablets sold by MedPlus Pharmacy:

If the supplier provided the full order quantity instantly in one lot, with no backordering allowed.
If the supplier provided the tablets gradually at a rate of 25 strips per day.
If backordering of strips was allowed, with a shortage cost of $2 per strip per year.

The economic order quantity (EOQ) and total inventory cost (TIC) were calculated for each scenario using the appropriate EOQ model equations. The results are summarized in Table 3.3 above.

The lowest TIC of $82.18 was achieved when the supplier supplied tablets gradually at 25 strips per day. Therefore, this gradual supply approach would be preferred by MedPlus Pharmacy from an inventory cost perspective.

Here are the steps to solve this problem:

(a) Given: Demand (D) per month = 8000 units Ordering cost (Co) = $35 per order Holding cost rate (i) = $2 per unit per year

Using the EOQ formula: EOQ = √(2DCo / i) = √(2800012*$35 / $2) = 1833 units

(b) Annual ordering cost = (Orders per year) * Co = (D/EOQ) * $35 = (8000*12/1833) * $35 = $1260

(c) Annual holding cost = (Average inventory) * i * Cost per unit = (EOQ/2) * i * Cost per unit
= (1833/2) * $2/unit * year * Cost per unit = $3664

(d) TIC = Annual ordering cost + Annual holding cost
= $1260 + $3664 = $4924

(e) Cycle time = EOQ/D = 1833/8000 months = 0.23 months = 7 days

(f) Orders per year = D/EOQ * 12 months/year = (8000/1833) * 12 = 8 orders

Okay,

Rosetta’s uses large quantities of vegetable oil monthly for food production. Vegetable oil is an expensive ingredient.
Currently, Rosetta’s procures oil from a local supermarket at $20/liter on an as-needed basis.
A local supplier, Oxxa, offers Rosetta’s $19.5/liter if they order 500 liters or more.
Occasionally, Oxxa runs promotions offering a 15% discount on larger orders placed before month’s end.
The question is whether Rosetta’s should keep ordering based on their EOQ or take advantage of discounts by ordering more.
A single price-break model is used to compare the total inventory costs (TIC) of ordering at $20/liter versus $19.5/liter for 500 liters or more.
If the discount offers lower TIC, Rosetta’s should order the larger discounted amount rather than stick to their EOQ. But the discount savings must exceed additional carrying costs from a larger order.
In this example, the $19.5/liter price for 500 liters results in lower TIC, so Rosetta’s should take the discount offer. But this may not always be the case.

Does this help summarize the key points about the single price-break model and Rosetta’s situation? Let me know if you need any clarification or have additional questions.

Here is a summary of the steps to solve for the optimal order quantity in an inventory problem with quantity discounts (all-units discount model):

Compute the EOQ for each unique purchase price/discount level using the basic EOQ formula.
Check if the calculated EOQs fall within the quantity range required to receive that price. If not, adjust the EOQ to the minimum of the range.
Use the adjusted EOQs to calculate the total inventory cost (TIC) for each purchase price/discount level using the TIC equation.
Compare the TIC values and select the EOQ that corresponds to the minimum TIC as the optimal order quantity under the discount structure.

The key aspects are:

Calculate EOQ for each purchase price
Check feasibility of EOQs against quantity ranges
Adjust infeasible EOQs
Compute TIC for adjusted EOQs
Select EOQ with minimum TIC as optimal

This procedure is demonstrated through numerical examples to find the best discount level and corresponding optimal order quantity to minimize total inventory costs.

Here are the key steps to solve this incremental discount model problem:

Define the price bands and corresponding unit purchase prices based on the given discount schedule.
Express the total purchase cost C(Q) as a piecewise function based on the price bands.
Compute the average purchase price C(Q)/Q for each price band.
Compute the order quantity Q using the EOQ formula for each average purchase price.
Calculate the total inventory cost TIC for each value of Q using the formula:

TIC = DCo + QC(Q)/Q * i + DC(Q)/Q

The optimal order quantity Q* is the one that results in the minimum TIC.

So in summary - define the price bands, determine the purchase cost and average price for each band, compute the EOQ and TIC for each, and select the option with the lowest TIC. The incremental discount model follows a similar approach to the all-units discount model but accounts for the step-wise nature of the discounts.

Here is a summary of the key points about one-off, fixed-period discounts:

Suppliers sometimes offer a special, one-time discount to clear existing stock before a new stock arrives. This is usually done to manage inventory levels.
When a discount is offered, customers will typically order more than their normal Economic Order Quantity (EOQ) to take advantage of the lower costs.
The optimal order quantity under discount (Qd) is calculated using a modified formula that accounts for the discounted cost and carries inventory over the discount period.
Some key assumptions are that the discount is a one-time offer, demand remains constant over the discount period, and items are not perishable.
Calculating Qd allows the customer to determine how much extra inventory to order under the discount to minimize total costs over the discount period and beyond.
This discount modeling approach provides a way for suppliers and customers to cooperate on inventory management through special promotional discounts. It helps both parties optimize costs.

