B.8 For further reading
W.2.5 RETAIL-STORE LOCATION MODELS
While we are discussing modeling by binary variables. we should also men- tion another typical modeling trick. To motivate it. suppose that we are considering the use of some transportation link, which should not be used if flow traveling on it is below a certain minimal threshold. Note that we are not saying that a certain activity level x must lie in the range [L, U ] , where L and U are lower and upper bounds, respectively. Doing so would enforce a strictly positive value of x; however, what we want to express is that zf x is positive. then it must stay within t h at interval. hlore formally, the feasible region for z is (0) U [L, U ] . Since this set is not convex,16 we cannot just re- sort to continuous linear programming. Yet. we may express the requirement within the mixed-integer linear programming framework, by introducing a bi- nary decision variable s, set to 1 if the service is activated (x
>
0). and set t o 0 otherwise. Our aim is easily accomplished by the following constraints:x
2
Ls, x 5 us.We see that if s = 0, then x = 0; if s = 1, then x E [L. U ] .
FOR FURTHER READlNG 89
2.6 FOR F U R T H E R READING
0 Background references which are relevant t o this chapter are [l] and
[a].
0 The analysis outlined in section 2.1.2 is a simplified version of what is proposed in [4]. to which we refer the reader for more details and further justification. In practice. organizational constraints niay dictate that transportation frequencies are restricted t o discrete values; a model to cope with this case is described in [8].
0 The example described in section 2.2.4 is a simplified version of a sirnilar model considered in
is].
0 In [7] the reader may find approaches to reflect uncertainties. safety stocks, and alternative transportation modes within a static modeling framework.
0 The reader interested in further information on location models can have a look. e.g.. at [6]. while [5] is useful to those working in the retail sector.
0 Commercially available optimization solvers and languages are described.
e.g., in http : //www
.
i l o g . corn and http : //www. amp1.
com0 To have an idea of what software is commercially available for the logis- tic network design. we suggest visiting http : //www. slirncorp
.
corn and http://www.bestroutes.comREFERENCES
1. R.K. Ahuja, T.L. hlagnanti. and J.B. Orlin. Network Flows: Theory.
Algorzthms, and Applzcatzons. Prentice Hall. Upper Saddle River. K J . 1993.
2. h l . 0 . Ball. T.L. hlagnanti. C.L. l l o n m a . and G.L. Nemhauscr. editors.
Network Routzng (Handbooks zn Operations Research and Mmagement Sczence. Vol. 8). Elsevier Science. Amsterdam. 1995.
3. R.H. Ballou. Buszness Logzstzcs Management (4th Ed.). Preutice Hall.
Upper Saddle River. KJ. 1999.
4. C.F. Daganzo. Logastzcs Systems Analysis (3rd Ed.). Springer-Verlag.
Berlin. 1999.
5 . 51. Levy and B.A. IVeitz. Retazling Management (5th Ed.). SlcGraw- Hill/Irwin. Kew York. 2003.
6.
P.B.
Nirchandani and R.L. Francis, editors. Dzscrete Location Theory.Wiley. Chichester, 1990.
7. J.F. Shapiro. hlodelzng the Supply Cham Duxbury/Thomson Learning, Pacific Grove, CA. 2001.
8. 1I.G. Speranza and W , Ukovich. Minimizing Transportation and Inven- tory Costs for Several Products on a Single Link. Operatzons Research, 421879-894, 1994.
9. H.P. Williams. Model Buzldzng an Mathematzcal Programmang (4th Ed.).
Wiley. Chichester. 1999.
Forecasting 3
3.1 INTRODUCTION
Before we discuss horn to forecast. we shall wonder whether we should do so and why. Over the last few years many managers and academics have been supporting the drive towards lead time reduction and Make to Order (AlTO).
A basic t r u t h about forecasts is t h a t they turn out to be wrong. Hence. some managerial theories suggest t h a t you would better not forecast: and actually.
if a company is quick enough. it does not need forecasting. But what does
“quick enough” mean? And is lead time reduction free?
Certainly, cutting lead times is a fruitful endeavor (e.g.. see [ l a ] ) . How- ever. reality is a little bit more complex than these theories suggest. First.
while these theories contrast Make to Order and Make to Stock (\ITS) sup- ply chains. almost all supply chains are partially driven by customers’ orders (think about the assembly of a car t h a t , at the least in Europe. is almost always custom-built) and partially driven by demand forecasts (think of coni- ponents or raw materials purchases).
Example 3.1 Dell computers is today one of t,he largest PC manufactur- ers in the world and is considered to be the champion of AIakc to Order supp1)- chains. Dell assembles PCs to customers‘ order. However. not the whole Dell supply chain is order-driven. Components‘ inventories are set ac- cording to demand forecasts. Thus, a more appropriate description of the Dell supply chain is: Distribution arid production are order-driven (LITO) while components are made to stock (AITS). This is a significant advantage over other competitors. as Dell carries inventories where consumption is more 91
predictable (component level) rather than where it is less predictable (single product configuration/single store). This redesign of the supply chain makes Dell a very efficient manufacturer and a very successful competitor in the tough PC business.
Also. Dell provides a very interesting answer to the question, what is “quick enough?” Dell significantly reduced the production lead time and can deliver in 23 days. Is that enough? The answer is that for PCs it is enough for most customers t h at do not need the computer they bought immediately. However.
it is not enough for all users. Think of a situation where you lost your PC and need to make an important presentation tomorrow. Dell is not your favorite supplier. Also. this depends on the product a company is selling. While 2-3 days is fair enough for most customers for a PC. it is definitely too long if we are speaking about drugs for acute diseases (for further information on these
examples see [17] and [IS]).
0
Moreover, many companies forecast demand implicitly. For example. in the grocery business many companies state that they do not generate any forecast (especially a t the store/item level). However, when one digs into the planning systems. he/she can see that one key input to the purchase/delivery plan is a demand forecast, though it is often fairly rudimentary. For example, at a couple of grocery retailers in Italy, the target inventory level for the next week depends on the demand during the previous week. Thus. these companies implicitly assume a stationary demand and use the so-called ”nai’ve approach’: that is. demand forecast for the next period (read “week” in the example) is equal to the demand in the previous one.
Generally speaking, when the Delivery Lead Time th at customers want is shorter than purchasing, production, and distribution lead time. one needs to perform some sort of forecast t o execute some activities before customers‘
orders are collected.
Example 3.2 In most retail outlets customers expect t o collect immediately the goods they are looking for. This means that most retail companies shall somehow forecast demand to plan inventories for the finished products carried at each single store.
However, for some product categories the situation is rather different. For food products such as pizza. we might not need to carry all possible product variants. as customers might be willing to wait while their pizza is being cooked. Does this mean that all operations in a pizza restaurant are made to order? Actually, in Italy the average customer is just willing t o wait while the raw materials are “assembled” and cooked. Most customers are not willing t o wait while the cook looks for and buys the topping(s) they have ordered.
Thus, even in a simple pizza restaurant we need to forecast the consumption of raw materials to purchase them in advance (pre-position raw materials). Quite interestingly in this case too we can see that different customers have different needs. While in traditional pizza restaurants pizzas are Made t o Order, in fast-food and most US pizza restaurants the basic cheese pizza is cooked and
THE VARIABLE TO BE PREDlCTED 93
then toppings are added according to customers' orders: as customers are not much willing t,o wait. In this case. customers are willing t o give up a bit of product quality to reduce Delivery Lead Time (DLT). For t,liem. 15 minutes Forecasting needs to cover and guide the portion of the supply chain oper- ations that, cannot, be driven by customers' orders (see the order decoupling point, concept in chapter 1). Let us consider a specific activity 1; and let us use i as the index for activities performed by the supply chain starting from the deliver>- to customers (we number activities starting from downstream and move upstream). If the lead time of all downstream activities
Ci=,
LT, is greater t,hari the DLT. then activity i cannot be driven by orders and we sliall perform some sort of forecast to plan i t .Concept 3.1 Forecasting is required when customers are not willing t o wait