So in summary, one-off discounts incentivize customers to order more than usual, which helps suppliers manage inventory levels, while customers benefit from lower average costs over the discount period. The model determines the optimal order amount under these short-term discounted conditions.

Here are the steps to solve this problem:

Calculate the EOQ without discount:

√(2 * Annual demand * Ordering cost) / Carrying cost rate √(2 * 1200 * $20) / 0.15 = 240

The supplier offers the following price discounts:

Order quantity Price per unit 0-400 $5 401-800 $4.75
801-above $4.50

Calculate the TIC for each price bracket:

a) 0-400 units Order quantity = 400 Ordering cost = $20 Carrying cost = 400 * $5 * 0.15 = $120 Purchase cost = 400 * $5 = $2000 TIC = $20 + $120 + $2000 = $2140

b) 401-800 units
Order quantity = 800 Ordering cost = $20
Carrying cost = 800 * $4.75 * 0.15 = $240 Purchase cost = 800 * $4.75 = $3800 TIC = $20 + $240 + $3800 = $4060

c) 801 units and above Order quantity = 1200 Ordering cost = $20 Carrying cost = 1200 * $4.50 * 0.15 = $360 Purchase cost = 1200 * $4.50 = $5400 TIC = $20 + $360 + $5400 = $5780

The optimal order quantity that minimizes the TIC is 400 units, with a TIC of $2140.

So the feasible and optimal order quantity is 400 units.

Using the lot-for-lot method, the solution is as follows:

Month 1: Order: 32 units Ordering cost: $40 Average inventory: 32/2 = 16 units
Holding cost: 16 * $1.5 = $24 Total cost: $40 + $24 = $64

Month 2: Order: 19 units
Ordering cost: $40 Average inventory: 19/2 = 9.5 units Holding cost: 9.5 * $1.5 = $14.3
Total cost: $40 + $14.3 = $54.3

Month 3: Order: 12 units Ordering cost: $40 Average inventory: 12/2 = 6 units Holding cost: 6 * $1.5 = $9 Total cost: $40 + $9 = $49

Month 4: Order: 15 units Ordering cost: $40 Average inventory: 15/2 = 7.5 units
Holding cost: 7.5 * $1.5 = $11.3 Total cost: $40 + $11.3 = $51.3

Month 5:
Order: 23 units Ordering cost: $40 Average inventory: 23/2 = 11.5 units Holding cost: 11.5 * $1.5 = $17.3 Total cost: $40 + $17.3 = $57.3

Month 6: Order: 12 units Ordering cost: $40 Average inventory: 12/2 = 6 units Holding cost: 6 * $1.5 = $9 Total cost: $40 + $9 = $49

Total inventory cost = $64 + $54.3 + $49 + $51.3 + $57.3 + $49 = $324.8

Therefore, using the lot-for-lot method, the total inventory cost is $324.8

The part-period balancing (PPB) lot-sizing heuristic calculates the holding costs as a function of the order horizon (number of periods an order spans).
It iteratively calculates the total holding cost over different order horizons and checks which horizon has a holding cost closest to the ordering cost. The optimal order quantity is the one for that horizon.
The example applies PPB to a problem with monthly demand over 6 months. It iteratively calculates total holding costs and closeness factors (difference between holding and ordering costs) for different order horizons and identifies the optimal order quantities and horizons.
The optimal solution from the example involves placing separate orders in January (36 units), February (60 units) and March (85 units) to meet demand in the individual months, as these horizons had the lowest closeness factors at each step.
PPB is a heuristic that balances ordering and holding costs to determine good, though not necessarily optimal, lot sizes in a multi-period production planning problem.

Here is a summary of the steps using the Silver-Meal heuristic to solve the lot sizing problem:

The demands for each month are: 36, 60, 85, 11, 39, 75 units
Ordering cost is $80 per order
Holding cost is $1.75 per unit per month

Iteration 1:

Place an order of 36 units in January to meet January demand
Total inventory cost = $80 + $31.50 holding cost = $111.50
PPC (per period cost) = Total cost / 1 period = $111.50

Iteration 2:

Place an order of 96 units in January to meet January (36 units) and February (60 units) demand
Total inventory cost = $80 + $83 holding cost = $163
PPC = Total cost / 2 periods = $81.50

Continue evaluating order horizons until the end is reached, choosing the horizon with the lowest PPC each time. The optimal solution and total inventory cost is determined.

In summary, the Silver-Meal heuristic minimizes the total relevant costs per unit time by evaluating different order horizons and choosing the one with the lowest per period cost.

Here is a summary of the key points regarding rred:

The Silver-Meal heuristic is used to determine the optimal lot sizing and order quantity. It involves sequentially testing different order horizons and choosing the one with the lowest per period cost (PPC).
Iterations are done by initially considering a single period, then combining periods sequentially until the PPC increases.
Costs considered are ordering cost of $80 per order and holding cost of $1.75 per unit per period.
PPC is calculated by dividing the total inventory cost over the number of periods in the order horizon.
The example analyzes the demands from January to June and determines that the optimal solution is to place a single order of 96 units at the start of March to fulfill demands of March and April, as this horizon has the lowest PPC.
Subsequent iterations where more periods are combined or a single period is considered individually have higher PPC, validating the March-April order horizon as the best solution according to the Silver-Meal heuristic.
The problem is to determine the optimal lot sizes and total inventory cost for a 6 month planning horizon using the Silver-Meal heuristic and least unit cost heuristic.
Under the Silver-Meal heuristic, the demands are batched incrementally into order horizons to minimize the per period cost (PPC). The optimal solution has orders of 63 units for months 1-3, 15 units for month 4, and 35 units for months 5-6, with a total inventory cost of $287.25.
Under the least unit cost heuristic, orders are batched to minimize the per unit cost (PUC). Iterations are done by increasing the order horizon and calculating the PUC. The optimal solution batches demands for months 1-3 in one order of 181 units placed in month 1.
Both heuristics provide a step-by-step process to determine order quantities that minimize costs over the planning horizon, with the Silver-Meal using PPC and least unit cost using PUC as the criteria to evaluate batching alternatives.
The problem involves calculating the optimal order quantities and production schedule over multiple periods (months) to minimize total inventory costs.
Demand and costs for each month (January to June) are given. Costs include a fixed ordering cost of $80 per order and a holding cost of $1.75 per unit per month.
A heuristic approach is used, starting with orders to meet one month’s demand and then incrementally combining demands of additional months.
Various ordering strategies are evaluated by calculating total inventory costs and per unit costs for each.
The optimal solution found after multiple iterations was to place a single order of 96 units in January to meet demands of January and February. This resulted in the lowest per unit cost of $2.802.
Higher ordering frequencies or more units per order led to higher holding costs and per unit costs based on the cost parameters provided.

So in summary, the heuristic approach identified the optimal production/ordering schedule to minimize total inventory costs given the demand and cost inputs over the 6 month period.

Here is a summary of the Wagner-Whitin Heuristic solution to the given lot sizing problem:

The planning horizon is 6 months, with monthly demand given. Holding cost is $1.75 per unit per month and ordering cost is $80 per order.
The algorithm solves the problem sequentially month by month using a forward recursive approach.
In Iteration 1, the optimal solution is to order 36 units to meet January demand, with a total cost of $111.50.
In Iteration 2, the optimal solution is to order separately for January (36 units) and February (60 units), with a total cost of $244.
In Iteration 3, the optimal solution is to order separately for January (36 units), February (60 units), and March (85 units), with a total cost of $354.50.
The algorithm continues solving iteratively for the remaining months until it finds the optimal solution for the entire 6 month planning horizon.

The key aspects of the Wagner-Whitin Heuristic are that it considers all ordering options month by month and selects the one with the lowest total inventory cost at each step through a forward recursive approach. This helps determine the optimal lot sizes and ordering plan for the full planning period.

The objective is to determine the optimal way to meet demand from January through May in a way that minimizes total inventory costs.
Five options are considered: 1) Place one order in January for all months, 2) Place order for January individually and February for remaining months, 3) Place order for January/February individually and March for remaining months, 4) Place order for January/February/March individually and April for remaining months, 5) Place order for January/February/March/April individually and May individually
For each option, the ordering and holding costs are calculated. Holding cost is based on average monthly inventory levels.
The costs for each option are compiled in Tables 5.12 and 5.13.
By comparing the total costs, Option 3 is found to be optimal both in Iteration 4 (covering demand through April) and Iteration 5 (covering demand through May).
Option 3 involves placing individual optimal orders for January/February and then ordering for the remaining consecutive months together in the next period (e.g. March order for March/April, April order for May).
This iterative approach determines the lowest cost solution for multi-period lot sizing problems by breaking it down month-by-month.

(a) The total inventory costs for the current Lot-for-Lot ordering policy is computed below:

Month Order Qty Holding Cost ($) Order Cost ($) Total Cost ($) January 18 22.5 60 82.5 February 12 15 60 75
March 16 20 60 80 April 19 23.75 60 83.75 May 21 26.25 60 86.25 June 11 13.75 60 71.75 Total 481

(b) Apply the Part-Period Balancing (PPB) heuristic to determine a better ordering policy for Promantia. Show the computation in a tabular format similar to above. (Answer shown in Table 5.17)

(b) Applying the Part-Period Balancing (PPB) heuristic:

Order 18 units in January to cover January demand
Holding cost = 18 * $2.5 = $22.5
Ordering cost = $60
Closeness factor = Holding cost - Ordering cost = $22.5 - $60 = -$37.5
Since closeness factor is negative, continue with PPB to next period
Demand from Feb to June = 12 + 16 + 19 + 21 + 11 = 79 units
Order 79 units in February to cover Feb to June demand
Holding cost = 79 * $2.5 * 5 months = $197.5
Ordering cost = $60
Closeness factor = $197.5 - $60 = $137.5
Since closeness factor is positive, this is the optimal solution.

5.4

Case Study – Finishing School for Investment Bankers

140

Total inventory cost using PPB heuristic = Ordering cost for January (18 units) = $60 Holding cost for January = 18 * $2.5 = $22.5 Ordering cost for February (79 units) = $60
Holding cost for February to June = 79 * $2.5 * 5 months = $197.5 Total inventory cost = $60 + $22.5 + $60 + $197.5 = $340

(d) Recommend the best ordering policy for Promantia based on your analysis.

Based on the analysis, the Part-Period Balancing (PPB) heuristic provides a better ordering policy with lower total inventory costs of $340 compared to $481 under the current Lot-for-Lot policy.

Hence, I would recommend Promantia adopt the PPB heuristic and place two orders - one for 18 units in January and another for 79 units in February to cover the demand from February to June. This results in significant savings of $141 compared to their current approach.

Here are the key points about Karla’s suggestion for using the ratio-based closeness factor rather than absolute numbers in the part-period balancing heuristic:

The ratio-based closeness factor (Cr) is the ratio of ordering cost (Co) to total holding cost of an order horizon (ΣC h).
The optimal order horizon is chosen such that the Cr is closest to 1, rather than the total holding cost being closest to the ordering cost.
Using this ratio-based approach on Rosetta’s example problem, the total inventory cost works out to be $761.01.
This is higher than the $680.25 cost obtained using the original part-period balancing heuristic.
So while Karla’s suggestion of using a ratio has theoretical merit, in this practical example it results in a higher total inventory cost compared to the standard approach.
Managers would need to test both approaches on their actual demand and cost data to see which one performs better for their specific situation. There is no single best method that applies universally.

So in summary, Karla’s ratio-based variant of the part-period balancing heuristic increases the cost in this example, but may produce better results for some other demand patterns and cost structures. Testing on real data is important.

Given:

Average demand (D): Median of demand distribution = 500 units Inventory carrying rate (i): 20% per year = 0.20 Cost per unit (C): $50 Lead time: 1 week Service level required: 85%

From the cumulative distribution plot, demand corresponding to 85th percentile is 720 units.

Safety stock (SSsl) = Demand at service level - Average demand = 720 - 500 = 220 units

Cost of safety stock (Css) = i x C x SSsl
= 0.20 x $50 x 220 = $4,400

Therefore, the safety stock is 220 units and the inventory carrying cost is $4,400.

Here is a summary of key points if the manufacturer desires service levels of 85% and 95%:

For a service level of 85%:
Calculate the reorder level (s) using the average demand, lead time, and z-value corresponding to 85% service level from the normal distribution function.
Calculate the safety stock (SS) as the difference between the reorder level (s) and the average demand.
The safety stock provides the extra inventory needed above the average demand to achieve an 85% service level.
For a service level of 95%:
Follow the same steps as above but use the z-value corresponding to 95% service level from the normal distribution function.
This will result in a higher reorder level (s) and larger safety stock (SS) compared to the 85% service level, as a 95% service level requires carrying more excess inventory.

In summary, to achieve different service levels, the reorder level and safety stock are adjusted using the normal distribution and z-values that correspond to the desired cumulative probability/service level. A higher service level requires carrying more excess inventory in the form of a larger safety stock.

Here is a summary of key points about determining the safety stock level when demand period is less than lead time:

If the demand period (e.g. daily demand) is smaller than the lead time, use Equation 6.6 to calculate the standard deviation of lead time demand. Equation 6.6 takes the square root of the sum of the variances of individual demand periods that make up the lead time.
Once the standard deviation of lead time demand is known, use Equation 6.4 to calculate the reorder level. Equation 6.4 adds the mean lead time demand to the standard normal variate corresponding to the desired service level multiplied by the standard deviation of lead time demand.
The standard normal variate is obtained from the normal distribution function and corresponds to the desired probability of not stocking out during lead time. A service level of 85% corresponds to a z-score of 1.04.
Worked examples are provided to demonstrate calculating the reorder level, fill rate, and safety stock needed to achieve a higher fill rate using the given equations.
Key data needed includes the mean and standard deviation of demand, lead time, desired service level, and whether demand period is greater or less than lead time to determine which equation to use.

So in summary, Equation 6.6 is used to calculate the standard deviation of lead time demand when demand period is less than lead time, and this is then used along with other data in Equation 6.4 to determine the reorder level.

Here is a summary of the key points about reorder level models with variable demand and lead time:

The reorder level (s) accounts for the average demand during lead time (d L) plus a safety stock component to protect against variability.
With only demand variable, s = d L + zσd L, where z is the standard normal variate and σd L is the standard deviation of demand during lead time.
With only lead time variable, s = d L + zdσL, where σL is the standard deviation of lead time.
With both demand and lead time variable, s is calculated using the square root of the combined variability:

s = d L + z√(σ2L + σd2/dL)

Periodic review models calculate order quantities (Q) and maximum inventory levels (S) based on anticipated demand over the review period plus lead time.
Q and S account for average demand (d(T+L)) plus a safety stock component (zσd(T+L)) to achieve a target service level.
Safety stock (SS) can be calculated separately as the safety stock component (zσd(T+L)) to maintain inventory levels between s and S.

So in summary, reorder level models use statistical techniques to set order points that balance anticipated demand against variability in demand and/or lead times to achieve target service levels.

Here are the key steps Juan can take to improve his inventory management using stochastic models:

Analyze historical demand data to determine the demand pattern. Fit it to a probability distribution (e.g. normal) and estimate the mean and standard deviation. This will help determine the safety stock.
Determine the review period using the economic order quantity model. Since lead time is constant, he can use a continuous review model.
Use the normal distribution assumptions to calculate safety stock and order-up-to level based on his desired service level using appropriate equations from the chapter.
Place orders of varying size after each review to maintain the inventory at the order-up-to level. The order size will fluctuate depending on the inventory position.
Continuously monitor demand and replenishment cycle performance. Update the model parameters as needed based on new data.
Communicate the changes to his supplier to ensure reliable fulfillment as per the updated cycle.

This will help Juan make data-driven decisions, maintain high service levels while optimizing costs through economic order quantities and safety stocks. Over time, it can improve profitability and competitiveness of his trading business. Proper inventory management is key for him given the global nature of his operations.

Juan owns a trading business that sources motors for various global brands. Six years after starting the business, it has grown significantly and supplies several large brands.
Being in the business for six years has taught Juan the importance of efficient inventory management. He wants to minimize stockouts while understanding he cannot meet every customer demand.
Juan analyzes sales data for a fast-moving motor model (FHPX3) over the past three years to improve his inventory management system. The table shows monthly sales figures.
Juan realizes individual item management is not optimal and wants to set up a continuous review system. He incurs $150 ordering costs and uses a 25% annual carrying cost.
The case study questions involve analyzing the FHPX3 motor data to determine average inventory, safety stock for 90% cycle service level, and reorder level assuming demand is normal with mean 300 and standard deviation 80 units and 1 month lead time.
Juan is taking steps to implement scientific inventory management techniques to support his growing business and large brand customers while minimizing stockouts and inventory costs.
Rosetta’s is considering ordering vegetable oil and corn flour based on the Economic Order Quantity (EOQ) model.
Table 7.1 lists the inventory data (annual demand, ordering cost, carrying rate, unit price) needed to compute the EOQ for each item.
Using the EOQ formula, the EOQ and average investment are calculated for each item and shown in Table 7.2.
The total average investment in inventory for the two items is $14,370.
However, Rosetta’s management wants to limit the investment to a smaller amount, such as $12,000, due to a budget constraint.
Since the vegetable oil and corn flour inventories are interdependent, the order quantities need to be adjusted downward for both items to satisfy the budget constraint of $12,000.
This is an example of an inventory model subject to a budget constraint. Manufacturing organizations often face constraints like budget, space, and number of orders limitations.
The chapter will review multi-item inventory models that are subject to budget, space, and number of orders constraints individually as well as models with more than one constraint.

In summary, Rosetta’s wants to limit inventory investment to $12,000 but the EOQ model results in $14,370 investment. To satisfy the budget constraint, the order quantities need to be adjusted using techniques discussed in the chapter like Lagrange multipliers.

The problem involves determining optimal order quantities for multiple items subject to a constraint on the maximum number of orders that can be placed.
A Lagrangean function is formulated using a Lagrange multiplier (θ) to incorporate the number of orders constraint.
Taking partial derivatives of the Lagrangean function with respect to Qj and θ yields two equations that can be solved for Qj and θ.
This gives an expression for the optimal order quantity Qj in terms of parameters like demand, costs, and the Lagrange multiplier θ.
The expression for θ depends on the inventory parameters of all items and the total number of allowed orders N.
To find the optimal Qjs and θ, the θ expression needs to be solved (often through trial and error) such that the resulting Qjs satisfy the number of orders constraint.
An example problem is presented to demonstrate how to apply this methodology to determine optimal order quantities for multiple items subject to a maximum number of allowed orders.
The company’s high ordering costs has led them to impose a restriction of no more than 20 orders per year.
The table provides inventory data for 3 products: annual demand, unit cost, ordering cost (per order), and carrying rate percentage.
To determine the optimal and feasible order quantities given the 20 order restriction, we first calculate the EOQ for each product ignoring the restriction.
We then calculate the number of orders needed based on the EOQs, which exceeds 20.
Using the Lagrangian multiplier method, we calculate a value for the multiplier θ.
Plugging θ into the modified EOQ equation allows us to calculate new EOQs that satisfy the order restriction of 20 per year.
These new EOQs are considered both optimal and feasible as they minimize total inventory costs while respecting the imposed ordering constraint.
If multiple constraints are present (e.g. order limit and budget), it may not be possible to satisfy both simultaneously. The goal is then to satisfy the most important constraint.
FreskoJugo produces fresh fruit juices and sources different fruits from various suppliers located in different regions.
Jerry and Tim from Fruit-o-Vision, an orchard producer in Mexico, met with Hector from FreskoJugo to propose supplying all the fruits under a coordinated replenishment model. This would lower ordering costs by placing joint orders.
Hector was impressed by the fruit samples but was hesitant as FreskoJugo had longstanding relationships with existing suppliers. However, he agreed to discuss the proposal with the company president.
In a meeting, the company president Isaac expressed concern over the rising inventory levels and money locked up in inventory. He wanted the team to focus on controlling inventory.
Coordinated replenishment of fruits from a single supplier Fruit-o-Vision was proposed as a way to potentially lower inventory costs by reducing the number of orders through joint replenishment of all fruit items. This case study explores the benefits of multi-item inventory coordination.
Inventory management of a large number of items can be challenging, as monitoring and controlling all items equally is expensive.
Selective inventory control models help inventory managers focus more on high-value, high-usage items rather than managing all items uniformly.
Popular selective inventory control techniques include ABC classification, VED classification, and FSN classification. These classify inventory items into different categories (usually three categories) to apply the appropriate level of control for each category.
ABC classification focuses on categorizing items based on their cumulative value (A items contribute 80% of total value, B items contribute 15-19%, C items contribute 1-5%). This allows managers to pay most attention to A items.
VED classification classifies based on vitality (business impact of an item), ease of identification, and difficulty of procurement.
FSN classification focuses on criticality (functional need), scarcity (supply risk), and value (economic importance) of items.
The chapter discusses these classification techniques and how they help inventory managers implement selective control of inventory items.

Here is a summary of the key points about Exchange Curves:

Exchange curves show the relationship between the total value of inventory held and the number of replenishments per year for a multi-item inventory system.
They can be used when cost data like ordering costs are unreliable or unavailable.
The exchange curve is a hyperbola that is derived based on the EOQ formula being applied to each item individually.
The total value of inventory held is calculated based on the EOQ quantity for each item and their individual purchase prices.
The number of replenishments is calculated as the total demand across all items divided by the EOQ quantity.
The curve allows inventory managers to easily see tradeoffs between inventory investment (total value) and replenishment frequency without needing precise cost data.
Inventory levels and reorder points can be set to achieve a desired position on the exchange curve based on budget or other factors.

So in summary, exchange curves provide a simpler alternative to explicit cost modeling for managing multi-item inventory systems using the concept of tradeoffs between total inventory investment and replenishment frequency.

Here are the key points summarized from the passage:

Equations 8.5 and 8.6 describe the number of replenishments (N) and total value of inventory (TV) in terms of ordering cost (Co) and inventory carrying cost (i).
Multiplying the two equations yields Equation 8.7, which represents the hyperbolic curve relationship between N and TV.
Dividing the equations gives Equation 8.8, which represents any point on the hyperbolic curve in terms of Co/i.
An exchange curve can be generated by calculating N and TV for different values of Co/i. This allows inventory managers to determine the best ratio of Co/i based on their desired N and TV.
The exchange curve concept is applied to Rosetta’s inventory using their given Co and i. Reducing Co/i lowers TV but increases N.
VED classification rates items based on criticality into Vital, Essential and Desirable categories using risk factors like lead time, supplier, customization, and unavailability impact.
FSN analysis classifies items as Fast, Slow or Non-moving based on consumption patterns to prioritize inventory holdings.
Combining techniques like ABC and VED allows for more granular classification of inventory into groups like A-V and C-D.

Here are the key aspects of Chapter 9:

Perishable items and style goods have unique characteristics that make traditional inventory models not directly applicable. Some key challenges include short life cycles, demand variation across time, and high obsolescence risk.
For perishable items like fruits, vegetables, meat, models consider factors like expiration dates, deterioration rates, and demand changes over time. The goal is to balance utilizing products before expiration with meeting fluctuating demand levels.
Fashion/style goods like apparel have short lifecycles and demand highly dependent on current trends. Models help decide order quantities and liquidation strategies across seasons to minimize stock-outs and excess inventory.
Periodic review models focus on replenishment quantities and timings for perishables. Continual review models treat demand as a continuous function and consider depletion/deterioration.
Probabilistic lifetime models incorporate product decay/failure over time using probability distributions. Forecasting tools like Croston’s method help estimate intermittent demand.
Material requirements planning (MRP) and distribution requirements planning (DRP) can be adapted for coordinated replenishment of perishables across supply chain stages.
Various expedited shipping, pricing, and stock rotation strategies can increase sales velocity and prevent losses for perishables and fashion items.

Let me know if you need explanations or have additional questions on any part of this chapter!

Maria Fernanda manages the sales outlet for Rosetta’s tortillas. Tortillas are sold in packs of 10 for $25 each, with a cost of $10 per pack.
The shelf life of a tortilla pack is 1 day. Maria receives a predetermined number of packs each morning when the outlet opens at 7am. Unsold packs are discarded at 11pm when the outlet closes.
Maria’s goal is to minimize losses from unsold inventory by determining the optimal number of packs to receive each morning.
A reprocessing unit has now agreed to buy unsold packs from Rosetta’s for $5 per pack. This changes Maria’s decision problem - she must now decide the optimal order quantity considering this additional option.
The chapter will cover inventory models for perishable items with finite shelf lives. Such items lose utility/value after a certain time period and can no longer be sold.
The models discussed will determine the optimal order quantity for items with deterministic and stochastic (random) demand, considering relevant costs like underage and overage costs.

Here is a summary of the key points related to the single period inventory model with stochastic demand:

Cost of a spare part - The cost to purchase and store one unit of the spare part.
Cost of holding an unused spare in inventory - The cost of storing a spare part in inventory that goes unused, such as opportunity cost of capital or physical storage costs.
Cost of resupplying a required spare part - The cost incurred if a spare part is needed but not in inventory, such as an emergency shipment cost.
The critical ratio compares the cost savings from having a spare part on hand versus the cost of holding an extra unused spare. It is used to determine the optimal inventory level.
Depending on the demand distribution (normal, uniform, Poisson), different equations can be used to calculate the optimal order quantity factoring in the mean, standard deviation/range, and critical ratio.
Software like Excel can help calculate probabilities and critical values related to different demand distributions to assist with determining the optimal inventory level.
The model aims to balance the costs of understocking/overstocking spare parts by setting an inventory target that maximizes expected profits or minimizes expected costs over the period.

Here are the steps to solve this problem:

Given: Demand is normally distributed with mean = 5 and standard deviation = 3
Cost of underestimating = Room tariff = $35
Cost of overestimating = Cost of accommodating at another hotel = $50
Critical ratio (Cr) = (Cost of underestimating - Cost of overestimating)/Cost of underestimating = (35 - 50)/35 = -0.41
Using the inverse normal CDF function in Excel: NORMSINV(-0.41) = 0.34
Number of rooms to overbook = Mean + Standard deviation * NORMSINV(Cr) = 5 + 3 * 0.34 = 6 rooms

Therefore, the number of rooms that the hotel staff may overbook is 6 rooms.

Fast-moving maintenance items can be managed using deterministic or stochastic inventory models like EOQ and (s,S) models discussed earlier in the book. These models aim to balance holding costs and shortage costs.
Demand for fast-moving items can sometimes be forecast, but is often uncertain. Stochastic models use reorder levels based on mean demand, lead time, demand variability, and desired service level.
Slow-moving items are classified as specials (long lead time), adequate warning (some lead time), or inadequate warning (short lead time). Special management approaches are required due to long/uncertain lead times.
Rotables are repairable parts that are repaired/reconditioned instead of discarded after failure. Return on repairs and availability of repair capacity impact optimal inventory levels for rotables.
The goal with all maintenance inventories is to minimize total inventory costs while avoiding equipment downtime through adequate spare part availability. Factors like demand pattern, lead times, and failure/repair characteristics must be considered for different item types.

Here is a summary of the key points regarding rue standby spares (or items that provide inadequate warning):

Rue standby spares refer to items that provide little to no warning of an impending failure. Their failure is unpredictable.
Both analytical and graphical methods can be used to manage inventory of these types of items.
The analytical method involves using equations to calculate the total annual cost of inventory based on factors like holding cost, stockout cost, ordering cost, lead time, and failure rate distribution. The goal is to determine the optimal number of spares (N) to minimize total cost.
The graphical method uses indifference curves developed by Mitchell to plot the cost ratio (stockout cost/holding cost) against demand rate. Based on where the point lies in relation to the curves, decision rules indicate whether to hold 0, 1 or 2 spares.
Both methods aim to determine the initial number of spares that should be kept in inventory to balance inventory carrying costs with risk of stockouts for items with unpredictable failures. Proper management is important as there is little warning before failure occurs.

The passage discusses inventory policies for maintaining spare parts at a thermal power plant. It describes the key components of the fuel system, including the pulverizer, coal-carrying ducts/pipes, and burners.

Some key points:

The pulverizer and coal-carrying chutes experience high failure rates due to wear and abrasion.
Grinding elements in the pulverizer fail randomly.
Stirrup assemblies and burners fail frequently due to mechanical stresses and clogging.
Other components like the main pulverizer shaft and gearbox have very low failure rates.
Doeh’s method and graphical techniques from the chapter could be used to determine optimal inventory levels of slow-moving and highly variable demand parts to achieve a target service level.
A differentiated inventory policy accounting for failure mode, rate, and criticality would be needed to manage the various pulverizer components and spares.

So in summary, it analyzes the maintenance needs of a power plant fuel system and discusses how inventory theory could help optimize spare part stocks for this application.

Here is a summary of the key steps and results in solving the two-stage inventory problem for Rosetta’s and their franchisee:

The model assumes deterministic (constant) annual demand of 6000 packs
Compute cost values: Cw = $10, Cr = $22, Cw’ = $10, Cr’ = $12
Compute n from Equation 11.15: n = 1.55 ~ 1 or 2
Calculate f(n) for n=1 and n=2 using Equation 11.14
f(1) = 264, f(2) = 256. Since f(2) is smaller, choose n=2
Compute Qr using Equation 11.12: Qr = √(4 + 8)(20 + 12) × 6000/2 = 600 packs
With n=2, compute Qw using Equation 11.9: Qw = 2×600 = 1200 packs

Therefore, the optimal order quantities are 600 packs for the franchisee and 1200 packs for Rosetta’s warehouse.

Here is the solution to the two-part case study question:

Complete the inventory analysis for this case and determine the order quantities for the businesses of Hector and Donato.

Given: D = 7000 kg Cow = $25 Cor = $50
Cw = $125/kg Cr = $400/kg i = 0.30

Using the two-stage inventory model equations: CΔr = Cr - Cw = $400 - $125 = $275 CΔw = Cw = $125

From equation 11.15: √(CowCor)/(CΔrCw) = √(2550)/(275125) = 1.41

Rounding up to the nearest integer, n = 2

From equation 11.12: Qr = √(2DCor)/(nCΔr) = √(2700050)/(2*275) = 250 kg

From equation 11.9: Qw = nQr = 2 * 250 = 500 kg

Therefore, the optimal order quantities are: Qr = 250 kg Qw = 500 kg

Also, analyze the costs if Donato decides to run his business independently (not as a franchisee).

If Donato runs independently: D = 3500 kg Cow = $50 Cor = same as above $50 Cw = assume same $125/kg Cr = same as above $400/kg i = 0.30

Repeating the calculations: CΔr = $275 CΔw = $125 n = 1
Qr = √(DCor)/(CΔr) = √(3500*50)/275) = 140 kg

The total costs would be higher if Donato runs independently due to smaller order quantities and losing the bulk purchase discount on procurement cost Cw.

Inventory models aim to determine optimal inventory policies and reduce costs like ordering, holding, and stockout costs. Common models include EOQ, lot sizing, periodic review, multiechelon etc.
EOQ model calculates optimal order quantity balancing ordering and holding costs. Assumptions include constant demand, no shortages, instantaneous receipt of orders.
Lot sizing techniques determine optimal lot sizes and timings over a planning horizon to minimize costs. Examples include Wagner-Whitin, Silver-meal heuristic, PPB.
Periodic review models evaluate inventory position at fixed time intervals to determine replenishment needs. Examples are continuous review allowing shortages, periodic review not allowing shortages.
Reorder policies specify rules for when/how much to order. Examples include reorder point, fixed order quantity policies.
Service level measures fill rate, on-time delivery targets. Safety stock ensures targets during demand/lead time variability.
Multiechelon models optimize inventory placement in supply chains. Examples are distributor-retailer, maintenance-repair-overhaul networks.
Selective inventory control classifies items based on metrics like cost, demand to prioritize management efforts. Techniques are ABC analysis, VED, FSN.
Perishable/style goods have additional complexities of decay, short life cycles, uncertain demand. Models estimate overage, underage costs.
Underage cost refers to the costs associated with being out of stock or facing a stockout situation.
January demand and March demand refer to the demand for a particular item or product in those respective months.
Principles refer to basic concepts or fundamental ideas in inventory management.
Total inventory costs refer to the total costs of holding inventory, including ordering costs, carrying costs, shortage costs etc.
Variable demand refers to demand that fluctuates or varies over time rather than being constant. Demand may vary by month, season or other time period.
The document outline provided shows the table of contents for a textbook or study material on inventory management. It covers topics like the basics of inventory management, different inventory control systems, deterministic and dynamic inventory models, lot sizing heuristics, stochastic inventory models, multi-item inventory models etc.

#book-summary